Method and device for transmitting data representing a digital hologram, method and device for constructing a digital hologram, and system for transmitting and constructing a digital hologram

Abstract

A method for transmitting data representative of a digital hologram (H) comprising the following steps: - determination (E3) of raw values ​​of a group of parameters, said raw values ​​being determined such that a first scalar product between said hologram (H) and a first decomposition wavelet (gγc) characterized by said raw values ​​is maximum; - for each parameter of said group, calculation (E4) of a refinement value as a function of a derivation scalar product determined on the basis of a scalar product between said hologram (H) and a derivative of said first wavelet (gγc) with respect to said parameter; - determination (E6) of a coefficient on the basis of a second scalar product between said hologram (H) and a second decomposition wavelet (gγf) characterized by said refinement values; - transmission (E10): i) of data representative of said refinement values;ii) said coefficient (cK). Figure for the abbreviation: figure 3.;

Description

Title of the invention: Method and device for transmitting data representative of a digital hologram, method and device for constructing a digital hologram and system for transmitting and constructing a digital hologram Technical field of the invention

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

[0002] It relates in particular to a method and a device for transmitting data representative of a hologram. It also relates to a method and a device for constructing a digital hologram. Finally, it relates to a system for transmitting and constructing a digital hologram. State of the art

[0003] It has been proposed to decompose a digital hologram on the basis of a dictionary of decomposition functions comprising a predetermined number of the latter. Each decomposition function is characterized by spatio-frequency parameters whose values ​​are selected from a set of discrete values. When the digital hologram is to be reconstructed by means of a remote holographic display, a representation of the hologram is then transmitted based on at least some of these decomposition functions.

[0004] Conventionally, to reconstruct a digital hologram faithfully, the digital hologram is decomposed on a dictionary comprising a large number of decomposition functions. The denser the dictionary, i.e. the greater the number of functions, the finer the decomposition. This results in the fact that the spatio-frequency parameters are selected from a large number of discrete values. When the dictionary is sufficiently dense, a redundant decomposition can then be obtained which makes it possible not to lose information during transmission.

[0005] It is also known, to obtain a parsimonious decomposition, to use an iterative decomposition method of the matching pursuit type. First, the decomposition function best representing the hologram is determined. Then, a residue of the hologram is calculated by subtracting from the hologram its part represented by the first function. A second decomposition function best representing the residue is determined and so on.

[0006] However, even with sparse decomposition, a dense dictionary results into a computationally time-consuming decomposition since the decomposition requires testing a large number of discrete values ​​at each iteration. The decomposition is also costly in terms of storage space since it is necessary to record all the discrete values ​​that the parameters can take. Finally, the amount of information to be transmitted can be significant when the hologram is decomposed over a large number of functions. Presentation of the invention

[0007] In this context, the invention proposes a method for transmitting data representative of a digital hologram comprising the following steps: - determining raw values ​​of a group of parameters, each raw value being determined from a discrete set of predetermined values, said raw values ​​being determined such that a first scalar product between said hologram and a first decomposition wavelet characterized by said raw values ​​is maximum; - for each parameter of said group, calculation of a refinement value as a function of a scalar product of derivation determined on the basis of a scalar product between said hologram and a derivative of said first wavelet with respect to said parameter; - determining a coefficient on the basis of a second scalar product between said hologram and a second decomposition wavelet characterized by fine values ​​obtained by a combination of said raw values ​​and said refinement values; - transmission: (i) data representative of said refinement values; ii) said coefficient (cK). Thus, thanks to the invention, a digital hologram can be decomposed on the basis of a dictionary comprising a limited number of functions which are here decomposition wavelets. Indeed, during the decomposition, the discrete values ​​determined during the successive iterations are adjusted. Consequently, it is not necessary to start from a large number of discrete values ​​to find the most adequate values, as in the state of the art.

[0008] In other words, calculating refinement values ​​for the parameters characterizing the decomposition functions makes it possible to limit the discrete set of predetermined values.

[0009] When implementing an iterative method, for example with a matching continuation method, the number of discrete values ​​to be tested at each iteration is thus greatly reduced, consequently limiting the computation time and the space of storage required.

[0010] In addition, the digital hologram can be finely decomposed since the refinement values ​​allow an optimization of the decomposition function which is determined at each iteration.

[0011] The amount of information to be transmitted to reconstruct the digital hologram is also reduced. On the one hand, because the decomposition functions accurately represent the hologram once optimized, a limited number of decomposition functions is sufficient. On the other hand, as will be described later, because the transmission of only a part of the data resulting from the decomposition makes it possible to reconstruct the hologram. The amount of information transmitted is then even more reduced.

[0012] Furthermore, the high quality of the spatio-frequency decomposition according to the invention makes it possible to improve numerous functionalities linked to digital holograms such as, for example, the analysis of holographic signals, hologram editing, motion estimation or the generation of dynamic holograms.

[0013] This transmission method can also be used in the case of holographic streaming dependent on the position of an observer: in fact, the refinement step makes it possible to provide more precision on the directions of light emission, and therefore improve the quality of the view reconstructed from a sub-hologram corresponding to the observation window corresponding to the position of the observer.

[0014] Other non-limiting and advantageous characteristics of the transmission method according to the invention, taken individually or in all technically possible combinations, are the following: - said group comprises at least one frequency parameter, said method comprising a step of transmitting, for each frequency parameter, metadata representative of said discrete set of values; - said group comprises at least one frequency parameter, and said data representative of said refinement values ​​comprise, for each frequency parameter, a real part of said scalar product of derivation; - said group comprises at least one spatial parameter, said method comprises a step of transmitting data representative of the raw value of each spatial parameter; - said method comprises a step of quantifying said refinement values, and a step of obtaining said fine values ​​on the basis of said quantified refinement values; - said method comprises a step of transmitting a decision relating to a comparison between the modulus of said first scalar product and the modulus of said second scalar product; - said method comprises the step of encoding said data representative of said refinement values ​​and of said coefficient into a data stream; - said method comprises a step of determining other raw values, characterizing another decomposition wavelet, of the group of parameters, and said data representative of the raw value of each spatial parameter comprise, for each spatial parameter, the raw value or the other raw value and a difference between the raw value and the other raw value.

[0015] The present invention also relates to a device for transmitting a digital hologram comprising: - a decomposition module programmed to perform the following steps: a) determining raw values ​​of a group of parameters, each raw value being determined from a discrete set of predetermined values, said raw values ​​being determined such that a first scalar product between said hologram and a first decomposition wavelet characterized by said raw values ​​is a maximum; b) for each parameter of said group, calculating a refinement value as a function of a scalar product of derivation determined on the basis of a scalar product between said hologram and a derivative of said first wavelet with respect to said parameter; c) determining a coefficient on the basis of a second scalar product between said hologram and a second decomposition wavelet characterized by fine values ​​obtained by a combination of said raw values ​​and said refinement values; - a transmission module designed to transmit: (i) data representative of said refinement values; (ii) the said coefficient.

[0016] The present invention also relates to a method of constructing a digital hologram comprising the following steps: - reception : i) data representative of refinement values ​​of a group of parameters, and ii) a coefficient associated with a decomposition wavelet; - determination of construction values ​​on the basis of said data representative of said refinement values, each construction value being associated with a parameter of said group; - determination of said decomposition wavelet characterized by said construction values; - construction of said hologram by weighting said decomposition wavelet by said coefficient.

[0017] This particularly advantageous method makes it possible to construct a digital hologram from a reduced number of data representative of this hologram. Indeed, it is not necessary to receive all of the data resulting from the decomposition to construct the hologram.

[0018] Other non-limiting and advantageous characteristics of the construction method according to the invention, taken individually or in all technically possible combinations, are the following: - said method comprises, for at least one parameter among the group of parameters, a step of determining, on the basis of said data representative of said refinement values, a raw value relating to this parameter among a discrete set of values; - said method comprises, at least for said parameter, a step of determining said construction value on the basis of said data representative of said refinement values ​​and of said raw value relating to said parameter, said parameter being in particular a frequency parameter; - said method comprises a step of receiving a decision and said decomposition wavelet is also determined on the basis of said decision; - said method comprises a step of decoding said data stream and extracting said data representative of refinement values ​​and of said coefficient; - said method comprises a step of receiving metadata and a step of determining said discrete set of values ​​on the basis of the metadata.

[0019] The present invention also relates to a device for constructing a digital hologram comprising: - a reception module designed to receive: i) data representative of refinement values ​​of a group of parameters, ii) a coefficient associated with a decomposition wavelet; - a decoding module programmed to perform the following steps: a) determining construction values ​​on the basis of said data representative of said refinement values, each construction value being associated with a parameter of said group; b) determining said decomposition wavelet characterized by said construction values; - a construction module programmed to execute the following step: c) construction of said hologram by weighting said decomposition wavelet by said coefficient.

[0020] The present invention finally relates to a system for transmitting and constructing a digital hologram comprising a transmission device as described above and a construction device as described above.

[0021] Other non-limiting and advantageous characteristics of the transmission and construction system according to the invention, taken individually or in all technically possible combinations, are the following: - the transmission device comprises an encoding module programmed to encode said data representative of said refinement values ​​and said coefficient into a data stream; - said reception module receives the data stream comprising said data representative of refinement values ​​and said coefficient, and said decoding module is programmed to decode said data stream and extract said data representative of refinement values ​​and said coefficient.

[0022] 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

[0023] Furthermore, various other characteristics of the invention emerge from the appended description given with reference to the drawings which illustrate non-limiting forms of embodiment of the invention and where:

[0024] [fig. 1] is a schematic representation of a light beam generated by the diffraction of an incident light wave and corresponding to a decomposition wavelet;

[0025] [fig.2] is a schematic representation of a device for transmitting a ho digital logram according to the invention;

[0026] [fig.3] is a block diagram representing a sequence of steps allowing the transmission of data representative of a digital hologram according to the invention;

[0027] [fig.4] is a schematic representation of a device for constructing a ho digital logram according to the invention;

[0028] [fig.5] is a block diagram representing a sequence of steps allowing the construction of a digital hologram according to the invention; and

[0029] [fig.6] is a block diagram representing a sequence of sub-steps of the block diagram of [fig.5].

[0030] We consider in the following a digital hologram H.

[0031] We now describe in a first part, the decomposition of the digital hologram H and the transmission of data representative of the digital hologram H.

[0032] The steps of the transmission method are here implemented by a transmission device 100. As shown in [fig.2], the transmission device 100 comprises a decomposition module 10, a scheduling module 20, an encoding module 30 and a transmission module 40.

[0033] The decomposition module 10 is designed to determine the data representative of the digital hologram H. For this, the decomposition module 10 is based on a dictionary D of decomposition wavelets.

[0034] The ordering module 20 is designed to order the data representative of the digital hologram H.

[0035] The encoding module 30 is designed to encode the data representative of the digital hologram H, here in the order defined by the ordering module 20, into a data stream to be transmitted. The encoding module 30 is also here designed to encode metadata relating to the dictionary D of decomposition wavelets.

[0036] The transmission module 40 is designed to transmit the data stream F prepared by the encoding module 30 over a communication network. As described later, the transmission module 40 here transmits the data stream F over the communication network to a device 200 for constructing a digital hologram H.

[0037] The aforementioned modules 10, 20, 30, 40 can in practice be implemented by the cooperation of at least one hardware element, such as a processor and a communication circuit, in particular for the transmission module 40, and software elements, such as computer program instructions executable by the aforementioned processor.

[0038] These computer program instructions are here recorded on a memory included in the transmission device 100 and to which the processor has access.

[0039] These computer program instructions may in particular be such that the transmission device 100 implements at least part of the steps described below with reference to [fig.3] when these instructions are executed by the processor of the transmission device 100.

[0040] Subsequently, when a module 10, 20, 30, 40 performs an action within the framework of a step of the method, this means that the processor executes the computer program instructions dedicated to carrying out this step or a part of this step. The processor, and therefore the aforementioned modules, are thus programmed to carry out the steps described below with reference to [fig.3].

[0041] [Fig. 3] represents the main steps of the method of transmitting data representative of the digital hologram H.

[0042] Step El

[0043] This method begins at step E1 in which the digital hologram H is selected from a holographic database, for example stored on a server. remote. The digital hologram H is for example received by transmission device 100 from the remote server. The digital hologram H is here recorded on the memory of the transmission device 100. The digital hologram H here consists of a two-dimensional matrix of complex numbers. The digital hologram H here is an uncompressed hologram.

[0044] Step E2

[0045] During a step E2, carried out here in parallel with step E1, a discretized dictionary D of decomposition wavelets is selected from a database, for example recorded on a remote server. The dictionary D is for example received by transmission device 100 from the remote server. Alternatively, the dictionary is pre-recorded in the memory of the transmission device 100.

[0046] As proposed in the article "Color digital hologram compression based on matching pur suit" by A. El Rhammad, P. Gioia, A. Gilles, M. Cagnazzo and B. Pesquet-Popescu in Applied Optics, Vol. 57, No. 17, June 10, 2018, a digital hologram H can be decomposed sparsely on a set of decomposition wavelets. Here, the decomposition wavelets are discretized Gabor gYn wavelets. Gabor wavelets are indeed particularly suitable for the decomposition of digital holograms since they present the best compromise of localization both in the spatial domain and in the frequency domain. As indicated below, the decomposition wavelets can however be other types of wavelets such as Morlet wavelets.

[0047] Each Gabor wavelet gYn, herein generally referenced by the index n, is characterized by a group of parameters, called spatio-frequency parameters. This group of parameters includes spatial translation parameters, called spatial parameters, here a first spatial parameter xn, and a second spatial parameter yn and frequency parameters, here a rotation parameter 0n, a spatial frequency parameter fn, and a dilation parameter on. The Gabor wavelet gYn is defined by the following formula:

[0048] [Math.l] g (x,y) = exp { - ( (x - xnf- + (y - yj2 ) ) exp | 2njf J ( x - xn ) cos ( 6„ ) + ( y - y; ) sin ( dn ) ]}

[0049] As illustrated in [fig.l], a Gabor gyn wavelet thus corresponds to a diffracted light ray R, coming from an incident light wave I, at the level of the point with coordinates (xn, yn) in the plane (xOy) of the digital hologram H and with a direction defined by an azimuth angle equal to the rotation parameter 0n, a diffraction angle <pn, et une dispersion angulaire déterminée par le paramètre de dilatation on.

[0050] The spatio-frequency parameters of the wavelet therefore present a duality with the diffraction parameters of the diffracted light ray R.

[0051] The diffraction angle <pn est donné par la formule <pn=arcsin(X-fn) où X est la longueur d’onde de l’onde de lumière incidente I.

[0052] The spatial parameters here relate to the position of the decomposition wavelet in a holographic plane, that is to say to the position of emergence of the light ray R diffracted by this wavelet. The frequency parameters here relate to the shape and direction of a light ray R diffracted by the decomposition wavelet.

[0053] The discretized dictionary D of decomposition wavelets comprises, for each parameter of the parameter group yn, a discrete set of values.

[0054] For example, when the resolution of the digital hologram H is NxxNy, with Nx and Ny predetermined positive integers, the discrete set of values ​​of the spatial parameters xn, yn is for example all the integer values ​​between 1 and respectively Nx and Ny.

[0055] For the spatial frequency parameter fn, the discrete set of values ​​is for example given by the formula at fn=(tA)1 where A is the distance between 2 adjacent pixels of the digital hologram H and t an integer between 1 and a predetermined integer T.

[0056] For the rotation parameter 0n, the discrete set of values ​​is for example given by the formula 0n=p-(2ir / P) where p is an integer between 0 and a predetermined integer P.

[0057] For the expansion parameter on, the discrete set of values ​​is for example given by the formula on= log(2*log(2) / (jt. rn2 FJ), where rn = a(s) with a an arbitrary linear function and s an integer between 1 and a predetermined integer S.

[0058] For the following, we denote by Nz the number of decomposition wavelets in the discretized dictionary D of decomposition wavelets. The number Nz of wavelets in the dictionary D is given by the product of the number of discrete values ​​for each frequency parameter, i.e. Nz = T*P*S.

[0059] Subsequently, for the frequency parameters, we use an equivalent representation based on the spatial frequency fxn in the x direction and the spatial frequency fyn in the y direction. fxn is calculated according to the formula fxn = fn-cos(0n) and fyn is calculated according to the formula fny = fn-sin(0n). The three frequency parameters are then the dilation on, spatial frequency in the x direction fxn and the spatial frequency in the y direction fyn . The more values ​​the discrete sets include, that is to say, the more decomposition wavelets the dictionary includes, the denser the dictionary is.

[0060] As explained later, thanks to the transmission device 100, it is possible to finely decompose the digital hologram H while using a dictionary D comprising a small number of decomposition wavelets. Use a sparse dictionary D saves storage space and reduces the computation time required to decompose the digital hologram H.

[0061] Here for example, for a digital hologram with a resolution of 4096x4096 each discrete set for the spatial parameters comprises between 1 and 4096 values. In the case where each frequency parameter is discretized on 8 levels, the redundancy of the decomposition is 83=512, and we have Nz=512 decomposition wavelets in the dictionary D.

[0062] The dictionary D here comprises both the analytical functions which define the decomposition wavelets and which are recorded in the memory of the transmission device 100 in the form of computer instructions, and the metadata making it possible to determine the discrete sets of values ​​of the spatio-frequency parameters.

[0063] The operation relating to a particular chromatic component (of wavelength X) of the digital hologram H is described here. The digital hologram H could however in practice comprise other chromatic components, each of the chromatic components then being decomposed and transmitted as described below.

[0064] Furthermore, the embodiment described here uses, as indicated above, a decomposition using Gabor wavelets. However, it would be possible as a variant to use other decompositions, for example using Morlet wavelets, as described for example in the article "Morlet Wavelet transformed holograms for numerical adoptive viewbased reconstruction", by K. Viswanathan, P. Gioia and L. Morin, in Proc. SPIE 9216, Optics and 15 Photonics for Information Processing VIII, August 2014, San Diego, USA.

[0065] We now describe in steps E3 to E8 an iterative decomposition algorithm of the matching pursuit type (better known as “matching pursuit”). We describe here in detail the first iteration of this algorithm.

[0066] Step E3

[0067] Once the digital hologram H and the dictionary D have been selected, during a step E3, the decomposition module 10 determines raw values ​​for the aforementioned group of parameters.

[0068] The raw values ​​of the parameters are here noted with an index c. When considering their raw value, the spatial parameters are then noted xc and yc and the frequency parameters oc, fxc, fyc. When considering the raw values, the parameter group is then noted yc and the Gabor wavelet that they characterize, called the first wavelet, is noted g7C.

[0069] To determine the raw values ​​of the parameters, the decomposition module 10 searches, among all the discrete values ​​contained in the dictionary D, for the values ​​which maximize the modulus of the scalar product between the digital hologram H and the first wavelet gYC. The dot product operator is described in more detail in step E4.

[0070] In practice, the decomposition module 10 performs this scalar product a number of times equal to the number of combinations between the discrete sets of each parameter and selects the scalar product whose modulus is the highest. This scalar product is called the first scalar product.

[0071] The raw values ​​thus define the decomposition wavelet from the dictionary D which is the most representative of the digital hologram H.

[0072] Step E3 is a classic step of an iterative decomposition algorithm of the matching pursuit type.

[0073] Step E4

[0074] Once the raw values ​​xc, yc, oc, fxc, fyc of the parameters have been determined, the decomposition module 10 proceeds to a step E4 of refining these raw values.

[0075] This refinement is based on an optimization of the scalar product between the digital hologram H and the first wavelet gYC. Theoretically, the optimum of this scalar product is determined by searching for the points where the derivatives with respect to each of the parameters cancel out. These points are here called the fine values ​​xf, yf, of, fxf, fyf of the parameters, noted with an index f.

[0076] The following paragraphs describe the mathematical formulas on which the decomposition module 10 is based to calculate the fine values ​​xf, yf, of, fxf, fyf. In the following, the scalar product operator is noted <.,.>. These formulas are here recorded in the memory of the transmission device 100 in the form of computer instructions.

[0077] The fine values ​​xf, yf, of, fxf, fyf of the parameters characterize a second wavelet g Yf. The second wavelet gYf is such that:

[0078] [Math.2] <H, g > = a<g , g >

[0079] where a is a scalar representing the scalar product between the digital hologram H and the second wavelet gYf.

[0080] The analytical formula of the scalar product<gYC,gYf> is as follows:

[0081] [Math.3] <g , g > = ff g (^,y) g (m) dxdy y f K y f

[0082] According to the following equation:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] [Math.4] it is possible to numerically calculate the derivative of the scalar product<H,gYC> in relation to each of the parameters. According to the following equation: [Math.5] < g .g > = Ç < g .g > ' y V, V,: ,f it is possible to theoretically calculate the derivative of the scalar product<gYC,gYf> with respect to each of the parameters by exploiting the analytical formulas of the Gabor wavelets given in step El. In this equation, ^YC is a complex-valued function which depends on the first wavelet gYC and the second wavelet gYf. By applying the derivative operator to the two terms of the equation [Math. 2], we obtain: [Math.6] < H. g > = a < g , g > and therefore, [Math.7] H, g > = a ç < g , g > dYc Yc y \ And so, we get: [Math. 8] We can then deduce refinement formulas linking the raw values ​​to the fine values. For this we use on the one hand the theoretical formula of ^YC given by the equation above and on the other hand the numerical values ​​of the scalar product of the derivatives of<H,gYC> with respect to the parameters. These refinement formulas therefore make it possible to determine the fine values ​​defining the second wavelet. The second wavelet is then such that its scalar product with the digital hologram H is maximum in modulo. The refinement formula for the dilation parameter is:

[0096] [Math.9] <7^. = uc + log ( - 1 +

[0097]

[0098] [Math. 10]

[0099] The formulas for refining the spatial parameters are as follows:

[0100] [Math. 11] 4- (T x — x c + —2-j-

[0101] and

[0102] [Math. 12]

[0103] The refinement formulas for the frequency parameters are as follows:

[0104] [Math. 13]

[0105] and

[0106] [Math. 14]

[0107] The notation R[.] represents the real part and elements in brackets.

[0108] The refinement formulas here involve derivation scalar products D xc, Dyc, Doc, Dfxc, Dfyc. Each derivation scalar product here represents a scalar product between the hologram H and a derivative of the first wavelet with respect to one of the parameters. The refinement formulas thus involve a derivation scalar product Dxc for the first spatial parameter, a derivation scalar product Dxy for the second spatial parameter, a derivation scalar product Doc for the dilation parameter, a derivation scalar product Dfxc for the frequency parameter along x and a derivation scalar product Dfxy for the frequency parameter along y.

[0109]

[0110] The general formula for a differentiating scalar product is: [Math. 15]

[0111] where D,c represents one of the derivative scalar products, where the derivative dyc represents the derivative with respect to one of the parameters, and where gyc represents the first wavelet defined by the raw values ​​xc, yc, oc, fxc, fyc.

[0112] The notations D,c and ^ both represent the scalar product of derivation, however D,c is calculated numerically, while ^yc is calculated theoretically.

[0113] We now describe the sub-steps carried out by the decomposition module 10 during step E4.

[0114] In a first sub-step, the decomposition module 10 numerically calculates the scalar products of derivation Dxc, Dyc, Doc, Dfxc, Dfyc, according to the above formula. To do this, the decomposition module 10 uses for example analytical formulas of the derivatives of the first wavelet with respect to the parameters which are recorded in the memory of the transmission device 100. The decomposition module 10 applies the raw values ​​determined in step E3 to these recorded formulas, then performs the scalar products with the digital hologram H.

[0115] In a second sub-step, the decomposition module 10 calculates, on the basis of the refinement formulas, the fine values. It first calculates the fine value of the dilation parameter. Then, it calculates the fine values ​​of the other two frequency parameters fxf, fyf and of the two spatial parameters xf, yf.

[0116] The decomposition module 10 more specifically calculates the fine values ​​on the basis of the real parts of the scalar products of derivation.

[0117] Thus, as shown in the refinement formulas, for each parameter, the decomposition module 10 determines the fine values ​​by combining the raw values ​​with refinement values. The refinement values ​​are here determined as a function of the real part of the scalar product of derivation associated with the parameter concerned, as visible in the refinement formulas above. The refinement values ​​for the parameters other than the dilation parameter are here also determined as a function of the fine value of the dilation parameter. These refinement values ​​are therefore the terms added to the right of the sum in the refinement formulas, i.e. the terms added to the raw values ​​to calculate the fine values.

[0118] With this step E4, the decomposition module 10 therefore determines the second decomposition wavelet gyf which is generally more representative of the digital hologram H than the first wavelet gyc. Indeed, the determination of the first gYC wavelet is limited by the discrete values, from the dictionary D, that the raw values ​​can take, while the fine values ​​are determined on continuous sets.

[0119] As described previously, this refinement step has several advantages, in particular obtaining fine decompositions, i.e. here of high quality, on the basis of a relatively dense dictionary and thus reducing the calculation time required for the decomposition.

[0120] To accelerate the execution of step E4, the decomposition module 10 can numerically calculate only the scalar products of derivation Dxc, Dyc, Doc for the spatial parameters and for the dilation parameter. Then, it calculates the real parts of the scalar products of derivation Dfxc, Dfyc of the frequency parameters using the following relations:

[0121] [Math. 16]

[0122] and

[0123] [Math. 17]

[0124] The notation ![.] represents the imaginary part of the elements in brackets.

[0125] Step E5

[0126] Remarkably, the decomposition method here comprises, once the decomposition module 10 has calculated the scalar products of derivation, a step of quantification of the fine values ​​and the refinement values.

[0127] During step E5, the quantization module 20 quantifies in particular the real parts of the scalar products of derivation, which are here generally denoted R[Dyc ]•

[0128] Here, during step E4, the fine values ​​are calculated on the basis of the real parts of the quantized scalar products of derivation R[Dyc].

[0129] Step E5 thus constitutes an anticipated quantification, with a view to transmission, of certain data representative of the digital hologram H.

[0130] The applicant has in fact found that quantifying the fine values ​​during their determination in step E4, i.e. during the iterations of the decomposition method of the continuation of the matching type, makes it possible to reduce, i.e. here to compensate as and when, the errors linked to the quantification at each iteration.

[0131] Here, the quantization module 20 implements a Lloyd Max quantizer, for example on 16 levels or on 32 levels.

[0132] Step E6

[0133] Once the decomposition module 10 has calculated the fine values ​​xf, yf, of, fxf, f yf of the parameters, the decomposition module 10 determines a fine coefficient cf on the basis of a second scalar product between the digital hologram H and the second wavelet gYf.

[0134] The decomposition module 10 more specifically calculates the fine coefficient cf as equal to the value of the second scalar product, that is to say according to the formula cf =<H,gYf> .

[0135] Step E7

[0136] Here, during a step E7, the decomposition module 10 also calculates a raw coefficient cc as equal to the value of the scalar product between the digital hologram H and the first wavelet gYC, that is to say according to the formula cc=<H,gYC> .

[0137] The decomposition module 10 then compares the modulus of the raw coefficient cc with the modulus of the fine coefficient cf. The decomposition module 10 therefore compares the second scalar product between the digital hologram H and the second wavelet gYf with the scalar product between the digital hologram H and the first wavelet gYC

[0138] The decomposition module 10 then generates a decision d relating to this comparison. Here, the decision d is equal to 1 when the modulus of the fine coefficient cf is greater than or equal to the modulus of the raw coefficient cc and equal to 0 when the modulus of the fine coefficient cf is less than the modulus of the raw coefficient cc.

[0139] A modulus of a fine coefficient cf greater than a modulus of a raw coefficient cc means that the second wavelet gYf is more representative of the digital hologram H than the first wavelet gYC, and vice versa. In practice, in the majority of cases, the modulus of the fine coefficient cf greater than the modulus of the raw coefficient cc.

[0140] The decomposition module 10 determines a stored coefficient cm and a stored wavelet gYm.

[0141] When the modulus of the fine coefficient cf is greater than or equal to the modulus of the raw coefficient cc, the stored coefficient cm is equal to the fine coefficient cf and the stored wavelet gYm is equal to the second wavelet gYf.

[0142] When the modulus of the fine coefficient cf is less than the modulus of the raw coefficient cc, the stored coefficient cm is equal to the raw coefficient cc and the stored wavelet gYm is equal to the first wavelet gYC.

[0143] The fine coefficient cf, the raw coefficient cc and the stored coefficient cm are here complex numbers.

[0144] The decision d therefore makes it possible to keep in memory which decomposition wavelet, among the first wavelet and the second wavelet, is actually used to decompose the digital hologram H during an iteration.

[0145] Step E8

[0146] The decomposition module 10 then determines a residue r on the basis of the digital hologram H, the stored coefficient cm and the stored wavelet gY m. The residue is here calculated according to the formula r=H-cm-gYm.

[0147] The calculation of the residue r is a classic step in a matching pursuit type algorithm. During the successive iterations of steps E3 to E8, which are not described in detail here, the operations implemented during these steps are carried out on the residue r instead of the digital hologram H and the residue is updated at the end of each step E8.

[0148] For example, for a residue r, the first equation described in step E4 is generalized by the following equation:

[0149] [Math. 18] < r, g > = a < g , g > Yc y Yr \f

[0150] During an iteration K, the residue r is updated according to the following formula: rK+i=rK-c m,K-g7m,K, where cm>K represents the stored coefficient determined during step E7 of iteration K and or gYm>K represents the stored wavelet determined during step E7 of iteration K.

[0151] Here, steps E3 to E8 are iterated a predetermined number of times. Steps E3 to E8 are here iterated L times, L being a positive integer.

[0152] Here, the number of iterations L is determined either by a bit rate criterion or by a quality criterion. With the bit rate criterion, the iterations are stopped when a predetermined maximum bit rate of the stream to be encoded is reached. With the quality criterion, the iterations are stopped when the norm of the residue is smaller than a predetermined threshold value.

[0153] Alternatively, steps E3 to E8 could be iterated a predetermined number of times. Alternatively, steps E3 to E8 could be iterated for a predetermined duration or until the last stored coefficient is less than a predetermined threshold value.

[0154] After having carried out L iterations, the decomposition module 10 has in particular determined the following data which are representative of the digital hologram H: L groups of raw values, L groups of fine values, L stored coefficients and L decisions.

[0155] As explained previously, the implementation in steps E3 to E8 allows a precise decomposition of the digital hologram H even on the basis of a sparse dictionary D. The values ​​of the parameters being refined, this also allows the number of wavelets to be extracted (and therefore the calculation time) to be reduced for a given decomposition quality.

[0156] A method of encoding data representative of the digital hologram H. This method, which is notably implemented by the encoding module 30, is particularly suitable for the decomposition presented above. This method makes it possible to encode and transmit a data stream F containing the minimum information necessary for the construction of the digital hologram H by the construction device 200, also suitable for this decomposition and which is represented in [fig.4].

[0157] Step E9

[0158] Prior to encoding, in order to limit the quantity of data to be transmitted, the scheduling module 20 orders the data representative of the digital hologram H from each iteration according to a line-by-line scanning scheme, better known as “raster scan” scheduling. Here, the scheduling module 20 orders only the data that is encoded and transmitted.

[0159] The scheduling is performed based on the spatial parameters. Then, the scheduling indices resulting from the scheduling are applied to the frequency parameters, coefficients and decisions.

[0160] Since stored wavelets are extracted in descending order of amplitude of scalar products (the most representative wavelet is determined first), encoding the spatial position in this order is very costly. Raster scan scheduling overcomes this by differentially encoding the spatial parameter values. During raster scan, the spatial parameter values ​​corresponding to the first wavelet encountered are encoded. Then, the spatial difference between the second wavelet encountered and the first is encoded, and so on.

[0161] Step E10

[0162] During a step E10, data representative of the hologram H are encoded and transmitted. Step E10 makes it possible to generate a data stream containing sufficient information to construct the digital hologram H. The sufficient information making it possible to construct the digital hologram H is described below.

[0163] First of all, during a sub-step of step E10, the encoding module 30 quantifies the data which are intended to be encoded. Here, the encoding module 30 implements a Lloyd Max quantizer.

[0164] The encoding method is characterized by an encoding rate. The encoding rate is here in particular the sum of a rate for encoding the values ​​of the parameters, a rate for encoding the stored coefficients and a rate for encoding the decisions. The encoding rate here corresponds to a number of bits necessary for the encoding, here binary, of the data.

[0165] In order to reduce the encoding rate of the parameter values, the module encoding 30 encodes, for frequency parameters, only the real parts of the scalar products of derivation. In [fig.3], the groups of values ​​coded for the frequency parameters are represented by the notation {R[Doc], R[Dfxc], R[Dfyc]}K, where the index K corresponds to one of the iterations of the decomposition.

[0166] Indeed, as described in detail in the construction part of the digital hologram H, it is possible, for the frequency parameters, to determine from a triplet of real parts of the scalar products of derivation the triplet of raw values ​​which was used to obtain it during the decomposition and therefore the triplet of fine values ​​associated with this triplet of real parts of the scalar products of derivation.

[0167] The applicant also found that the refinement values ​​of the spatial parameters are negligible compared to the raw values. In other words, the fine values ​​xf, yf of the spatial parameters are substantially equal to the raw values ​​xc, yc.

[0168] Furthermore, the refinement formula of the expansion parameter can be approximated by calculating [3 as follows:

[0169] [Math. 19] cr J - 4^51 [D 1 + 7F\ -ct,.

[0170] The term corresponding to the real parts of the scalar products of derivations of the spatial parameters is in fact negligible compared to the other terms of the denominator.

[0171] This means that the scalar products of derivations of the spatial parameters are not necessary for the construction of the digital hologram H by the construction device 200.

[0172] For the spatial parameters, it is therefore planned here to encode and transmit only the raw values ​​xc, yc.

[0173] Limiting the encoding of the parameter values ​​to the real parts of the scalar products of the frequency parameters R[DOC], R[Dfxc], R[Dfyc] and to the raw values ​​xc, yc for the spatial parameters makes it possible to reduce the bit rate for encoding the parameter values ​​and therefore the encoding bit rate.

[0174] During step E10, the encoding module 30 therefore encodes here into a data stream F: i) the stored coefficients, grouped under the notation Cm>K, ii) positions, grouped under the notation pK, consisting of the raw values ​​of the spatial parameters, and iii) the real parts of the scalar products of derivation for the frequency parameters, grouped under the notation {R[DOC], R[Dfxc], R[Dfyc]]K, iv) decisions, grouped under the notation dK.

[0175] A position p is defined with respect to the raw values ​​xc, yc of the spatial parameters according to the following formula p = (yc-l)*Nx+xc where Nx is the spatial resolution of the digital hologram H along the x direction.

[0176] Thanks to the ordering module 20, the position encoding rate is reduced by encoding the wavelet positions differentially after the raster scan ordering.

[0177] As shown in [fig.3], the encoding module 30 here encodes in the data stream F metadata M representative of the sets of discrete values ​​for the frequency parameters. It is in fact not necessary to transmit metadata representative of the sets of discrete values ​​for the spatial parameters since the raw values ​​of the spatial parameters are transmitted.

[0178] This metadata M includes, for example, the formulas, presented during step E2, making it possible to determine the discrete sets, as well as the analytical formulas of the Gabor wavelets and their derivatives with respect to the parameters.

[0179] Alternatively, the encoding module could not transmit metadata. The construction device receiving the data stream could, for example, be designed to specifically construct decomposed digital holograms based on the dictionary used by the decomposition device.

[0180] Here, the encoding module 30 implements an entropic coding to generate the data stream F. The data stream F is here a sequence of binary elements.

[0181] Then, the transmission module 40 transmits the data stream F, here to the construction device 200. The transmission is carried out by means of a communication network, for example via the internet, via a wired connection or via a wireless connection.

[0182] We now describe in a second part, the construction of the hologram H on the basis of the transmitted data.

[0183] The steps of the construction method are here implemented by the construction device 200, which is here specifically designed to construct the digital hologram H on the basis of the data stream F. As shown in [fig.4], the construction device 200 comprises a reception module 50, a decoding module 60 and a construction module 70.

[0184] The receiving module 50 is designed to receive the data stream F and send it to the decoding module 60.

[0185] The decoding module 60 is designed to decode the data stream F and extract the data representative of the digital hologram H.

[0186] The construction module 70 is designed to construct the digital hologram H on the basis of the representative data of the digital hologram H extracted by the decoding module 60.

[0187] The aforementioned modules 50, 60, 70 of the construction device 200 can in practice be implemented by the cooperation of at least one hardware element, such as a processor and a communication circuit, in particular for the reception module 50, and software elements, such as computer program instructions executable by the aforementioned processor.

[0188] These computer program instructions are here recorded on a memory included in the construction device 200 and to which the processor can have access.

[0189] These computer program instructions may in particular be such that the construction device 200 implements at least part of the steps described below with reference to [fig.5] when these instructions are executed by the processor of the construction device 200.

[0190] Subsequently, when a module 50, 60, 70 of the construction device 200 performs an action within the framework of a step of the method, this means that the processor executes the computer program instructions dedicated to carrying out this step or a part of this step. The processor, and therefore the aforementioned modules, are thus programmed to carry out the steps described below with reference to [fig.5].

[0191] [Fig.5] represents the main stages of the process of constructing the digital hologram H.

[0192] Eli Step

[0193] The construction method begins with a step El 1 during which the reception module 50 receives the data stream F and transmits it to the decoding module 60.

[0194] The decoding module 60 decodes the data representative of the digital hologram H. The decoding module 60 here decodes the data which are encoded in step E10 of the transmission method. As shown in [fig.5], this means here that the decoding module 60 extracts from the data stream F: i) the stored coefficients, (ii) the positions, iii) the real parts of the scalar products of derivation for the frequency parameters, (iv) decisions, and iv) M metadata.

[0195] The data extracted by the decoding module 60 are grouped into packets, one packet containing all the data from a single iteration of the decomposition method. In other words, the decomposition module determines which stored coefficient, position and decision are associated with a given triplet of real parts of the scalar products of derivation for the frequency parameters {R[DOC], R[Dfxc], R[D fyc]} •

[0196] In [fig.5], all terms with the index K come from iteration number K of the decomposition process. Thus, the real parts of the scalar products of derivation for the frequency parameters {R[Doc], R[Dfxc], R[Dfyc]]K are associated with the position pK, the decision dK and the stored coefficient Cm,K.

[0197] Step E12

[0198] Once the data representative of the digital hologram H have been extracted, the decoding module 60 determines from which raw values ​​the real parts of the scalar products of derivation of the frequency parameters are derived.

[0199] For this, the decoding module 60 determines, for each triplet of real parts of the scalar products of derivation for the frequency parameters {R[DOC], R[Dfxc], R[Dfyc]}, the triplet of raw values ​​{oc, fxc, fyc] which served as a basis, during an iteration of step E4 of the decomposition method, for the determination of this triplet of real parts of the scalar products of derivation for the frequency parameters {R[DOC], R[Dfxc], R[Dfyc]}. Since the decomposition was carried out in L iterations, the decoding module 60 therefore determines L triplets of raw values ​​here.

[0200] Here, during a sub-step of step E12, the decoding module 60 determines, on the basis of the metadata M and for each frequency parameter, the discrete set of values ​​from the dictionary D. The decoding module 60 uses for example the formulas presented in step E2 and whose parameters are transmitted via the metadata M.

[0201] Alternatively, the decoding module could be designed to process only digital holograms decomposed on the basis of the dictionary D. The discrete sets could for example be pre-recorded on the memory of the construction device.

[0202] Here we describe in detail how the decomposition module 60 performs step E12, as well as a following step E13, for a triplet of real parts of the scalar products of derivation for the frequency parameters {R[DOC], R[Dfxc], R[Dfyc]}K resulting from iteration K, among the L iterations, of the decomposition method. In practice, the decomposition module 60 performs steps E12 and E13 for all the triplets, that is to say for the L triplets, of real parts of the scalar products of derivation for the frequency parameters.

[0203] The decoding module 60 first determines a triplet of raw values ​​associated with this triplet of real parts of the scalar products of derivation for the frequency parameters {R[DOC], R[Dfxc], R[Dfyc]]K.

[0204] For this, as shown in [fig.6], the decomposition module 60 iteratively tests all the triplets of raw values ​​which can be defined on the basis of the discrete sets of values. The decomposition module 60 therefore tests in a iterative Nz triplets of raw values ​​that correspond to all the composition wavelets initially contained in the dictionary D.

[0205] Here, all these triplets of raw values ​​are determined on the basis of the metadata M. The decomposition module 60 thus considers one triplet of raw values ​​per test. [fig.6] represents the set of tests carried out for a triplet of real parts of the scalar products of derivation for the frequency parameters {R[Doc], R[Dfxc], R[Dfyc]]K.

[0206] During a first sub-step E50 of step E12, the decomposition module 60 determines, on the basis of the triplet of raw values ​​considered and the scalar products of derivation for the frequency parameters, test values ​​ot> fxt> fyt.

[0207] The decomposition module 60 first calculates, on the basis of the raw value considered for the expansion parameter and the scalar products of derivation for the frequency parameters, a test value for the expansion parameter ot. It calculates this test value for the expansion parameter ot in accordance with the refinement formula presented in step E4 and the approximate formula of [3 presented in step E10.

[0208] The decomposition module 60 then calculates, on the basis of the raw value considered for the spatial frequency parameter along the x direction, the test value for the dilation parameter ot and the scalar products of derivation for the frequency parameters, a test value fxt for the spatial frequency parameter along the x direction. It calculates this test value fxt for the spatial frequency parameter along the x direction in accordance with the refinement formula presented in step E4.

[0209] The decomposition module 60 finally calculates a test value fyt for the spatial frequency parameter along the y direction in the same way as for the spatial frequency parameter along the x direction.

[0210] Then, during a second sub-step E51 of step E12, the decomposition module 60 checks whether the calculated test value triplet {ot, fxt, fyt] verifies the following verification equations:

[0211] [Math.20]

[0212] And

[0213] [Math.21] '2æ / &,f + o c f 1 'cy

[0214] In the two verification equations above, the terms oc> fxc and fxy represent the raw values ​​considered during this test.

[0215] In a first case, when the triplet of raw values ​​considered does not verify the two equations above, the decoding module 60 tests another triplet of raw values. In [fig.6], this first case is represented by the arrow going from step E51 to step E50.

[0216] In a second case, when the triplet of raw values ​​considered verifies the two equations above, the decoding module 60 evaluates that the triplet of raw values ​​considered {oc, fxc, fyc]K is the one from which the triplet of real parts of the scalar products of derivation for the frequency parameters {R[DOC], R[Dfxc], R[Dfyc]]K is derived.

[0217] In this second case, the decoding module 60 ends its iterative test for this triplet of real parts of the scalar products of derivation for the frequency parameters {R[DOC], R[Dfxc], R[Dfyc]]K.

[0218] In this second case, the decoding module 60 retains this triplet of raw values ​​considered {oc, fxc, fyc]K for step E13. In [fig.6], this second case is represented by the arrow going from step E50 to step E13.

[0219] When no calculated test value triplet {ot,fxt,fyt} verifies the verification equations, the considered raw value triplet {oc, fxc, fyc]K which is kept for step E13 is the one which best verifies the verification equations, i.e. the one for which the differences between the members of the equalities are the smallest.

[0220] Step E13

[0221] Once the triplet of raw values ​​considered {oc, fxc, fyc]K has been determined, during a step El3, the decoding module 60 determines a third decomposition wavelet gyK called construction wavelet. This wavelet is characterized by a group yK of construction values ​​xK, yK, oK, fxK, fyK ​​attributed to the spatial and frequency parameters.

[0222] For this, the decoding module 60 here takes into account the decision dK associated with this triplet of real parts of the scalar products of derivation for the frequency parameters {R[DOC], R[Dfxc], R[Dfyc]]K.

[0223] When the decision dK indicates that the wavelet stored during iteration number K of the decomposition method is the second wavelet characterized by the fine values, that is to say here when the decision dK is equal to 1, the decoding module 60 determines the construction values ​​oK, fxK, fyK ​​of the frequency parameters as equal test values ​​{ot, fxt, fyOK which have verified the verification equations in step E12. This triplet of test values ​​{ot, fxt, fyt]K is the one which comes from the triplet of raw values ​​considered {oc, fxc, fyc]K determined in step El2. In other words, the decoding module 60 finds the fine values ​​of the frequency parameters resulting from iteration K of the decomposition method and characterizes the construction wavelet gyK on the basis of these fine values.

[0224] This means that, when the decision dK indicates that the wavelet stored during iteration number K of the decomposition method is the second wavelet characterized by the fine values, for the frequency parameters, the construction values ​​oK, fx K, fyK ​​for the triplet of real parts of the scalar products of derivation for the frequency parameters {R[DOC], R[Dfxc], R[Dfyc]]K are then substantially equal to the fine values ​​of, fxf, fyf resulting from iteration K. Here, by "substantially equal" we mean that these values ​​are equal to the approximation on the parameter [3 described previously.

[0225] When the decision dK indicates that the wavelet stored during iteration number K of the decomposition method is the first wavelet characterized by the raw values, that is to say here when the decision dK is equal to 0, the decoding module 60 determines the construction values ​​oK, fXK, fyK ​​as equal to the triplet of raw values ​​considered {oc, fxc, fyc]K determined in step El2. In other words, the decoding module 60 then uses the raw values ​​of the frequency parameters resulting from iteration K of the decomposition method and characterizes the construction wavelet gyK on the basis of these raw values.

[0226] Regardless of the decision dK, the decoding module 60 determines the construction values ​​xK, yK of the spatial parameters based on the position pK. Here, the construction values ​​xK, yK of the spatial parameters are more specifically equal to the position pK. This means that the decoding module 60 uses the raw values ​​of the spatial parameters, determined during the decomposition, to characterize the construction wavelet gyK.

[0227] Once steps E12 and E13 have been applied to all the triplets of real parts of the scalar products of derivation for the frequency parameters {R[DOC], R[Dfxc], R[D fyJÎK, i.e. here applied L times, the decoding module 60 has therefore determined L construction wavelets gyK.

[0228] Step E14

[0229] Once determined, the construction wavelets gyK are sent to the construction module 70.

[0230] During a step El4, the construction module 70 calculates the digital hologram H by summing the contribution of the different construction wavelets weighted by their associated stored coefficient. The stored coefficient associated with a wavelet of construction is the one associated with the triplet of real parts of the scalar products of derivation for the frequency parameters and the decision which were used to determine the construction wavelet.

[0231] The construction module 70 thus determines the digital hologram H by performing the sum Scm>K-gYK for K ranging from 1 to L, that is to say for the L construction wavelets. The construction module 70 therefore constructs the digital hologram H by performing the sum of the construction wavelets gyK weighted by their associated stored coefficient cm>K.

[0232] As shown in [fig.4], the construction device 200 here comprises a display module 80 designed to display the hologram H constructed as indicated above by the construction module 70.

[0233] The display module 80 comprises, for example, a spatial light modulator, or SLM for “Spatial Light Modulator”, which is possibly integrated into a head-mounted display, for example an augmented reality head-mounted display.

Claims

Claims

1. Method for transmitting data representative of a digital hologram (H) comprising the following steps: - determining (E3) raw values ​​of a group of parameters, each raw value being determined from a discrete set of predetermined values, said raw values ​​being determined such that a first scalar product between said hologram (H) and a first decomposition wavelet (gYC) characterized by said raw values ​​is maximum; - for each parameter of said group, calculating (E4) a refinement value as a function of a derivation scalar product determined on the basis of a scalar product between said hologram (H) and a derivative of said first wavelet (gYC) with respect to said parameter;- determination (E6) of a coefficient on the basis of a second scalar product between said hologram (H) and a second decomposition wavelet (gYf) characterized by fine values ​​obtained by a combination of said raw values ​​and said refinement values; - transmission (E10): i) of data representative of said refinement values; ii) of said coefficient (cK).;

2. Transmission method according to claim 1, wherein said group comprises at least one frequency parameter, said method comprising a step of transmitting (E10), for each frequency parameter, metadata (M) representative of said discrete set of values.

3. Transmission method according to one of claims 1 to 2, in which said group comprises at least one frequency parameter, and in which said data representative of said refinement values ​​comprise, for each frequency parameter, a real part of said scalar product of derivation ({R[DOC], R[Dfxc], R[Dfyc]}K).

4. Transmission method according to one of claims 1 to 3, said group comprises at least one spatial parameter, said method comprising a step of transmitting (E10) data representative of the raw value of each spatial parameter.

5. Transmission method according to one of claims 1 to 4, comprising a step of quantifying (E5) said refinement values, and a step of obtaining said fine values ​​on the basis of said quantified refinement values.

6. Transmission method according to one of claims 1 to 5, comprising a step of transmitting (E10) a decision (dK) relating to a comparison (E7) between the modulus of said first scalar product and the modulus of said second scalar product.

7. Transmission method according to one of claims 1 to 6 comprising a step of encoding said data representative of said refinement values ​​and said coefficient (cK) into a data stream (F).

8. Device (100) for transmitting a digital hologram (H) comprising: - a decomposition module (10) programmed to execute the following steps: a) determination (E3) of raw values ​​of a group of parameters, each raw value being determined from a discrete set of predetermined values, said raw values ​​being determined such that a first scalar product between said hologram and a first decomposition wavelet (gYC) characterized by said raw values ​​is maximum; b) for each parameter of said group, calculation (E4) of a refinement value as a function of a derivation scalar product determined on the basis of a scalar product between said hologram (H) and a derivative of said first wavelet (gYC) with respect to said parameter;c) determining (E6) a coefficient on the basis of a second scalar product between said hologram (H) and a second decomposition wavelet (gYf) characterized by fine values ​​obtained by a combination of said raw values ​​and said refinement values; - a transmission module (40) designed to transmit: i) data representative of said refinement values; ii) said coefficient (cK).;

9. Method for constructing a digital hologram (H) comprising the following steps: - reception (Eli): i) of data representative of refinement values ​​({R[DOC], R[Dfxc ], R[Dfyc]}K) of a group of parameters, and ii) of a coefficient (cm>K) associated with a decomposition wavelet; - determination (E13) of construction values ​​(oK, fXK, fyx) on the basis of said data representative of said refinement values ​​({R[DOC ], R[Dfxc], R[Dfyc]]K), each construction value (oK, fxK, fyK) being associated with a parameter of said group; - determination (E13) of said decomposition wavelet (gyK) characterized by said construction values ​​(oK, fxK, fyK); - construction (El4) of said hologram (H) by weighting said decomposition wavelet (gyK) by said coefficient (cm>K).

10. Method according to claim 9, comprising, for at least one parameter among the group of parameters, a step of determining (E12), on the basis of said data representative of said refinement values ​​({R[DOC], R[Dfxc], R[Dfyc]]K), a raw value ({oc, fxc,fyc] K) relating to this parameter among a discrete set of values.

11. Method according to claim 10, comprising, at least for said parameter, a step (El3) of determining said construction value ({ot, fxt, fyt}K) on the basis of said data representative of said refinement values ​​({R[DOC], R[Dfxc], R[Dfyc]]K) and of said raw value ({oc, fxc, fyc]K) relating to said parameter.

12. Method according to one of claims 9 to 11, comprising a step of receiving (Eli) a decision (dK) and in which said decomposition wavelet (gyK) is also determined on the basis of said decision (dK

13. )■ Method according to one of claims 9 to 12, comprising a step of decoding said data stream (F) and extracting said data representative of refinement values ​​({R[DOC], R[Dfxc], R[Dfyc]]K) and of said coefficient (cm>K).

14. Method according to one of claims 9 to 13, comprising a step of receiving (El 1) metadata (M) and a step of determining (E12) said discrete set of values ​​on the basis of the metadata (M).

15. Device (200) for constructing a digital hologram (H) comprising: - a reception module (50) designed to receive: i) data representative of refinement values ​​({R[DOC], R[Dfxc ], R[Dfyc]]K) of a group of parameters, ii) a coefficient (cm>K) associated with a decomposition wavelet; - a decoding module (60) programmed to execute the following steps: a) determination (E13) of construction values ​​(oK, fxK, fyK) on the basis of said data representative of said refinement values ({R[DOC], R[Dfxc], R[Dfyc]]K), each construction value (oK, fxK, fyj being associated with a parameter of said group; b) determination (E13) of said decomposition wavelet (gyK) characterized by said construction values ​​(oK, fxK, fyK); - a construction module (70) programmed to execute the following step: c) construction (El4) of said hologram (H) by weighting said decomposition wavelet (gyK) by said coefficient (cm>K).

16. A system for transmitting and constructing a digital hologram (H) comprising a transmitting device (100) according to claim 8 and a constructing device (200) according to claim 15.

17. System according to claim 16, wherein the transmission device (100) comprises an encoding module (30) programmed to encode said data representative of said refinement values ​​and said coefficient into a data stream (F).

18. System according to claim 17, wherein said reception module (200) receives the data stream (F) comprising said data representative of refinement values ​​and said coefficient, and wherein said decoding module (60) is programmed to decode said data stream (F) and extract said data representative of refinement values ​​({R[DOC], R[Dfxc], R[Dfyc]]K) and said coefficient (cm>K).

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