Method and device for encoding a set of coefficients, method and device for decoding a set of coefficients, associated data stream and computer program

Abstract

We describe a method for encoding a set of coefficients (Wk) participating in a representation of a digital hologram by being respectively associated with multiplets, each formed by a first spatial parameter, a second spatial parameter, a first frequency parameter, and a second frequency parameter. This method comprises the following steps, performed for at least one pair of respective values ​​of the first and second frequency parameters: - encoding (E150; E154) indicative position data associated respectively with non-zero coefficients from a set of positions associated in a predefined manner with the coefficients associated respectively with the different multiplets defined by said pair of values ​​of the first and second frequency parameters; - encoding (E156) of the coefficients associated respectively with the positions indicated by said indicative data.A decoding method, as well as encoding and decoding devices, a data stream, and a computer program, are also described. See Figure 10 for the abstract.

Description

Description Title of the invention: Method and device for coding a set of coefficients, method and device for decoding a set of coefficients, associated data stream and computer program Technical field of the invention

[0001] — The present invention relates to the technical field of digital holography.

[0002] — It relates more particularly to a method and a device for coding a set of coefficients participating in a representation of a digital hologram, as well as a method and device for decoding a set of coefficients par- participating in a representation of a digital hologram, a data stream and a associated computer program. State of the art

[0003] A digital hologram is the digital recording of a section, at the level of a reference plane, of a light field propagating in a space three-dimensional, with a view to being able to subsequently restore this light field to a user.

[0004] — The physical properties of light fields have led to the representation of ho- digital lograms by means of coefficients respectively associated with elements of a spatio-frequency domain defined by two spatial dimensions (which correspond to the reference plane) and by the two frequency dimensions associated, that is to say to multiplets each formed by a first spatial parameter, a second spatial parameter, a first frequency parameter and a second parameter frequency. Presentation of the invention

[0005] = The invention proposes a method for coding a set of coefficients participating to a representation of a digital hologram being respectively associated with multiplets each formed by a first spatial parameter, a second parameter spatial, a first frequency parameter and a second frequency parameter,

[0006] the method comprising the following steps, carried out for at least one pair of respective values ​​of the first frequency parameter and the second frequency parameter quantitative:

[0007] — - coding of data indicative of positions associated respectively with coef- non-zero ficients among a set of positions associated in a predefined manner with the coefficients associated respectively with the different multiplets defined by said pair of values ​​of the first frequency parameter and of the second frequency parameter;

[0008] — - coding of the coefficients associated respectively with the positions indicated by said indicative data. Grouping the coefficients relating to multiplets defined by the same pair of frequency parameter values ​​for their coding makes it possible to code better localized information, generally at the level of certain coefficients only, and thus to increase the efficiency of the coding. According to one possibility, at least one indicative data among said indicative data can represent a difference between a position associated with a non-zero coefficient and another position associated with another non-zero coefficient. Alternatively, said indicative data may designate at least one position associated with a non-zero coefficient without designating at least one other position associated with another non-zero coefficient and indicated by indicative data coded for another pair of respective values ​​of the first frequency parameter and the second frequency parameter. The position of the non-zero coefficients is thus coded relative to those encountered for another pair of values, which increases the efficiency of the coding. It can be provided that the coefficients associated with the different multiplets defined by said pair of values ​​of the first frequency parameter and the second frequency parameter are ordered in a predefined manner in an ordered sequence of coefficients. The data indicative of a position associated with a non-zero coefficient can then indicate the position of this non-zero coefficient in said ordered sequence of coefficients, which makes it possible to limit the quantity of data necessary for coding the positions. It can also be provided that at the coefficient coding stage, the non-zero coefficients are coded in the order defined by the ordered sequence. The invention also proposes a method for decoding a set of coefficients participating in a representation of a digital hologram by being respectively associated with multiplets each formed by a first spatial parameter, a second spatial parameter, a first frequency parameter and a second frequency parameter, the method comprising the following steps, carried out for at least one pair of respective values ​​of the first frequency parameter and the second frequency parameter: - decoding data indicative of positions associated respectively with non-zero coefficients among a set of positions associated in a predefined manner with the coefficients associated respectively with the different multiplets comprising said pair of values ​​of the first frequency parameter and of the second frequency parameter; - decoding of the coefficients associated respectively with the positions indicated by the said indicative data. As already indicated for the coding method, it can be provided that at least one indicative data among said indicative data represents a difference between a position associated with a non-zero coefficient and another position associated with another non-zero coefficient. Alternatively, said indicative data may designate at least one position associated with a non-zero coefficient without designating at least one other position associated with another non-zero coefficient and indicated by decoded indicative data for another pair of respective values ​​of the first frequency parameter and the second frequency parameter. The invention further proposes a device for coding a set of coefficients participating in a representation of a digital hologram by being respectively associated with multiplets each formed by a first spatial parameter, a second spatial parameter, a first frequency parameter and a second frequency parameter, comprising: - a first coding module designed to code, for at least one pair of respective values ​​of the first frequency parameter and the second frequency parameter, data indicative of positions associated respectively with non-zero coefficients among a set of positions associated in a predefined manner with the coefficients associated respectively with the different multiplets defined by said pair of values ​​of the first frequency parameter and the second frequency parameter; - a second coding module designed to code the coefficients associated respectively with the positions indicated by said indicative data. The invention further proposes a device for decoding a set of coefficients participating in a representation of a digital hologram by being respectively associated with multiplets each formed by a first spatial parameter, a second spatial parameter, a first frequency parameter and a second frequency parameter, comprising: - a first decoding module designed to decode, for at least one pair of respective values ​​of the first frequency parameter and the second frequency parameter, data indicative of positions respectively associated with non-zero coefficients among a set of positions associated in a predefined manner with the coefficients respectively associated with the different multiplets comprising said pair of values ​​of the first frequency parameter and the second frequency parameter; - a second decoding module designed to decode the coefficients associated respectively with the positions indicated by said indicative data. The invention also proposes a data stream representing a set of coefficients participating in a representation of a digital hologram while being respect- tively associated with multiplets each formed by a first spatial parameter, a second spatial parameter, a first frequency parameter and a second frequency parameter, the data stream comprising, for at least one pair of respective values ​​of the first frequency parameter and the second frequency parameter: - data indicative of positions associated respectively with non-zero coefficients among a set of positions associated in a predefined manner with the coefficients associated respectively with the different multiplets defined by said pair of values ​​of the first frequency parameter and the second frequency parameter; - data representative of the coefficients associated respectively with the positions indicated by said indicative data. The invention further provides a computer program comprising instructions designed to implement a method as proposed above when these instructions are executed by a processor. The methods proposed above can thus be implemented by this processor, for example when this processor equips a computer or a coding or decoding device as mentioned above and described below. The invention finally provides an information medium (for example non-transitory) readable by a computer, on which such a computer program is recorded. Of course, the various features, variants and embodiments of the invention may be combined with each other in various combinations to the extent that they are not incompatible or mutually exclusive. Detailed description of the invention In addition, various other characteristics of the invention emerge from the appended description given with reference to the drawings which illustrate non-limiting embodiments of the invention and where: [Fig.1] schematically represents a digital hologram; [Fig.2] represents an example of a digital holography device; [Fig.3] represents an example of a method implemented by a processing module of the digital holography device of [Fig.2]; [Fig.4] represents a method of decoding a digital hologram from data received in a data stream; [Fig.5] represents an example of a coding device according to the invention; [Fig.6] represents an example of a decoding device according to the invention; [Fig.7] represents a method of exchanging data between the encoding device of [Fig.5] and the decoding device of [Fig.6]; [Fig.8] represents an alternative embodiment of the method of [Fig.7]; [Fig.9] represents a partitioning process of the space-frequency domain D; [Fig.10] represents a method of coding coefficients associated respectively with elements of the space-frequency domain D; [Fig.11] represents a decoding method corresponding to the coding method of [Fig.10]; [Fig.12] represents an example of a coding device in accordance with the teachings of the invention; and [Fig.13] represents an example of a decoding device in accordance with the teachings of the invention. [Fig.1] schematically represents a digital hologram defined by means of a function rpo in a reference plane P,: of equation (z=0) in a propagation space E where the three-dimensional coordinates of a point are defined in an orthonormal frame (O,x,y,z). In other words, the axes (Ox) and (Oy) (or more simply the x and y axes) are included in the reference plane P,. and / or define the reference plane P,.. The propagation direction (before application of the transformation mentioned below) thus corresponds here to the axis (Oz); in this situation, the propagation direction (z) is perpendicular (or orthogonal) to the reference plane Pt. The wave field (representing here the monochromatic light field of wavelength λ) associated with this hologram at a point in the propagation space E with coordinates r=(x,y,z) is then written (before application of the transformation mentioned below): [Math.1] wfxy)=#1peF © (n, n,)dn,dn, where the Fourier transform of the function 1y9 is defined (in the reference plane P ref) by [Math.2] fn, n,)= 1 peFln-n) pfx r)dxdy Where is the wavelength of the (monochromatic) light concerned, n = (No Ny» Nz) with n, = SQRT(1 - n° - n,°), SQRTO) being the square root operator,<r,n> is the scalar product of r and n, and D; is the domain defined by {n.2 + 1,2 < 1}. The wave field defined by the digital hologram can thus be seen as a sum (in theory continuous or infinite) of plane waves of wavelength λ. In order to take into account the particularities of holograms, we use representations of these holograms in the form of a distribution in a 4-dimensional space-frequency domain D (or phase space), of which the first 2 dimensions correspond to the spatial coordinates in the plane P of the hologram and the other 2 dimensions correspond to the spatial frequencies in this same plane. Such a distribution includes, for example, the light energy values ​​respectively associated with the spatial coordinates and the spatial frequencies of the space-frequency domain D. According to a first example, we can apply a windowed Fourier transform to the wave field "y; the distribution W,® is then written: [Math.3] Wô(x,2)=ly(x+H)o(x-+)e5Eay where ® is a so-called window function, 1y* is the (complex) conjugate of 1), X represents the spatial coordinates (x, y) and E the spatial frequencies (E,, Ë,). According to a second example, we can use a Wigner-Ville distribution W,, obtained by applying a Wigner-Ville transform to the 7y wave field: [Math.4] Wix,2)=ly(Xx+H)y(XF)esay with as previously X representing the spatial coordinates (x, y) and Z the spatial frequencies (E,. E,). So this is a particular windowed Fourier transform, in which the window function used is function 1. In a third example, we can use a decomposition into Gabor frames, which corresponds to a discretization of the windowed Fourier transform. To do this, we define a mesh A of the space-frequency domain D as follows: [Math.5] A= {(x »é E,) eR*: (x born, E,) = Au, ueZ*} Where A is an invertible matrix of dimensions 4x4. The decomposition into Gabor frames can then be written: [Math.6] p= Er WP (CA(C)® where ®P is the dual window of the function ®, (€) is the translation in the space-frequency domain D of vector Ç and with the following modulation / translation operator: [Math.7] R(C)F(Y) = Ei73Zf(YX) where X, Z are respectively the spatial component (two-dimensional) and the frequency component (two-dimensional) of the vector €, i.e.: € = (X , E), and where < , > represents the scalar product (here in the plane). Here we study the field 1); obtained when we apply a transformation T of the three-dimensional space E to the digital hologram. According to Kyoji Matsushima, Hagen Schimmel & Frank Wyrowski, "Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves", in J. Opt. Soc. Am. At 20, 1755-1762 (2003), the wave field (or light field) modified by the transformation T is written as follows (at a plane parallel to the reference plane P,.; and with coordinate z): [Math.8] win v)= Hip eFSTP Rfa, n,)dn, da, This expression involves in particular the scalar product of the coordinate vector (xyz)' of the three-dimensional propagation space E and the vector Tn resulting from the application of the transformation T to the wave vector (n,. N,» N) of predefined norm C and whose first two coordinates are the frequency variables (n,, y) respectively associated with the spatial coordinates (x,y) in the reference plane P,: of the digital hologram. The predefined norm C depends on the representation used and is here equal to 1 (normalized representation). Alternatively, the predefined norm could be equal to the wavelength λ. By writing: [Math.9] e(rn)=<r, Tn> The expression of the function 1p," given above can be seen as a Fourier integral operator used in semi-classical analysis in the field of quantum mechanics, where the function defined above is the generating function associated with this operator. By considering a particular plane P, parallel to the reference plane, with coordinate z in the direction perpendicular to the reference plane P,., we can write the generating function as a function of four variables (i.e. a function with values ​​on R4) as follows: [Math.10] x | 5 | o(snés)=<[7}4| Ep TEE The generating function m is therefore the scalar product: - of a first vector (of three-dimensional coordinates), of which the first two coordinates correspond to the first two variables of the four variables and whose third coordinate corresponds to the z coordinate of the plane P, concerned, and - of a vector resulting from the application of the transformation T to a second vector, whose first two coordinates correspond to the last two variables of the four variables and, here, whose norm C is a predefined constant (this norm C being here 1 due to the normalization already mentioned; alternatively, in other representations, this norm C could for example be equal to the wavelength λ). The explanations are given in the following for a plane P, with a given z coordinate (plane parallel to the reference plane P,:), but are valid for any plane parallel to the reference plane P,.: (i.e. for any z). For the sake of simplification, we denote in the following @ the generating function m, associated with this plane P,. In the context defined above, if we denote by x the symplectomorphism of the space-frequency domain D towards itself which corresponds to the transformation T, the subset (or graph) l of R*x R* comprising the elements of the form (e, %(e)), for e varying in R“, can also be defined as the set of elements of the form: [Math.11] % of of of (& 4 55 Sn Un nr n,) for (X,ÿ,Nu, Ny) varying in R*. For further explanations on this subject, please refer to the book "Semi-classical Analysis", by Victor Guillemin and Shlomo Sternberg, International Press, 2013, ISBN 1571462767, 9781571462763. We recall that a symplectomorphism is a diffeomorphism which preserves the symplectic form, that is to say whose Jacobian matrix M verifies: J=MIM, with: [Math.12] ï O0 60 0 QO 0 0 — | year 0 -1i 0 Noting [Math.13] phew, N°) =(5(6 5 man, Elan n, n,) we can give the expression of the variables n, and n, as a function of e = (x,y,6x6,): [Math.14] (n, n)=0#(E, 5) The 5th and 6th coordinates (u, v) of the elements of the subset I' can therefore be written: [Math.15] (uv) =( (on oMs y E, 5) fs »ob(ex 65) We thus obtain a parametric expression of the subset l' as a function of its first four coordinates (x,yE&,), which makes it possible to obtain the following expression of the symplectomorphism x (being recalled that the subset I' corresponds to the elements of the form (e, y(e)) for e varying in R*): [Math.16] to an &)= ( Se la mobs y Es 5). = (x 5 0h (x 4 Ep 6,)). os vê, a) Now considering that the transformation T studied is a rigid transformation of the propagation space E, this transformation T is therefore the combination of a translation of vector (t,.t,.t;) and a rotation R which can be decomposed into 3 rotations using the Euler angles: R = R=,R*R7, where R*, and Rp are rotations around the z axis with respective angles α and B, and R*, is a rotation around the x axis with angle 6. We can thus define symplectomorphisms %, Xus Xus Xp respectively associated with the translation and with these 3 rotations Ra, R*o, R, and whose composition is the symplectomorphism x associated with the transformation T: Y=%p 0 %o O Ya0 %, WHERE 0 is the composition operator. The symplectomorphisms % Xas Xp associated with the translation and rotations Ra, R*y, R, around the Z axis are simply written: VXY En Ey) = (X+toYFty Bo Ey) HalX,Y Ex &y) = (x.cos ay.sin a,x.sin a+y.cos a, E,.cos aE,sin à, E, sin a+E,.cos a) Xp(<,y ExEy) = (x.cos B —y.sin B,x.sin B +y.cos B, E,.cos B —E, sin B, E,sin B +E,.cos B) We note that the third component t, of the translation is taken into account in the propagation, that is to say by considering the plane P,- We propose to use the developments set out above to determine the symplectomorphism %y associated with the rotation R*, of angle © around the x axis. In this case, the generating function is written: [Math.17] sinf 1 0 0 F p(rn)=<r, Ren> -|rdjo cosé im, n,n) O0 sinf cost either : [Math.18] o(rn) = xn,+»{n,cos6 - nsin6) + z{n,sin6+ 7.c0s6) Using the fact that: [Math.19] (E,6,)=(52, =) (see above the definition of the subset l') and replacing n; by its expression as a function of n, and of n, given above, we obtain: E=Tk E, = (n,.cos 60) —- SQORT(1 — n,° — n,°).sin D By taking the square of the two terms of this equation, we obtain a second-degree equation whose only solution having a physical meaning is: mn, = (E,-cos 6) + SORT(1 — E2 — E,2).sin O Using again the definition of the subset [', we can finalize the expression of the symplectomorphism %, as follows: VolX,Y Ex Sy) = (U,VE, (E,.cos 0) + SORT(I — E,2 — E,2).sin 0) with [Math.20] U= En =x -(ysino = 2cosé hs [Math.21] v=5 = »{cosd-siné 25 | z|sino + cos0225) Note that the variables n, and n, in these last expressions are expressed as a function of &, and Ë, a few lines above. We are now interested in the consequences of the transformation T of the three-dimensional propagation space E on the representation W,®, W, of the digital hologram (also called distribution). The representations W,?, W, of the hologram in the space-frequency domain D can be seen as the symbol P of a pseudo-differential operator Op(P). Continuing the parallel with theories of quantum mechanics, we can refer to the article "How Wigner Functions Transform Under Symplectic Maps", by Alex J. Dragt and Salman Habib, in Proceedings of the Advanced Beam Dynamics Workshop on Quantum Aspects of Beam Physics (Monterey, CA) 1998. In the first example given above (windowed Fourier transform), the differential operator with symbol W,® is Op(W,*) =1®9> <w| where we use the usual notation in quantum mechanics introduced in the article "A new notation for quantum mechanics”, by PAM Dirac, in Mathematical Proceedings of the Cambridge Philosophical Society, July 1939, pp. 416-418. In the second example (Wigner-Ville distribution), the differential operator with symbol W is: Op(W,)=1lwy> <yl Concerning the third example (Gabor frames), we note that the decomposition uses functions of the same type as those used in the first example (windowed Fourier transforms), within a sum on the elements of the mesh, and the developments below therefore apply because they apply to the different terms of the sum. Continuing the parallel with the theories of semi-classical analysis (for example, we can refer to the article "Uniform semiclassical estimates for the propagation of quantum observables" by A. Bouzouina and D. Robert in Duke Mathematical Journal, 111(2) 223-252, 1+ February 2002), the effects of the transformation T on the hologram can then be rendered by applying the propagation operator Op(x) (associated with the symplectomorphism x) to the pseudo-differential operator Op(P) so that the symbol P' of the propagated differential operator Op(x)Op(P)[Op(4)]! forms a representation of the hologram resulting from the transformation T. According to Egorov's theorem (see for example the article by A. Bouzouina and D. Robert cited above), the symbol P” of the propagated differential operator Op(y)Op(P)[OpOo1" can be written: [Math.22] P=P(Y)+L 0", where x is the symplectomorphism associated with the transformation T as explained above, λ is the wavelength of the light concerned as already mentioned, and where the functions f, are defined as a sum of integrals of bi-differential differential operators; for example, in the Weyl quantization used, the function f, is zero and the functions f, can be defined as follows for n > 1: [Math.23] Ft 2.5 YOU =DL{L, Pox,} 0x. where H, and x, are respectively the Hamiltonian and the Hamiltonian flow at time t (see below), i is here as before the imaginary number such that i?=-1, and where the extended Poisson bracket is defined as follows: [Math.24] {8h}, _ Le = Ebjt Br O1 pH 0G8 where g and h are scalar functions of (q, p) on the space-frequency domain D. Thus, when the generating function m is non-quadratic, that is, the symplectomorphism % is non-linear as explained in the article "How Wigner Functions Transform Under Symplectic Maps" mentioned above, the representation P' of the hologram deformed by the transformation T is not limited to a deformation of the space-frequency domain D by means of the symplectomorphism % (term P(x) in the formula above), but includes additional corrective terms which each depend on the wavelength λ, precisely which each include a factor equal to a power of the wavelength λ. In practice, as indicated below, one can use a single additional corrective term which includes a factor equal to the wavelength λ or, here, equal to the square λ of the wavelength λ. The Hamiltonian H, and the Hamiltonian flow %, are related by Hamilton's equations: [Math.25] êLH, \ ; | â H| 27 -è In practice, we can decompose the Hamiltonian flow x into two Hamiltonian flows respectively linked to a translation and a rotation, and therefore consider a Hamiltonian Hrés linked to the translation and a Hamiltonian H'* linked to the rotation. The Hamiltonian linked to the translation H*"* simply corresponds to free propagation in a homogeneous medium of refractive index no (in practice we can take no = 1 for propagation in air): Hs = SORT(ne?-Ip). Concerning the Hamiltonian linked to the rotation H', we can obtain the expression of its derivatives (which alone are necessary to evaluate the functions f, defined above) by reporting the literal expression of the symplectomorphism %y in the Hamilton formulas recalled above: [Math.26] to _ to E, . EE siné-Rcos9) u-- Ÿ = ycost= + ysinÿ- Hé cineReos0) sa [Hede, cosf+Rsin6)F [Math.27] aH® LV - _vana Me $ y -5-- ysind-57# cos9 - sind FE [Math.28] aHt _ _ ON, ms A = [Math.29] ax _ On, . sr He E,sin0- Rcos0 with R=SQRT(1 — &,2 — E,2). Higher-order derivatives can be obtained on this basis by numerical methods (such as finite difference). [Fig.2] represents an example of a digital holography device 10 using the teachings of the invention. This digital holography device 10 comprises a processing module 2, a storage module 4, an acquisition module 6 and a holographic restitution module 8. The digital holography device 10 is for example produced in the form of a visualization headset or augmented reality glasses. Processing module 2 is for example a processor, here a microprocessor. The acquisition module 6 comprises at least one motion sensor (for example of the accelerometer or gyroscope type) which transmits measurement signals (in analog or digital form) to the processing module 2, on the basis of which the processing module 2 can develop data representative of the position and / or orientation of the digital holography device 10. The storage module 4 comprises, for example, a memory and / or a hard disk. The storage module 4 stores in particular computer program instructions designed so that the processing module 2 implements at least some of the steps of the method described below with reference to [Fig. 3] when these instructions are executed by the processing module 2. As explained below, the storage module 4 further stores a representation W of a digital hologram in the already mentioned space-frequency domain D. In practice, the storage module stores values ​​W(L) respectively associated with different elements L of the space-frequency domain D (i.e. in practice with different elements of R*). The holographic rendering module 8 here comprises a light modulator and a light source of wavelength λ, and allows the rendering of the digital hologram represented by the representation W to a user. Reference may for example be made to the patent application published as WO2019 / 001968 on this subject. [Fig. 3] represents an example of a method implemented by the processing module 2 of the digital holography device 10. This method begins with a step E2 of receiving measurement signals from the acquisition module 6. The processing module 2 then determines data representative of the position and / or orientation of the digital holography device 10 on the basis of the measurement signals received (step E4). In order to present the digital hologram to the user taking into account the movement of the digital holography device 10 (and thus to simulate the reciprocal movement of the digital hologram relative to the user), the processing module 2 applies to the digital hologram (represented by the representation W as mentioned above) a transformation T defined in the three-dimensional propagation space E as a function of the aforementioned representative data. To do this, the processing module 2 determines in step E6 the symplectomorphism x associated with this transformation T using the method proposed above. As already indicated, in a plane P, parallel to the reference plane P,, the function y (symplectomorphism) is such that the subset of the elements of the product space D x D of form (e, x(e)) is the subset defined by the elements of the form (x, y, 9e, 3e, 3e, 2e, N,.71,) for (x, Y, ",, N,) Variant in RS, where is a non-quadratic generating function of 0 O7, WHERE, four-variable generating function defined as a scalar product: - of a first vector, the first two coordinates of which correspond respectively to the first two variables of the four variables and the third coordinate of which corresponds to the coordinate of said parallel plane P, in the direction z perpendicular to the reference plane P.…:, and - of a vector resulting from the application of the transformation to a second vector, the first two coordinates of which correspond respectively to the last two variables of the four variables and, here, the norm of which is predefined. The processing module can thus determine in step E8 the representation W' of the transformed digital hologram (or digital hologram modified by application of the transformation T) on the basis of the representation W stored in the storage module 4 and the function % (symplectomorphism) determined in step E6. Alternatively, the representation W (i.e. in practice data representative of the aforementioned values ​​W(L)) could be received by the digital holography device 10 by means of a communication module (not shown). In accordance with what has been stated previously, the representation W' of the transformed digital hologram can be determined as follows: [Math.30] W{(L)= Wox{L)+E perl F (EL) for the different L of the space-frequency domain D used in the representation concerned, where N is a predetermined value for a given digital holography device (which corresponds to the desired degree of precision), À is as already indicated the wavelength associated with (and therefore used to restore) the digital hologram, o is as already indicated the composition operator and where the functions f, are defined above. In practice, we can use only the first term (called "corrective term") non- zero of the sum in the above formula; the processing module determines in this case the representation W' of the modified digital hologram as follows (the factor f; being zero with the Weyl quantization used here): [Math.31] W{L)=Wox{L)+2?.f(L) with [Math.32] Yes: = A{H, Wox,} ox,de Where {.}+ is the Poisson bracket defined above. The processing module 2 is thus designed to apply the % function when applying the transformation T to the digital hologram. The function x is notably applied when composing this function with the representation W (term W ox). Furthermore, as indicated above, it is provided here that the distribution W' representing the digital hologram transformed by the transformation T is determined by the processing module 2 using at least one corrective term which depends on the wavelength λ. This corrective term is non-zero because the function % is non-linear (the generating function @ being non-quadratic as explained above). The processing module 2 can then control the restitution of the transformed digital hologram (represented by the representation or distribution W') by means of the holographic restitution module 8. To do this, the processing module 2 reconstructs, for example, in step E10 the transformed digital hologram from the representation W' obtained in step E8. This reconstruction step may in practice comprise a summation of light contributions respectively associated with the values ​​W'(L) defining the representation W' for different elements L of the space-frequency domain D. The processing module 2 then sends, in step E12, signals representative of the reconstructed digital hologram to the holographic restitution module 8 (in practice to the light modulator equipping this holographic restitution module 8) in order to allow the restitution of the transformed digital hologram to the user, here by illuminating, with the light source of wavelength λ, the light modulator configured on the basis of the signals representative of the reconstructed digital hologram. Alternatively, the restitution of step E12 could be carried out on a stereoscopic system. Step E12 then comprises a stereoscopic conversion sub-step to convert the reconstructed hologram into stereoscopic signals and a sub-step of displaying on a screen of the stereoscopic system from the stereoscopic signals. [Fig.4] represents a method implemented in another context of use of the invention. It is a method of decoding a digital hologram H,,; from data received in a data stream. This method is implemented in a decoding device. Such a decoding device comprises, for example, a processor and a memory storing computer program instructions designed to implement at least certain steps of the method of [Fig. 4] when these instructions are executed by the processor. This decoding device may be a computer (e.g., a personal computer) or a digital holography device as described above with reference to [Fig.2]. The method of [Fig.4] begins with a step E20 of receiving a data stream. The decoding device receives, for example, this data stream from a remote server, typically by means of a communication module of the decoding device. The method continues with a step E22 of obtaining a reference digital hologram H,. The decoding device can obtain the reference digital hologram by decoding data received in the aforementioned data stream. These data are for example representative of a representation W, of the digital hologram H, (without reference to another digital hologram). Alternatively, the digital hologram H, can be obtained by means of a method of the same type as that described here for obtaining the digital hologram H,,. The method also comprises a step E24 of decoding a residue e, from other data received in the data stream. The method also comprises a step E26 of obtaining a PRED predictor, for example by reading from a memory of the decoding device. Alternatively, the PRED predictor can be obtained by decoding data contained in the received data stream. The method then comprises a step E28 of predicting a predicted digital hologram H', by applying to the reference digital hologram H, a transformation T defined by the predictor PRED, using the techniques described above to transform the representation P into a representation P', which therefore comprise the application of a function y determined as described above. As in the process of [Fig.3], the reference digital hologram H, is for example represented by a representation W in the domain spatio-frequency domain D (i.e. by values ​​W(L) respectively associated with different elements L of the spatio-frequency domain D). In this case, the prediction step E28 may include a determination of a distribution W' representing the predicted digital hologram H°, on the basis of the representation W of the reference digital hologram H, in accordance with what is set out above for step E8 of [Fig.3], i.e. as follows: [Math.33] W{L)= Wox(L)+E nl "F (L) for the different L of the space-frequency domain D used in the representation concerned, where N is a predetermined value for a given decoding device (which corresponds to the desired degree of precision, with for example N = 1, in which case the formula contains a single corrective term à.f,(L)), À is as already indicated the wavelength associated with the digital holograms, o is as already indicated the composition operator and where the functions f, are defined above. The function x is thus notably applied during the composition of this function with the representation W (term W o ”). Furthermore, as indicated above, it is provided here that the distribution (or representation) W' representing the predicted digital hologram H', is determined by the decoding device using at least one corrective term which depends on the wavelength λ. This corrective term is non-zero because the function x is non-linear as explained above. The method can then comprise a step E30 of obtaining the decoded hologram H,,, by combining the residue e, and the predicted digital hologram H”,. For example, for the different L of the space-frequency domain D used in the representation concerned, the representation (or distribution) W°' representing the decoded digital hologram H,,, is obtained as follows: W''(L) = W'(L) + E(L) where E is the representation of the residue e, in the space-frequency domain D. When the decoding device comprises a holographic restitution module (for example when the decoding device is a digital holography device like that of [Fig.2]), the method may further comprise a step of reconstructing the hologram to be rendered on the basis of the representation W”* of the decoded hologram H,,; and / or a step E32 of restitution of the decoded (and reconstructed) digital hologram by means of the holographic restitution module. [Fig. 5] represents an example of a coding device 20 according to the invention. This coding device is for example located within a server so as to deliver data representative of a sequence of digital holograms to a customer electronic device, as described below. The coding device 20 here comprises a first coding unit 22, a prediction unit 24, a residue determination unit 26, a second coding unit 28 and a communication unit 30. The coding device 20 is for example produced in the form of an electronic device comprising a processor (such as a microprocessor); in this case, each of the aforementioned units can be implemented due to the execution, by this processor, of computer program instructions stored within the electronic device forming the coding device 20 (for example in a memory of this electronic device). However, as a variant, at least one of the aforementioned units can be produced by means of a dedicated electronic circuit, for example an application-specific integrated circuit. The first coding unit 22 is designed to produce data D1 which are representative of a digital hologram H,, here a reference digital hologram, without reference to data relating to another digital hologram. An example of an embodiment that can be envisaged for the coding carried out by the first coding unit 22 is described below with reference to [Fig. 10]. The prediction unit 24 is designed to predict a digital hologram H”, called “predicted digital hologram”, by transforming the reference digital hologram H,, using the techniques which have been presented above with reference to figures 1 to 4, in particular by applying the function % defined above for the determination of the predicted digital hologram. The residue determination unit 26 is designed to determine a residue e,, between the predicted digital hologram H”, produced by the prediction unit 24 and the current digital hologram Hjs1- The second coding unit 28 is designed to produce data D3, D4 representative of the residue €, produced by the residue determination unit 26. Additional elements relating to the operation of these different units are given further on with reference in particular to [Fig.7]. Finally, the communication unit 30 is designed to transmit the representative data produced by the first coding unit 22 and / or by the second coding unit 28 to the client electronic device. [Fig.6] represents an example of a decoding device 40 in accordance with the invention. This decoding device 40 is for example an electronic device (such as the aforementioned client electronic device) designed to receive data representative of a sequence of digital holograms from a server (such as the aforementioned server). The decoding device 40 comprises a first decoding unit 42, a second decoding unit 44, a prediction unit 46, a combination unit 48, a reconstruction unit 49 and a communication unit 50. The decoding device 40 is for example produced in the form of an electronic device comprising a processor (such as a microprocessor); in this case, each of the aforementioned units can be implemented due to the execution, by this processor, of computer program instructions stored within the electronic device forming the decoding device 40 (for example in a memory of this electronic device). However, as a variant, at least one of the aforementioned units can be produced by means of a dedicated electronic circuit, for example an application-specific integrated circuit. The first decoding unit 42 is designed to obtain a digital hologram H,, here a reference digital hologram, from data D1 representative of this digital hologram. These representative data D1 are for example received by the communication unit 50 (from the coding device 20 in the examples described below). An example of a decoding method which can be implemented by the first decoding unit is described later with reference to [Fig. 11]. The second decoding unit 44 is designed to decode a residue e, from data D3, D4 representative of this residue e,. These data D3, D4 representative of the residue are here received by the communication unit 50 (for example from the coding device 20). The prediction unit 46 is designed to predict a digital hologram H',, called "predicted digital hologram", by transforming the reference digital hologram H,, using the techniques which have been presented above with reference to FIGS. 1 to 4, in particular by applying the function % defined above for the determination of the predicted digital hologram. Its operation is similar to that of the prediction unit 24 of the coding device 20. The combination unit 48 is designed to obtain a digital hologram Fly ni (called "decoded digital hologram") by combining the residue e,.; decoded by the second decoding unit 44, and the predicted hologram H, produced at the output of the prediction unit 46. The reconstruction unit 49 is designed to reconstruct the decoded digital hologram Hz. on the basis of a representation of this digital hologram, this representation here using a decomposition into Gabor frames. Additional elements relating to the operation of these different units are given further on with reference in particular to [Fig.7]. [Fig.7] shows a method of exchanging data between the coding device 20 and the decoding device 40 for example for the restitution, on a holographic restitution device, of a sequence of digital holograms coded by the coding device 20, transmitted from the coding device 20 to the decoding device 40 (for example via a communications network), and decoded by the decoding device 40. This process begins with a step E2 of initializing the index k which designates the current digital hologram H, in the sequence of digital holograms processed. The index k is here initialized to 0. The method continues with a step E4 of decomposition of the current digital hologram H, into Gabor frames W,. As previously indicated, the current digital hologram H, is then represented by a set of first coefficients (here complex) W,(C) respectively associated with elements Ç of the space-frequency domain D. It is recalled that each of these elements of the space-frequency domain D is formed by a first spatial parameter x, a second spatial parameter y, a first frequency parameter n and a second frequency parameter E. The coefficients W,(C) can for example be calculated by the following formula: W,(£) = < #(0)æ, H, > by taking the notations of the formula [Math. 6] above and with < f , g > the scalar product between the functions f and g. In practice, the representation of the current digital hologram Hz used is for example a sparse representation, that is to say that the coefficients W,(C) are chosen to best represent the current digital hologram H, while being limited in number. To do this, we use for example a basic pursuit algorithm (or "basis pursuit" according to the commonly used English terminology) to select the coefficients W,(C) resulting from the decomposition of the current digital hologram H, into Gabor frames to be used in the sparse representation. We can refer for example to the article "Basis pursuit", by S. Chen and D. Donoho in Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers (vol. 1, pp. 41-44), October 1994 regarding the basic pursuit algorithm. The method of [Fig.7] then continues with a step E6 of coding the current digital hologram H,, that is to say here of coding the coefficients W,(C) representing the current digital hologram H,. This coding step is here carried out by the first coding unit 22 mentioned above. An example of a possible implementation for step E6 is described further with reference to [Fig.10]. Step E6 makes it possible to generate coded data D] representative of the current digital hologram H,. These coded data D1 are transmitted, by the communication unit 30 of the coding device 20 and via a communication network, to the decoding device 40 (step E8). Alternatively, the encoded data D] could be stored within the encoding device 20 (for example for later use in the case where the encoding device 20 and the decoding device 40 are the same and unique electronic device). In the steps E10 to E14 now described, the digital hologram H, of index k is used as a reference digital hologram for the differential coding (i.e. in the form of a residue) of the digital hologram H, which follows the digital hologram H, in the sequence of digital holograms. During step E110, the prediction unit 24 determines a transformation T,+; (here a rigid transformation as already indicated) on the basis of the reference digital hologram H, and the following digital hologram H,s1, then determines a predicted digital hologram H', by transformation of the reference digital hologram H, using the function (or symplectomorphism) % associated as explained above with the determined transformation T,-. The transformation T, is for example determined by motion analysis between the scene represented by the reference digital hologram H, and the following digital hologram H,.1, As proposed in patent application WO 2021 / 004 797 The representation W', of the predicted digital hologram H', (by means of second coefficients W',(£)) is then determined from the representation W, of the reference digital hologram H, (by means of the first coefficients W,(e)) using the function % associated with the transformation T,. in accordance with what was previously described, that is to say that we have according to a simplified notation: von W',=W,0% + À P, where o is the function composition operator, λ is the recording wavelength of digital holograms and P are complex functions defined on the space-frequency domain D as explained previously. A coefficient associated with an element (xo, Yo. No, Ec) and participating in the representation of the predicted digital hologram H', is therefore determined using the formula: WiCX(<0s Yo» Nos Ëo) ) + E to p, Co, Yo» Nos Eo)- Thus, for the determination of a second coefficient W',(£0) associated with an element € formed by a first value x, relative to the first spatial parameter, a second value y, relative to the second spatial parameter, a third value n, relative to the first frequency parameter and a fourth value Ë, relative to the second frequency parameter, we use in particular the first coefficient W, associated with the image, by the function x, of the element €, formed by the first value x, the second value yp, the third value ny and the fourth value Ep. According to the formula proposed above to calculate the coefficients W',(e) representing the predicted digital hologram H'4, we use a corrective term E ,; XP, which depends on the wavelength Å of acquisition of the digital hologram. This corrective term being a sum of functions, we can according to a possible variant use a single term of this sum as a corrective term when determining the coefficients W°,(e). According to another variant, to simplify the processing, the corrective term may be disregarded; in this case, any second coefficient W',(£o) determined in step E10 and associated with an element £, formed by a first value x, relative to the first spatial parameter, a second value yo relative to the second spatial parameter, a third value np relative to the first frequency parameter and a fourth value &, relative to the second frequency parameter, is equal to the first coefficient W, associated with the image, by the function x, of the element £, formed by the first value xo, the second value yo, the third value no and the fourth value E,. Furthermore, it is also possible to obtain the coefficients W',(e) by multiplying the expression given above (with or without use of the corrective term), which then forms an intermediate value, by a real-valued space-frequency distribution function A over the space-frequency domain D and varying only according to the two frequency dimensions (i.e. there exists a two-variable function f such that A(x,y,nE)=f(n,E) for any multiplet (x,y,nE)), for example to obtain an attenuation of the digital hologram in a certain direction. This space-frequency distribution function is for example of the form: A(x,ym,E) = cos 6 + sin 0 [Math.34] ËE. fire with 6 a predetermined value linked to the direction of attenuation, and the general formula which gives the expression of the coefficients W', representing the predicted hologram H*, is then: W',=[W.0%+ to P,}A- The method then comprises a step E12 of decomposing the digital hologram H,. into Gabor frames Wy.1. This step is similar to step E4 carried out for the digital hologram H; and makes it possible to obtain, to represent the digital hologram H,,1, a set of coefficients (here complex) W,.1(C) respectively associated with elements € of the domain spatio-frequency D. The method of [Fig.7] continues with a step E14 of determining a residue e.g. between the digital hologram H,,, and the predicted digital hologram H”,, here by difference between the digital hologram H,4, and the predicted digital hologram H”,. This step is here carried out by the residue determination unit 26. In practice, this difference is made between the coefficients W,(C) representing the digital hologram H,,, and the coefficients W°,(C) representing the predicted digital hologram H'k, and we thus note in a simplified manner: en = Wai-Wh More precisely, for all the elements € of the space-frequency domain D for which at least one of the coefficients W,-,(e) and W',(e) is non-zero, the residue determination unit 26 determines a (complex) coefficient e,4;(e) of the residue e,… by the operation: Epn(e) = Wii(e) = W'(£) The communication unit 30 can then transmit in step E16 representative data D2, D3, D4 of the transformation Ty, and of the residue e,, to the decoding device 40 (via the aforementioned communication network). Alternatively, these representative data could be stored in a memory of the coding device 20 for later use. The D2 data representative of the transformation T, includes values ​​which characterize the transformation T,.1, for example the values ​​of the components of the vector defining the translation involved and the angle values ​​defining the different rotations involved. It is proposed to code the residue e,,, as follows for its transmission to the decoding device 40. Alternatively, the coding method described below with reference to [Fig.10] could be used. Here we treat separately the real part and the imaginary part of each of the coefficients e,.1(€). We form images I;; which each group the real part of the coefficients ex (€) associated with elements whose first frequency parameter and the second frequency parameter are fixed. In other words, a pixel in row p and column q of an image [;; has the value: T,(pq) = Re[ epsi ((Xp Ypo lis &;)) 1 where Re[y] denotes the real part of the complex number y and m; and &; are respectively the first frequency parameter and the second frequency parameter associated with the image I TA The sequence of images formed by the images L;; (when i and j vary so as to scan all the pairs first frequency parameter 1; - second frequency parameter- quential &, used in the representation) is then encoded using a video encoder (for example in accordance with an AVC or HEVC type standard). The above sequence of images can be formed by taking the images L, in the following order: the different images I,; with j increasing, then the different images I,; with j decreasing, then the different images L,; with j increasing, etc. The coded data D3 produced by the coding of the image sequence [,; are sent to the decoding device 40 by the communication circuit 30. In the same way, we form images J; which each group the imaginary part of the coefficients e,.1(e) associated with elements whose first frequency parameter and the second frequency parameter are fixed. In other words, a pixel in row p and column q of an image J;; has the value: J,;(pq) = Im[ exsr ((Xp> Ype Mi» &;) ) 1 where Im[y] denotes the imaginary part of the complex number y and n; and &; are respectively the first frequency parameter and the second frequency parameter associated with the image J,;. The sequence of images formed by the images J;; (when i and j vary so as to scan all the pairs first parameter n; - second parameter Ë; used in the representation) is then coded by means of a video coder (for example in accordance with a standard of the AVC or HEVC type). The above sequence of images can be formed by taking the images J;; in the following order: the different images J,; with j increasing, then the different images J., with j decreasing, then the different images J4; with j increasing, etc. The coded data D4 produced by the coding of the image sequence J; are sent to the decoding device 40 by the communication circuit 30. The process of [Fig.7] continues with a step E18 of incrementing (by one unit) the index k for processing the following digital hologram. The method then comprises a step E20 where the coding device 20 determines whether a reset of the differential coding is necessary, i.e. whether the new digital hologram Hz to be coded must be coded entirely (as in step E6) or can still be coded by differential coding. The criterion for determining whether a reset is necessary is, for example, a frequency criterion (so as to obtain a predetermined number of successive digital holograms coded by differential coding) or an error limitation criterion (by limiting to a predetermined threshold an error measurement between the original digital hologram and the reconstructed digital hologram after decoding as explained below). If the coding device 20 determines in step E20 that a reset is necessary, the method continues (arrow P) in step E22 for a new increment. mentation of the index k (by one unit) then loops to step E4 for the processing of the new digital hologram, now designated H,. If the coding device 20 determines in step E20 that a reset is not necessary, the method continues (arrow N) to step E10 for differential coding of the new digital hologram H, 1. We now describe (still with reference to [Fig.7]) the decoding of the data transmitted by the coding device 20 as explained above with a view to the reconstruction of the digital hologram sequence. Upon receipt of the coded data D1 representative of the digital hologram H,, the first decoding unit 42 decodes the coded data D1 (step E30) so as to obtain the coefficients W,(C) forming the representation of the digital hologram H,. An example of a possible decoding method is described further with reference to [Fig.11]. The reconstruction unit 49 can then reconstruct the digital hologram H, in step E32 on the basis of the coefficients W,(C) decoded in step E30. To do this, we use the inverse transformation of that used in step E4 to obtain the representation of the digital hologram. In the example described here, we therefore use the inverse transformation to that used to obtain the decomposition into Gabor frames. The digital hologram H, is therefore reconstructed here according to the formula [Math. 6] presented above (using the decoded coefficients W,(C) as values ​​of we in this equation). The digital hologram HF can then be restored by means of a holographic restoration device (step E34). Such a holographic restoration device comprises, for example, a light modulator and a light source of wavelength λ. By respectively applying the values ​​of the pixels of the digital hologram H to the pixels of the light modulator and by illuminating the light modulator by means of the light source, the digital hologram H is restored. Subsequently, upon receipt of the coded data D2, D3, D4, the second decoding unit 44 decodes this data in step E40 so as to obtain the transformation Ty and the residue €; The second decoding unit 44 determines the transformation T,+1 from the coded data D2, here from the values ​​of the components of the vector defining the translation characteristic of the transformation T,+ and the angle values ​​defining the different rotations characteristic of the transformation Tru. The second decoding unit 44 further reconstructs the image sequence I;; to from the coded data D3 and can thus determine the respective real parts of the coefficients e,.1(£) representing the residue ex. Similarly, the second decoding unit 44 reconstructs the image sequence J;; from the coded data D4 and can thus determine the respective imaginary parts of the coefficients e,,1(£) representing the residue ex. The second decoding unit 44 can thus determine the (complex) coefficients ew(e), i.e. decode the residue e,., from the data D3, D4 received from the coding device 20. The prediction unit 46 can furthermore predict the predicted hologram H', in step E42 by transformation of a reference digital hologram, for example the digital hologram H, decoded in step E30 or a digital hologram obtained during a previous passage to step E44 described below. During this step E42, the coefficients W',(e) of the predicted digital hologram H', are determined on the basis of the coefficients W,(e) representing the reference digital hologram H, and of the transformation T,+; (decoded in step E40 on the basis of the data D2 received from the coding device 20), according to a process identical to that used in step E10 described above and which will therefore not be described again. The determination of the predicted digital hologram H', during decoding therefore also uses the function % associated as explained above with the transformation Tya1. In step E44, the combination unit 48 can thus obtain the decoded digital hologram H,.1 by combining the residue €, (decoded in step E40) and the predicted digital hologram H',, here by summation (coefficient to coefficient) of the residue e,,; and the predicted digital hologram H*,: Hp = H4 + Ets In other words, for any element € of the space-frequency domain D corresponding to a coefficient in the representation of the residue e,,, Or of the predicted digital hologram H',, the combination unit 48 determines the coefficient Wk+1(e) associated with the element e in the representation of the decoded digital hologram H,., as follows H,-(€)= H4(E) + Eepn1(E) The reconstruction unit 49 can then reconstruct the digital hologram Hy;; in step E46 on the basis of the coefficients W,,1(€) obtained in step E44, in the same way as was done for the digital hologram H, in step E32. The digital hologram H,41 can then be rendered by means of the holographic rendering device (step E48), here by respectively applying the values ​​of the pixels of the digital hologram Hz; to the pixels of the light modulator and by illuminating the light modulator by means of the light source. [Fig.8] represents an alternative embodiment of the method of [Fig.7] according to in which we consider several objects O, (here M objects O,, Oz. …., Om) in the three-dimensional scene represented by the digital holograms. The method of [Fig.8] can also be implemented by the cooperation of the coding device 20 and the decoding device 40. The method of [Fig.8] also begins with the initialization (for example to the value 0) of an index k designating the digital hologram being processed (step E50). The coding device 20 then performs a step E54 of decomposing the current digital hologram H into Gabor frames W. This step E54 is identical to step E4 described above with reference to [Fig.7] and will therefore not be described in detail. Step E54 thus makes it possible to obtain coefficients (here complex) W,(C) respectively associated with elements Ç of the space-frequency domain D and representing the current digital hologram H,. The coding device 20 then proceeds to a step E56 of coding the coefficients W,(0) representing the digital hologram H,. This coding step is identical to the step E6 described above and here carried out by the first coding unit 22 mentioned above. This coding step uses for example a coding as explained later with reference to [Fig.10]. The coding step E56 makes it possible to produce coded data D1 representative of the coefficients W,(t). The communication unit 30 can then send in step E58 the data D1' representative of the coefficients W,(C) to the decoding device 40. Step E58 is here identical to step E8 described above. The method then comprises a step E60 (identical to step E12 of the method of [Fig.7]) of decomposition of the digital hologram H,,, into Gabor frames Wys1- This step E60 makes it possible to obtain, to represent the digital hologram H,+1, a set of coefficients (here complex) W,.1(C) respectively associated with elements Ç of the space-frequency domain D. The method of [Fig.8] continues with a step E61 of partitioning the spatio-frequency domain D into a plurality of disjoint parts P, respectively associated with the objects O, An example of a method for obtaining such a partition is given below with reference to [Fig.9]. The coding device 20 can then form in step E62 disjoint sets by grouping in a given set E,, the coefficients W,,1(C) associated with elements € belonging to a part P,, of the space-frequency domain D associated with this given set E,. In other words, a coefficient W,-1(C) belongs to a set E, if and only if the element € belongs to part P,.. The coefficients W,,1(G) of a set E, thus represent a partial digital hologram H,,1,. which corresponds to the object O,. In the example described here (and as explained below when describing [Fig.9]), we propose to determine as follows to which set E, belongs a coefficient W,1(C) associated with an element € = (x,yn,E) of the space-frequency domain D. We convert the frequency coordinates (n,E) into spatial coordinates (p,,py) with: p, = 1 / tan(arcsin(\.n)) and p, = 1 / tan(arcsin(AE)), then we determine to which subset G, mn the pair (p,. py) belongs, for example by calculating on which side of each line (s,ymol» Sxy,m;+1) SC finds the point (p » Py). (We recall that the subsets G,ym. delimited by the segments [Syymis Sxy, mi] are defined by the implementation of the method described below with reference to [Fig.9] during step E61.) The coefficient W,.1(C) associated with the element Ç = (x,y,n.€) will then be attributed to the set E, associated with the subset G,ym- The method continues with a step E63 of initialization (here to the value 1) of an index m designating the object O, (and therefore also the set E,) currently being processed. The prediction unit 24 then predicts in step E64 a partial predicted digital hologram H',n By transformation of a partial reference digital hologram H,m defined by the coefficients W,(Xn(E)) associated with the elements %n(E) for € varying in the part P, associated with the object On As in step E10 of the embodiment of [Fig.7], this step E64 uses a function %n associated with the transformation T,+1,m associated with the object O, in accordance with what is described above for the symplectomorphism x. The transformation T,+1,m is therefore determined here by means of an algorithm for estimating the movement of the object O,… As already indicated, the solution proposed in patent application WO 2021 / 004 797 can be used. Here the prediction unit 24 determines the coefficients W',m(£) of the partial predicted hologram H*,.n as follows: W'em(e) = Wim Xn(E) ) + E # pe) for the elements € belonging to the part P, of the space-frequency domain D, that is to say in order to predict the coefficients W,1(€) belonging to the set En (these coefficients are noted W,+1m(£) in the following). The residue determination unit 26 can then determine a partial residue e,+1,m between the partial digital hologram H;-1,n and the partial predicted digital hologram B'4m» Here by difference between the partial digital hologram Hy+1,n and the predicted partial digital hologram H',n., EITHER for any element € belonging to the part P, of the space-frequency domain D (here for any coefficient W,+1,2(€) belonging to the set E,,): Erstm(t) = Wii me) - We ml£). The communication unit 30 then transmits at step E68 data D2' representative of the transformation Tp+1,n €t of the partial residue e,,1m- To obtain these data D2”, we use for example a coding identical to that described above for the coding of the transformation T, and of the residue e,,;. In particular, according to one possible embodiment, the partial residue e,+1,n can be coded using the coding method described below with reference to [Fig.10]. The coding device 20 then determines in step E70 whether all the objects O have been processed, i.e. here whether am=M. If not (arrow N), the index m is incremented by 1 (step E72) and the process loops to step E64 described above. If so (arrow P), the method continues to step E74 described now. At step E74, the index k is incremented by 1. The method then comprises a step E76 (identical to step E20 described above) where the coding device 20 determines whether a reset of the differential coding is necessary, i.e. whether the new digital hologram Hz; to be coded must be coded entirely or can still be coded by differential coding. Reference may be made to the description of step E20 regarding the criterion for determining whether a reset is necessary. If the coding device 20 determines in step E76 that a reset is necessary, the method continues (arrow P) in step E78 for a new incrementation of the index k (by one unit) then loops in step E54 for the processing of the new digital hologram, now designated H,. If the coding device 20 determines in step E76 that a reset is not necessary, the method continues (arrow N) to step E60 for differential coding of the new digital hologram Hyui. We now describe, still with reference to [Fig. 8], the decoding of the data D1', D2” transmitted by the coding device 20 as explained above with a view to reconstructing the sequence of digital holograms. This decoding method comprises a step E80 of decoding the data D1” as received by the communication unit 50 so as to obtain the disjoint sets E, and the coefficients W,(£) contained in each of these disjoint sets Eu The reconstruction unit 49 can then reconstruct the digital hologram H, at step E82 on the basis of all the coefficients W,(0) decoded in step E80 (i.e. the coefficients contained in all the sets E,,). Note that the information relating to the disjoint sets E,, is not used in this step, but will be used later. This step E82 is similar to step E32 described in the description of [Fig.8] and will therefore not be described in detail. The digital hologram FI can then be restored in step E84 using a holographic restoration device of the same type as that used in step E34 described above. The decoding of a digital hologram H,,, differentially coded with respect to a reference digital hologram H, (such as for example the digital hologram decoded in step E80), here by means of the data D2' mentioned above, is now described. The coding device 20 transmits, for example, signaling data to the decoding device 40 (within the data stream transmitted by the communication module 30 and received by the communication module 50) to indicate this differential coding of the next digital hologram of the sequence. This signaling data can, for example, indicate the number M of objects present in the three-dimensional scene. The decoding device 40 then initializes an index m to 1 (step E86). The decoding device 40 then decodes in step E88 the data D2” received so as to obtain the transformation T,+1,m €t the partial residue ex m- The prediction unit 46 can then predict in step E90 the partial predicted digital hologram H',n on the basis of the transformation T,+1,m and the partial reference digital hologram H,… defined by the coefficients W,(Xn(€)) such that the element € belongs to the part P, of the space-frequency domain D associated with the current object O,. The processing operations carried out during this step E90 are identical to those carried out during step E64 during coding and will therefore not be detailed again here. These processing operations make it possible to obtain the coefficients W',m(£) representing the partial predicted digital hologram H',m- The combination unit 48 then obtains the partial digital hologram Hy+im By combining the partial residue €+;,n (decoded in step E88) and the partial predicted digital hologram H',m» here by summation (coefficient to coefficient) of the partial residue ex+1,m €t of the partial predicted digital hologram H'ym: Hi-im = H'ym + ChHime In other words, for any element € belonging to the part P, of the space-frequency domain D, the combination unit 48 determines the coefficient Wy-im(€) associated with the element e in the representation of the partial digital hologram H;-1,m As follows: Wine) = W'eml£) + Exsim(E) - The decoding device 40 then determines in step E94 whether all the objects O, have been processed, i.e. here whether am=M. If not (arrow N), the index m is incremented by 1 (step E96) and the process loops to step E88 described above. If so (arrow P), the method continues at step E74 with a step of merging all the coefficients W,+1,0(€) obtained during the various passages at step E92 and which represent (together) the decoded digital hologram H,,. The reconstruction unit 49 can then reconstruct the digital hologram A, in step E100 on the basis of the coefficients merged in step E98, in the same way as was done for the digital hologram H, in step E82. The digital hologram H,,; can then be rendered by means of the holographic rendering device (step E102), here by respectively applying the values ​​of the pixels of the digital hologram Hz, to the pixels of the light modulator and by illuminating the light modulator by means of the light source. We now describe with reference to [Fig.9] a method for partitioning the space-frequency domain D. In the example described here, we partition the space-frequency domain D into parts P n €n partitioning, for each point of the digital hologram with coordinates (x,y), a set M,, containing all the pairs (u,v) of frequency variables used in the representation of the digital hologram concerned, that is to say all the directions associated with these pairs (u,v), or, which is equivalent, by partitioning a part of a PPN plane parallel to the plane of the digital hologram, as described below. The process thus begins by initiating a loop which runs through the set of points X with coordinates (x,y) of the digital hologram (step E122). For each point X, the method initiates at step 124 a loop which runs through the set of objects O,, from the object furthest from the plane of the hologram to the closest object. In some application cases, the objects, their positions and their shapes are known. This is the case, for example, when the digital hologram in question has been constructed from a representation of the three-dimensional scene comprising these objects. In other application cases, objects are reconstructed from the relevant digital hologram, for example using the techniques described in the article "Comparative analysis of autofocus functions in digital in-line phase-shifting holography", ESR Fonseca, PT Fiadeiro, M. Pereira and A. Pinheiro, , Appl. Opt., AO, vol. 55, no. 27, pp. 7663-7674, September 2016. For each object O,, the method initiates at step E126 a loop which runs through all the points P of the object O,,. It is assumed that the object is discretized into a finite number of points and we denote (P,, P,, P;) the coordinates of the current point P. For each point P of the object O,, we determine in step E128 the point P' intersection of the segment [PX] and the plane PPN parallel to the (reference) plane of the digital hologram. Here we take as plane PPN the plane of equation z=1 (being recalled that the reference plane is the plane of equation z=0). Here, the coordinates of point P” are therefore ((P,-x) / P,(P,-y) / P,.1). Then, in step E130, a point P” of the digital hologram with coordinates (P”',,P”',) is determined such that no other point of the digital hologram is closer to the point P* than the point P”°. We can then fill in step E132 an element of a matrix G,, of the same dimensions as the digital hologram: we set the element with coordinates (P”',,P”',) in the matrix G,y to the value m (corresponding to the current object O,.). If this element has already been filled in during a previous passage to step E132, the previous value is overwritten (i.e. replaced by the current value of the variable m). Once the loops on the objects Om and their points P mentioned above are completed, we proceed to step E134 in which we define sets G,ym: Gm = {,y"): Gay(*°,ÿ") = m}. In other words, a given set G,,,m is the set of pairs (x',y”) for which the element of coordinates (x',y”) in the matrix G,, is equal to m. The sets G,,m are therefore disjoint sets and each correspond (thanks to the perspective projection of center (x,y,0) carried out in step E128) to the set of directions where the object O, concerned is located (from the point of coordinates (x,y,0)), that is to say to the set of pairs of frequency coordinates (u,v) of the set M,, associated with these directions. The definition of the sets G, yn thus amounts to a partitioning of the set M xy and thus, when this is done for all the pairs (x,y), to a partitioning of the space-frequency domain D into parts P,, with the following equivalence: (x,y,u,v) belongs to P, if and only if the pair (1 / tan(arcsin(\.u)) , 1 / tan(arcsin(À.v))) belongs to G,ym- The method continues with a step E136 of determining, for each set G,y,m, a set of segments [S,y,miSxymi-1] delimiting the set G,ym. For example, we go through the set of points bordering the set G,ym (i.e. neighbors with a point which does not belong to the set G,,.n) and we use each of these points as one of the points S,,m; defining a boundary of a segment [SxymisSx,y, mil. After step E136, the method optionally loops to step E124 for processing. of a new point X of the digital hologram, until all points of the digital hologram have been processed. We will now describe with reference to [Fig. 10] a method for coding coefficients associated respectively with elements of the space-frequency domain D and used to represent a digital hologram. In the example described here, this involves the coding of the coefficients W,(t) representing a digital hologram H, so as to obtain data D1 representative of this digital hologram H,. In the context described above, this method is implemented by the first coding unit 22 of the coding device 20. Alternatively, however, this method could be used to code other types of coefficients, for example the coefficients forming the residue e,., mentioned above, As indicated above, the digital hologram H, is here represented by a plurality of coefficients W,() associated respectively with elements Ç which are part of a mesh A of the space-frequency domain D (see equation [Math 5] above for the definition of the mesh A). We recall that the coefficients W,(£) are complex numbers. In the following, we note x (x integer varying from 1 to N,) the indices respectively associated with the values ​​** of the first spatial parameter used in the representation of the digital hologram H,, '> ("> integer varying from 1 to N,) the indices respectively associated with the values ​​Ÿx of the second spatial parameter used in this same representation, Lx (Lx integer varying from 1 to M,) the indices respectively associated with the values ​​7m, of the first frequency parameter used in the representation and #Ly (y integer varying from 1 to M,) the indices respectively associated with the values ​​&,, of the second frequency parameter used in the representation. To facilitate the following exposition, we define blocks Bm,m, as follows (for all quadruplets (74, ty, Mlx, y) used in the representation): Brune, Ty) = W,f Cm, Yu Tim, Em) ) If the representation of H, includes a co- efficient associated with the element (Xne, Frs, "rt,, Ep.) Bmx, Ny) = 0 otherwise. In other words, each block Bm,n includes (all) the coefficients associated with the elements having fn, as the value of the first frequency parameter and &,,, as the value of the second frequency parameter, organized in the form of a matrix according to the respective values ​​of the first spatial parameter and the second spatial parameter. The element defined by the position (x, ") in the block Bm,m, is zero when no coefficient is associated with the element (*rs, J'y, in, En) in the representation of the digital hologram H,. The method of Figure 10 begins with a step E150 of coding the positions of the co- non-zero efficient in a first block B4,4, with here #x= 1 and #y =1. The definition of a block Bm,, (as proposed here) is a particular way of associating in a predefined manner a set of positions (in the block) with the coefficients associated respectively with the different multiplets of the form (x,y, 7m,, State In practice, the position used for coding can be defined within an ordered sequence of coefficients within the relevant Bæ,yn; block (here the Bray, = Bin block. To do this, for the block concerned B»1.m,, we order for example the coefficients of the block in raster scan order (commonly called "raster scan order"): we order the coefficients Brm,m(1, !*) in ascending order of index "> relative to the second spatial parameter (”Y increasing from 1 to N,), then the coefficients Bm,m,(2, >) in descending order of index '*» (y decreasing from N, to 1), then again in ascending order of index » for the coefficients Br,m.(3, ?5), etc. Here we propose to code the positions of the non-zero coefficients Ba,4,(x, >) by means of indicative data representing the difference between the positions of two successive non-zero coefficients in the ordered sequence of coefficients (except for the first coefficient whose position will for example be coded in absolute value). Thus, for example, the positions of the non-zero coefficients c,, C2, C3, C4 in a sequence (0 c1 0 0 c2 c3 00 0 c4 0 0 0) will be coded by the numbers: 2, 3, 1, 4, where 2 represents the position of the first non-zero coefficient c;, 3 the difference between the position of the second non-zero coefficient cz and the position of the first non-zero coefficient c;, 1 the difference between the position of the third non-zero coefficient cz and the position of the second non-zero coefficient c, and 4 the difference between the position of the fourth non-zero coefficient c, and the position of the third non-zero coefficient cs. In the following, we denote by D1 | the data indicative of the positions of the non-zero coefficients in the block B,0,, The method then initiates a loop at step E152 so as to process all the blocks Bm,m, other than the block Bust, The different blocks Bu,m, can for example be processed in a frame scanning order by considering all the blocks Br, as elements of a frame: the blocks By,, are processed in order of increasing index ”*» (from 2 to My in the example described here), then the blocks B3,,, in order of decreasing index ”*> (here from My to 1), then the blocks By, in order of increasing index y (here from 1 to My), then the blocks B4,,, in order of increasing index r (here from 1 to My), etc. Whatever the order of processing of the blocks, we note in the sequence B'm,n, the block processed immediately before the current block Brmyr; (this block B'mn, which can be the block Bu,4, during the processing of the first block Brun: designated by the loop initiated at step 152, or a block previously processed in step E152 described below). For all blocks Bm,n, other than the block But, (and here in the processing order defined above), the method performs in step E154 the coding of the positions of the non-zero coefficients of this block Brin, (current block). In the example described here, we propose to code on the one hand (within data D12) the positions of the non-zero coefficients in the previous block B'mn,sn, for which the corresponding coefficient in the current block Bm,n, is zero, and on the other hand (within data D13) the positions of the non-zero coefficients in the current block Bmyn; for which the corresponding coefficient in the previous block B'mym, is zero. In other words, data D12 represents the positions of the coefficients which "disappear" from the representation when we move from the previous block B msn, to the current block Bm,…n., while data D13 represents the positions of the coefficients which "appear" in the representation when we move from the previous block B'in,yns to the current block Brun. Thus, the data D13 designates at least one position associated with a non-zero coefficient in the current block Bm,yn,, without designating on the other hand at least one other position associated with another non-zero coefficient when this other position is already indicated by coded indicative data (as part of the coding of the positions in the previous block B'imum,) for another pair of respective values ​​of the first frequency parameter and the second frequency parameter. The data D12 designates positions corresponding (each) to a zero coefficient in the current block Bmyn,, but for which the corresponding coefficient was non-zero in the previously processed block B'myny, these positions being therefore indicated in indicative data coded for another pair of respective values ​​of the first frequency parameter and the second frequency parameter. No data is therefore coded in the data stream when, for a given position, the coefficients of the current block and the previous block are both zero, or are both non-zero. The positions coded in step E154 are, for example, the absolute positions of the coefficients concerned within the ordered sequence (in frame scanning order) defined above within each Braun block. The method then comprises a step E156 of coding the (non-zero) coefficients associated with the positions indicated by the indicative data D11, D12, D13. These coefficients are for example coded in the order of the processing carried out in steps E150 and E154, that is to say starting with the block B«y; (here the block Bs1) then in frame scanning order within the blocks Brin, and, within each block, in the frame scanning order (described above in the context of step E150). For the coding of a given coefficient W,( (Ÿr., Fay, Tm,, E,,) ), a part to the quantification of the real part of this coefficient and on the other hand to the quantification of the imaginary part of the coefficient, the quantified real part and the quantified imaginary part then being concatenated. The quantizer used for quantization is for example a uniform scalar quantizer or a quantizer as described in the article "Exact global motion compensation for holographic video compression", by Raees Kizhakkumkara Muhamad et al. in Applied Optics58, G204-G217 (2019). In the example described here, the coding of the coefficients of step E156 is carried out after the coding of the positions of steps E150 and E154. Alternatively, the coding of the coefficients could be interposed between position coding steps: for example, the coding of the (non-zero) coefficients of a block Bm,my could be carried out following the coding of the positions of the non-zero coefficients in this block Bmsn, as carried out in step E150 or in step E154. All of the data obtained by the different coding steps mentioned above (step E150, E154, E156) can further be coded by an entropic coder, for example an adaptive arithmetic coder, in order to obtain the data D1 to be transmitted to the decoding device 40 (or alternatively to be stored for subsequent decoding). Finally, markers can be inserted between the different types of data (here between the D1 1 data, the D12 data, the D13 data and the real and imaginary parts of quantized coefficients) to allow these data to be found at the decoder level. Other solutions can however be used, such as the use of a fixed length for the data representing the real and imaginary parts of the coefficients, for example. The data stream DI transmitted (from the encoding device 20 to the decoding device 40 in the context described above) to represent the digital hologram H, therefore comprises: - data D11 indicative of the positions associated respectively with non-zero coefficients within the block B,x, (that is to say among a set of positions associated in a predefined manner with the coefficients associated respectively with the different multiplets defined by the value 7#, for the first frequency parameter and by the value &, y, for the second frequency parameter); - then successively for each of the other blocks Bm,m., data D12, D13 indicative of the positions associated respectively with non-zero coefficients within the block Bnmy concerned (i.e. among a set of positions associated in a predefined manner with the coefficients associated respectively with the different multiplets defined by the value 77, for the first frequency parameter and by the value &,,, for the second frequency parameter); - for each block, data representative of the coefficients associated respectively with the positions indicated by said indicative data relating to the block concerned. As already indicated, for each block, the position of the coefficients used for coding can be defined within an ordered sequence of the coefficients within the block Bi,sm concerned, for example the frame scanning order already presented. A method for decoding such a data stream is described below with reference to [Fig. 11], as implemented for example by the decoding device 40 in step E30 described above. For each block Bm,n. defined above in the context of the coding method of Figure 10, the decoding device (precisely the first decoding unit 42 in the context described with reference to Figure 6) decodes in step E160 the data indicative of the positions associated with non-zero coefficients in the block Br, concerned, that is to say among a set of positions associated in a predefined manner (here by definition of the block) with the coefficients associated respectively with the different multiplets whose first frequency coordinate is the value sm, associated with the index x and whose second frequency coordinate is the value €, associated with the index "?v. The different blocks are for example transmitted (and therefore presented within the data stream) in an order predefined by convention between the coding device 20 and the decoding device 40, such as the already mentioned order of frame scanning within the blocks arranged in the form of a block matrix. Alternatively, additional data could be placed in the header of the data relating to a block Bm,n and indicate parameters designating the block Br,yny concerned (these parameters being for example the indices x and y of the block concerned). In the case of block Bu. (here block B; 1), the data D11 indicative of the positions of the non-zero coefficients (here within an ordered sequence of coefficients of block Bu,#,) represent a difference between a position associated with a non-zero coefficient and another position associated with another non-zero coefficient, as explained during the description of the coding method. In the case of blocks Bri,m, other than block Bu,+,, the data D12, D13 indicating the positions of the non-zero coefficients (here within an ordered sequence of coefficients of block Bn,) designate either the positions of the zero coefficients in the current block Bm,n. while the coefficient at the same position was non-zero in the previously decoded block B'm,n (data D12), or the positions of the non-zero coefficients in the current block Br, while the coefficient at the same position was zero in the previously decoded block B'mn (data D13). Thus, the data D13 designates at least one position associated with a non-zero coefficient without designating at least one other position associated with another non-zero coefficient when this other position has been indicated by indicative data decoded in relation to another block, that is to say for another pair of respective values ​​of the first frequency parameter and the second frequency parameter (this pair of values ​​being associated with the coefficients forming the other block). When the data indicative of the positions of the non-zero coefficients have been decoded for a given block Bm,n,, the decoding device 40 (precisely here the first decoding unit 42) can decode the coefficients associated respectively with the positions indicated by these indicative data. The decoding device 40 thus finds the non-zero coefficients Br,n,("x, >), that is to say the non-zero coefficients W,( (Pts Frs, Pr, Er) )- By scanning the set of Brun blocks (for which the data are successively transmitted in the data stream), the decoding device 40 thus obtains the set of non-zero coefficients W of the representation of the digital hologram H. It is noted that, as already indicated in the context of the coding method of FIG. 10, the decoding device 40 can receive all the data indicative of the positions of the non-zero coefficients for the set of blocks Ban, then the coefficients associated with these positions, or, as a variant, by successively considering the different blocks Bin,m, the data indicative of the positions of the non-zero coefficients of this block and the coefficients associated with these positions. An example of a coding device 60 in accordance with the teachings of the invention will now be described with reference to [Fig. 12]. It may be a coding device such as the coding device 20 described above with reference to [Fig. 5], in which case the modules described below are part of the first coding unit 22 mentioned above. The coding device 60 is for example produced in the form of an electronic device comprising a processor (such as a microprocessor); in this case, each of the modules described below can be implemented due to the execution, by this processor, of computer program instructions stored within the coding device (for example in a memory 70 of this coding device). However, as a variant, at least one of the modules described below can be produced by means of a dedicated electronic circuit, for example an application-specific integrated circuit. The coding device 60 comprises an initial block processing module 62, a subsequent block processing module 64, a coefficient processing module 66 and a finalization module 68. The coding device 60 is thus capable of implementing the method described above. with reference to [Fig.10], here when the processor of the coding device 60 executes some of the computer program instructions stored in the memory 70 of the coding device and already mentioned above. As explained above with regard to figure 10, the coefficients to be coded by the coding device 60 are coefficients respectively associated with multiplets each formed by a first spatial parameter *, a second spatial parameter Yn,, a first frequency parameter ” / ,,, and a second frequency parameter #,,. As already indicated, the case is described here where these coefficients are W coefficients, which form (on their own) a representation of a digital hologram. Alternatively, these coefficients could represent a digital hologram in combination with other elements, for example in the case where the coefficients define a residue, such as the residue €, mentioned above. The modules 62, 64, 66, 68 can access the memory 70 of the coding device 60 where the coefficients W, to be coded are stored and can therefore process these coefficients in the form of blocks Bas4,, Bm,sny, as explained now. The initial block processing module 62 is designed to encode data D11 indicative of the positions of the non-zero coefficients within the block Bw..«, of coefficients W, defined above, by coding the difference between two successive positions associated with non-zero coefficients. This block Ba, groups together the coefficients associated with the multiplets whose first frequency parameter is equal to +, and therefore the second frequency parameter is equal to E su The subsequent block processing module 64 is designed to encode data D12, D13 indicative of the positions of the non-zero coefficients within each of the blocks Bu,m, of coefficients W, defined above, by encoding the positions of the non-zero coefficients in the preceding block B'.yn for which the corresponding coefficient in the current block Bmy», is zero (data D12), and by encoding the positions of the non-zero coefficients in the current block Brin, for which the corresponding coefficient in the preceding block B'ni,sn; is zero (data D13). As explained above, for each pair (x, y), 1st block Bm,sn, groups the coefficients W, associated with the multiplets whose first frequency parameter is equal to ”m, and therefore the second frequency parameter is equal to ë,, The coefficient processing module 66 is designed to code the non-zero coefficients W, i.e. the coefficients W, whose positions are indicated in the indicative data D11, D12, D13, according to a predefined order, for example by frame scanning order within all the blocks Ba, Bm,m,, and, within each block, by frame scanning order among the coefficients W, of the block. We denote by D14 the coef- coded ficients. The finalization module 68 performs the entropy coding of the data D11, D12, D13, D14 and / or inserts markers between the different types of data in order to obtain the data D1 to be transmitted. An example of a decoding device 80 in accordance with the teachings of the invention is now described with reference to [Fig. 13]. It may be a decoding device such as the decoding device 40 described above with reference to [Fig.6], in which case the modules described below are part of the first decoding unit 42 mentioned above. The decoding device 80 is for example produced in the form of an electronic device comprising a processor (such as a microprocessor); in this case, each of the modules described below can be implemented due to the execution, by this processor, of computer program instructions stored within the decoding device (for example in a memory of this decoding device). However, as a variant, at least one of the modules described below can be produced by means of a dedicated electronic circuit, for example an application-specific integrated circuit. The decoding device 80 comprises an analysis module 82, an initial block construction module 82, a subsequent block construction module 84 and a coefficient decoding module 88. The decoding device 80 is thus able to implement the method described above with reference to [Fig. 11], here when the processor of the decoding device 80 executes certain of the computer program instructions stored in the memory of the decoding device and already mentioned above. The analysis module 82 receives the data DI and finds the different data D11, D12, D13, D14 therein, for example using the aforementioned markers. The analysis module 82 may optionally perform an entropic decoding step (when an entropic coding has been performed within the finalization module 68 described above). The initial block construction module 84 is designed to decode the data D11 representative of the differences between two successive positions associated with non-zero coefficients within the block B#,x, of coefficients W,, so as to obtain the positions of the non-zero coefficients within this block B«,«,. It is recalled in this regard that the coefficients of the block 84,4 are ordered in a predefined manner, for example a frame scanning order. Various solutions are possible for memorizing the positions of these non-zero coefficients. For example, the initial block construction module 84 initializes to zero the elements of a table corresponding to the coefficients of the form W, (x,y, #x, y), then sets to a predefined non-zero value (for example the value 1) the elements corresponding to the coefficients indicated as non-zero according to the data D11. (When the coefficients are complex numbers, this can be done on the one hand for the real part of the coefficients and on the other hand for the imaginary part of the coefficients.) For each pair (x, y) (different from ('v, #,;)), the subsequent block construction module 86 is designed to obtain the positions of the non-zero coefficients W, within this block Bin, by decoding on the one hand the data D12 indicative of the positions of the non-zero coefficients in the previously processed block B'myny for which the corresponding coefficient in the current block Bm,yn; is zero and the data D13 indicative of the positions of the non-zero coefficients in the current block Ban,m, for which the corresponding coefficient in the previously processed block B'm,m, is zero. Here again, various solutions are possible for storing the positions of these non-zero coefficients. For example, the subsequent block construction module 86 initializes to zero the elements of a table corresponding to the coefficients of the form W,(x,y, "x,y), and then sets to a predefined non-zero value (for example the value 1) the elements corresponding to the coefficients indicated as non-zero according to the data D12 and D13. (When the coefficients are complex numbers, this can be done on the one hand for the real part of the coefficients and on the other hand for the imaginary part of the coefficients.) The coefficient decoding module 88 is designed to decode the data D14 representing the coefficients W, (non-zero) associated respectively with the positions indicated by the data D11, D12, D13. As shown below, the coefficients W, are coded within the data D14 in a predefined order, so that the coefficient decoding module 88 can associate each decoded coefficient with a position of a non-zero coefficient, and thus find the value of a coefficient W,( (Vs Ya, Ur, Epn) )- For example, in the implementation possibility described below, the coefficient decoding module 88 traverses the aforementioned tables in a predefined order corresponding to the coefficient coding order, and then, when a coefficient is decoded, the value of the decoded coefficient is assigned to the next non-zero predefined value element in the table being processed.

Claims

Claims

1. Method for coding a set of coefficients (W,) participating in a representation of a digital hologram (H,) while being respect- tively associated with multiplets each formed by a first spatial parameter, a second spatial parameter, a first parameter frequency and a second frequency parameter, the method comprising the following steps, carried out for at least a pair of respective values ​​of the first frequency parameter and the second frequency parameter: - coding (E150; E154) of data (D11; D12, D13) indicative of positions associated respectively with non-zero coefficients among a set of positions associated in a predefined manner with the coefficients associated respectively with the different multiplets defined by said pair of values ​​of the first frequency parameter and of the second frequency parameter quantitative; - coding (E156) of the coefficients associated respectively with the positions indicated by the said indicative data.

2. A coding method according to claim 1, wherein at least one indicative data among said indicative data represents a difference between a position associated with a non-zero coefficient and a another position associated with another non-zero coefficient.

3. The encoding method of claim 1, wherein said data indicative designates at least one position associated with a coefficient non-zero without designating at least one other position associated with another non-zero coefficient and indicated by coded indicative data for another pair of respective values ​​of the first frequency parameter and the second frequency parameter.

4. Coding method according to one of claims 1 to 3, in which the coefficients associated with the different multiplets defined by said pair of values ​​of the first frequency parameter and the second frequency parameter quential are ordered in a predefined way in an ordered sequence of coefficients and in which the data indicative of a position associated with a non-zero coefficient indicates the position of this coefficient non-zero in said ordered sequence of coefficients.

5. The coding method of claim 4, wherein, in the step of coefficient coding (E156), non-zero coefficients are coded in the order defined by the ordered sequence.

6. Method for decoding a set of coefficients (W,) participating in a representation of a digital hologram being respectively associated with multiplets each formed by a first parameter spatial, a second spatial parameter, a first frequency parameter and a second frequency parameter, the method comprising the following steps, carried out for at least a pair of respective values ​​of the first frequency parameter and the second frequency parameter: - decoding (E160) of data (D11; D12, D13) indicating positions associated respectively with non-zero coefficients among a set positions associated in a predefined manner with the associated coefficients respectively to the different multiplets comprising said pair of values ​​of the first frequency parameter and the second frequency parameter quantitative; - decoding (E162) of the coefficients associated respectively with the positions indicated by said indicative data.

7. A decoding method according to claim 6, wherein at least one indicative data among said indicative data represents a difference between a position associated with a non-zero coefficient and a another position associated with another non-zero coefficient.

8. A decoding method according to claim 6, wherein said indicative data designates at least one position associated with a co- efficient non-zero without designating at least one other position associated with another non-zero coefficient and indicated by indicative data decoded for another pair of respective values ​​of the first frequency parameter and the second frequency parameter.

9. Device (60) for coding a set of coefficients (W,) participating to a representation of a digital hologram while being respect- tively associated with multiplets each formed by a first spatial parameter, a second spatial parameter, a first parameter frequency and a second frequency parameter, comprising: - a first coding module (62; 64) designed to code, for at least minus a pair of respective values ​​of the first parameter [frequency and the second frequency parameter, data (D11; D12, D13) in- indicative of positions associated respectively with non- coefficients null among a set of predefined associated positions to the coefficients associated respectively with the different multiplets defined by said pair of values ​​of the first frequency parameter and the second frequency parameter; - a second coding module (66) designed to code the coefficients associated respectively with the positions indicated by said data in- indicative.

10. Device (80) for decoding a set of coefficients (W,) by- participating in a representation of a digital hologram while being res- respectively associated with multiplets each formed by a first spatial parameter, a second spatial parameter, a first parameter frequency and a second frequency parameter, comprising: - a first decoding module (84; 86) designed to decode, for at least minus a pair of respective values ​​of the first frequency parameter and the second frequency parameter, data (D11; D12, D13) in- indicative of positions associated respectively with non- coefficients null among a set of predefined associated positions to the coefficients associated respectively with the different multiplets comprising said pair of values ​​of the first frequency parameter and of the second frequency parameter; - a second decoding module (88) designed to decode the coef- ficients associated respectively with the positions indicated by the said indicative data.

11. Data stream representing a set of coefficients (W,) par- participating in a representation of a digital hologram while being res- respectively associated with multiplets each formed by a first spatial parameter, a second spatial parameter, a first parameter frequency and a second frequency parameter, the data stream comprising, for at least one pair of values ​​res- aspects of the first frequency parameter and the second frequency parameter quantitative: - data (D11; D12, D13) indicative of associated positions res- respectively to non-zero coefficients among a set of positions associated in a predefined manner with the associated coefficients res- respectively to the different multiplets defined by said pair of values of the first parameter [frequency and of the second frequency parameter; - data (D14) representative of the associated coefficients respec- tively at the positions indicated by said indicative data.

12. | Computer program comprising instructions designed to implementing a method according to one of claims 1 to 8 when These instructions are executed by a processor.