Method for obtaining a high-resolution image of a sample
Patent Information
- Application Number
- FR2023009082
- Authority / Receiving Office
- FR · FR
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2023-08-30
- Publication Date
- 2025-03-07
Smart Images
Figure 00000000_0000_ABST
Abstract
Description
Title of the invention: Method for obtaining a high-resolution image of a sample Technical field of the invention
[0001] The present invention relates generally to the field of microscopy.
[0002] It relates more particularly to a method for obtaining a high-resolution image of a sample.
[0003] It also relates to an imaging device suitable for implementing this method.
[0004] The invention finds a particularly advantageous application in the production of optical devices making it possible to exceed the diffraction limit. State of the art
[0005] Microscopy, particularly fluorescence microscopy, is a major tool in cell biology. However, its resolution is limited by diffraction to approximately 300 nm in the visible spectrum, which is often insufficient for the study of biological macromolecules. Over the last two decades, several super-resolution fluorescence imaging techniques have been developed to overcome the diffraction limit, including stimulated emission microscopy (STED), single-molecule localization microscopy (STORM or PALM), structured illumination microscopy (known by the English acronym SIM for "Structured Illumination Microscopy") or scanning microscopy (known by the English acronym ISM for "Image Scanning Microscopy").Each of these techniques has drawbacks that limit their applicability, particularly for the observation of living organisms, since their intense lighting or prolonged acquisition time is harmful to living cells. In addition, the difficulty of their implementation makes their use dependent on the supervision of specialized experts.
[0006] SIM and ISM technologies are currently the most widely deployed technologies for high spatial and temporal resolution imaging of living organisms. A SIM or ISM image, which can be described as super-resolved, is digitally formed from several low-resolution images obtained for different positions and orientations of a harmonic or other illumination, such as a light grid, relative to the sample (the object to be imaged).
[0007] Thus, the digital reconstruction of SIM or ISM images is based on precise knowledge of the illuminations (structure, position, orientation). SIM or ISM technology therefore requires careful calibration of the system and rigorous control of the illuminations on the sample. In addition, aberrations caused by the sample itself can distort the illuminations, which then distorts the reconstruction of the image.
[0008] Recently, it has been proposed to replace deterministic illuminations with uncontrolled random (i.e. totally random) illuminations. This technique is commonly called RIM after the English acronym "Random Illumination Microscopy". The main limitation of the RIM technique lies in the high number of illuminations and therefore low-resolution images (more than a hundred) necessary for a correct reconstruction. Indeed, the reconstruction algorithm requires determining, or at least approaching, the asymptotic covariance of the random illuminations (i.e. the covariance obtained for an infinite number of illuminations). However, the covariance obtained with a finite number of random illuminations slowly converges towards its asymptotic value. This high number of images, although it contributes to the robustness of the method, limits the capabilities of the RIM technique for high temporal resolution imaging. Presentation of the invention
[0009] In this context, the present invention provides a method for obtaining a high-resolution image of a sample comprising the following steps: a) generating a sequence of successive pseudo-random illuminations, an empirical statistical property of the sequence having a predetermined value, b) exposing the sample to the sequence of pseudo-random illuminations, c) acquiring a plurality of low-resolution images of the sample by an image capture device, each low-resolution image being acquired while the sample is exposed to one of said pseudo-random illuminations of the sequence, d) calculating a measured value of an empirical statistical property of the plurality of low-resolution images, e) determining, on the basis of the predetermined value of the empirical statistical property of the pseudo-random illumination sequence, a model of the empirical statistical property of the plurality of low-resolution images, f) determining the high-resolution image by minimizing, by model fitting, a deviation between the model of the empirical statistical property of the plurality of low-resolution images and the measured value of the empirical statistical property of the plurality of low-resolution images.
[0010] The following definitions allow the meaning of several basic concepts of the invention to be understood.
[0011] An empirical moment w] of a sequence of M elements (the elements, called um with m=l...M, are data for example in the form of tables, and re- present for example images of a sample recorded for M different illuminations or directly the intensity of the M different illuminations at any point of the sample) associated with an operator Q (which is a function acting on the elements um) corresponds to the average over all the elements um of the sequence Q(um) and is therefore given by the formula:
[0012] [Math.l] Im
[0013] The term empirical here means that an average is taken over a finite number of elements. It differs from the term asymptotic which indicates an average over an infinite number of elements (see below). An empirical statistical property is an empirical moment or a combination of empirical moments involving different operators, such as the operator Q above. An empirical statistical property is for example the empirical variance, empirical covariance. As illustrated later, since the statistical property is defined by a sum (cf. (Math. 1]) it is not necessary to know each illumination individually.
[0014] An asymptotic moment, or asymptotic statistical property, is defined as the limit as M tends to infinity of the associated empirical moment or of the associated empirical statistical property. It is then assumed that the sequence of the M elements is obtained by a random drawing process following a certain probability law.
[0015] A pseudo-random sequence of illuminations corresponds to illuminations for which an empirical statistical property (for example, the empirical covariance) is known. Remarkably, estimating certain empirical moments of a sequence of illuminations does not require knowledge of each illumination. However, when the illuminations are known individually, their empirical moments are known. A sequence of known deterministic illuminations therefore constitutes a sequence of pseudo-random illuminations.
[0016] A sequence of random, or totally random, illuminations corresponds to illuminations for which only one or more asymptotic statistical properties (and no longer empirical) are known. The M illuminations are therefore considered to come from M random draws according to a certain probability law. A particular random illumination sequence is, for example, that of fully developed speckle. The illuminations can be written as a sum of plane waves (thus verifying the wave equation) having complex amplitudes according to a circular Gaussian probability law. This type of field is, for example, obtained at the output of a diffusing medium crossed by a laser beam, as described in "Speckle phenomena in optics: theory and applications", Goodman, Joseph W, 2007, Roberts and Company Publishers.
[0017] Thus, thanks to the invention, a high-resolution, or even super-resolved, image of the sample (the resolution of which is higher than the diffraction limit) can be obtained quickly and simply. The method according to the invention is thus well suited to the temporal resolution of life sciences.
[0018] The invention proposes an improvement to the RIM technique in which the totally random illuminations are replaced by a sequence of pseudo-random illuminations. The use of a sequence of pseudo-random illuminations for which an empirical statistical property is known makes it possible to significantly reduce the number of low-resolution images required for the reconstruction of the high-resolution image compared to the RIM technique. Indeed, in the latter, random illuminations are used for which only asymptotic statistical properties are known. A large number of illuminations is then necessary for the empirical statistical properties calculated with a finite number of illuminations to approach the asymptotic statistical properties.The method according to the invention makes it possible to reduce the number of low-resolution images to be acquired to a few dozen, whereas more than two hundred images are conventionally necessary in the RIM technique. Thus, the invention does not require precise knowledge of the illuminations, but only knowledge of at least one empirical statistical property of the illumination sequence.
[0019] Compared to SIM or ISM techniques which require precise knowledge of each illumination (typically knowledge of the intensity distribution or the square of the intensity) to form the super-resolved image, the method according to the invention is much more robust to aberration and diffusion phenomena. Indeed, the latter affect the empirical statistical properties of the illuminations less than the illuminations themselves. The robustness of the invention to aberrations facilitates, for example, the in-depth imaging of fluorescent objects.
[0020] Advantageously, the method according to the invention is easily adapted to the usual optical configurations in microscopy. More generally, the present method applies to numerous optical imaging modalities: fluorescence (the illumination is then proportional to the intensity of the light), diffraction microscopy (the illumination is then proportional to the electric field), non-linear optical imaging (the illumination then depends in a non-linear manner on the electric field) or acoustic imaging (the illumination is then proportional to the pressure field).
[0021] Advantageously, the invention can be applied to all existing fluorescence microscopes in which the sample is illuminated successively under various illuminations (SIM, ISM, spinning disk). Indeed, it is easy to determine the empirical statistical properties of the deterministic illumination sequences used in all these techniques in order to apply the reconstruction method according to the invention. The invention makes it possible to improve the resolution as well as the optical sectioning of these techniques and it makes it possible to improve the robustness to aberrations and misalignments as described above. The invention is compatible with single-objective and multi-objective configurations, in single-photon or two-photon regime. The method according to the invention also works for all wavelengths.
[0022] Optionally and advantageously, said sequence of pseudorandom illuminations is optimized so as to obtain empirical statistical properties close to the asymptotic statistical properties of fully developed speckle-type random illuminations. In a particular implementation of the invention, the reconstruction is based on the empirical variance and covariance of the illuminations. In this particular implementation, it is interesting to obtain a uniform empirical mean and variance over the entire sample and an empirical covariance depending only on the distance between the two points. An algorithm for optimizing such a sequence is proposed in the detailed invention.
[0023] Other advantageous and non-limiting characteristics of the method according to the invention, taken individually or in all technically possible combinations, are the following: - the model of the empirical statistical property of the plurality of low-resolution images is also based on a point spread function; - the empirical statistical property of the sequence and the empirical statistical property of the plurality of low-resolution images comprise at least one of the following or a combination of at least two of the following: mean, variance, covariance, spatial correlation, standard deviation, kurtosis; - in step f), the deviation is calculated as a difference between a theoretical value, obtained using the model, of the statistical property of the low-resolution images and the measured value of the statistical property of the plurality of low-resolution images; - each pseudo-random illumination of said sequence of pseudo-random illuminations comprises a light beam having a spatial intensity distribution, all of the spatial intensity distributions of the illuminations of said sequence being generated in a pseudo-random or deterministic manner; - said sequence of pseudo-random illuminations comprises a sequence of pseudo-random speckle images or a sequence of periodic patterns or a sequence of single or multiple focus spot type patterns; - the illuminations of said pseudo-random sequence of illuminations are determined so that the covariance of the pseudo-random sequence of illuminations is a circulant matrix; - said sequence of pseudo-random illuminations is optimized so as to increase the uniformity of its variance, while maximizing the entropy of the illumination; - said sequence of pseudo-random illuminations optimized so as to increase the uniformity of its variance is obtained by an iterative method comprising the following steps: (h) recording an initial sequence of pseudo-random illuminations having an initial variance value and associated with an initial value of a global parameter representing the uniformity of the variance and the entropy of the sequence of pseudo-random illuminations, (i) determining a provisional sequence of pseudo-random illuminations by randomly modifying at least one illumination of a previously recorded sequence, j) calculation of a provisional value of the variance of the provisional sequence and a provisional value of the global parameter, k) comparison of the provisional value of the global parameter with a previously recorded value of the global parameter, 1) recording the provisional sequence and the provisional value of the global parameter in place of the previously recorded sequence and the previously recorded value of the global parameter, when this comparison indicates that the provisional value of the global parameter is greater than the previously recorded value of the global parameter, potentially, m) repeating steps h) to 1); - the deviation is calculated as a Kullback Leibler statistical distance, a [3-divergence or a difference of squares; - the minimization of the gap is carried out using a conjugate gradient type minimization algorithm; - each illumination of said sequence of pseudo-random illuminations is generated by interference of controlled phase plane waves or by means of a spatial light modulator imposing a spatial intensity distribution, all of the spatial intensity distributions of the illuminations of said sequence being generated in a pseudo-random manner; - the images are acquired by a fluorescence imaging device, white light transmission imaging or acoustic transmission imaging; - each low-resolution image is composed of a pixel matrix and wherein each step d), e) and f) is performed for each pixel or for one or more predetermined groups of pixels of each low-resolution image.
[0024] The invention also proposes a device comprising: - a generator of a sequence of successive pseudo-random illuminations, an empirical statistical property of the sequence having a predetermined value, - a sample support, - an image capture device adapted to capture a plurality of low-resolution images of the sample exposed to one of said pseudo-random illuminations of said sequence, - one or more processors programmed to: - calculating a measured value of an empirical statistical property of the plurality of low-resolution images, - determining, on the basis of the predetermined value of the empirical statistical property of the pseudo-random illumination sequence, a model of the empirical statistical property of the plurality of low-resolution images, - determining a high-resolution image by minimizing, by adjusting the model, the deviation between the model of the empirical statistical property of the plurality of low-resolution images and the measured value of the empirical statistical property of the plurality of low-resolution images.
[0025] The invention thus proposes an optical assembly particularly suited to the generation of illuminations whose statistical property is controlled. This assembly is advantageously simpler to implement. In addition, the illumination generator can be easily adapted to conventional optical microscopes.
[0026] 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
[0027] The description which follows with reference to the appended drawings, given as non-limiting examples, will make it clear what the invention consists of and how it can be implemented.
[0028] In the attached drawings:
[0029] [Fig. 1] is a schematic representation of a first embodiment of an imaging device according to the invention.
[0030] [Fig.2] is a schematic representation of an alternative of the device of the [Fig.l] showing an intermediate Fourier plane.
[0031] [Fig.3] is a schematic representation of a second embodiment of a imaging device according to the invention.
[0032] [Fig.4] is a block diagram of a sequence of steps for obtaining an image high resolution of a sample.
[0033] [Fig.5] is a timing diagram representing the synchronization of the states of several elements of the device of [Fig.l], and of the device of [Fig.3], as a function of time (t).
[0034] [Fig.6] is a block diagram of a sequence of steps for optimizing the pseudo-random illumination sequence intended to obtain the high-resolution image of the sample.
[0035] [Fig.7] is a representation of several views characterizing an example of a sequence of pseudo-random illuminations.
[0036] [Fig.8] is a representation of the views characterizing another example of a sequence of pseudo-random illuminations.
[0037] [Fig.9] is a comparison of images of the same sample obtained by a process conventional (left) and by a method according to the invention (right).
[0038] [Fig. 10] is a graphical representation of two intensity profiles from the images of [Fig.9] on corresponding segments.
[0039] An imaging device 1 according to the invention is shown in Figures 1 and 4. A first embodiment of the imaging device 1 is shown in [Fig.l] while a second embodiment of the imaging device 1 is shown in [Fig.3]. Corresponding or identical elements of each embodiment of the invention will be identified by the same reference signs, and will not be described in detail each time.
[0040] The imaging device 1 (and the method it implements, presented later) is described here in the context of optical fluorescence imaging. The invention is however in no way limited to this specific type of imaging.
[0041] The first embodiment is first described, in particular with reference to [Fig. 1]. As shown in this figure, the imaging device 1 comprises: - a generator 10 of pseudo-random illumination sequences; - a sample support 20; - a set of optical elements 30 arranged to expose the sample 2 to the pseudo-random illuminations produced by the generator 10; - an image capture device 40; - at least one 50 processor; - a 60 synchronization unit.
[0042] Sample 2 is here thin in the sense that its thickness (depending on the direction of propagation of the light illuminating it, from left to right in [Fig.l]) is significantly less than its width and its length. For example, sample 2 is a slice or section of a biological tissue or an inert material such as a polymer or metallic material.
[0043] The support 20 is adapted to receive the sample 2. Here, the support 20 more specifically comprises a plate 21 extending along an extension plane (here perpen dicular the direction of propagation of the light at the level of the support). The sample 2 is arranged on the plate 21. In addition, the support 20 is also adapted to move the sample 2. For this purpose, the support 20 comprises actuators 22, for example piezoelectric, adapted to move the plate 21 in its extension plane.
[0044] The generator 10 comprises in particular a light source 11 and a modulator 12. Here, the light source 11 comprises a plurality of laser sources 13, for example laser diodes, operating at distinct wavelengths. The five laser sources 13 shown in [Fig. 1] emit for example laser beams at 633 nm, 561 nm, 488 nm, 445 nm, 405 nm. The laser beams are combined using beam-combining dichroic mirrors 14. Alternatively, the light source may comprise a single laser source (as shown in [Fig. 2]) or another light source such as a lamp.
[0045] The light source 11 thus produces a light beam, here coherent, which is transmitted to the modulator 12. This light beam is called the source beam and is referenced FS in [Fig.l]. The source beam FS arrives at the input of the modulator 12.
[0046] The modulator 12 is adapted to modify, in a time-varying manner, the intensity and / or the phase of the source beam FS to generate the pseudo-random illuminations. The modulator 12 more specifically produces a light beam called a modulated beam and referenced FM in [Fig.l]. The modulated beam FM thus transports the pseudo-random illuminations to the sample 2.
[0047] For the purposes of the invention, “illumination” means a wave suitable for exciting the sample 2, i.e., for interacting with it, such as an electromagnetic wave or a pressure wave. In the context of the imaging device 1 shown in FIGS. 1 and 4, “illumination” denotes the spatial distribution of the intensity (or the square of the intensity) of the modulated beam M, which is an electromagnetic wave, emitted by the modulator 12 and conveyed to the sample 2 by the set of optical elements 30. From a mathematical point of view, each illumination can, for example, be written as a sum of plane waves (satisfying the wave equation) having complex amplitudes following a circular Gaussian probability law. For example, the pseudo-random illuminations are speckles, i.e., speckle-type patterns.
[0048] The modulator 12 therefore has the role of temporally and spatially modulating the source beam FS. In other words, the intensity of the modulated beam FM evolves temporally, thanks to the modulator 12, to form, at different times, different pseudo-random illuminations.
[0049] We will now describe the modulator 12 for obtaining this modulation. Here, as shown in [Fig.2], the modulator 12 is a spatial light modulator (better known as a “spatial light modulator” or SLM). The modulator 12 is more specifically a phase modulator comprising a matrix of pixels whose phase can be electronically controlled, which makes it possible to control the phase of the signal reflected by each pixel. Here, each pixel can take a phase value between 0 and 2Pi. The pixels are for example nematic pixels. The modulator 12 is then for example a liquid crystal screen. Alternatively, the modulator is an amplitude modulator whose pixels can have a transmission value ranging for example from 0% to 100%.
[0050] To generate pseudo-random illumination, each pixel of the modulator is assigned a phase (or transmission) value. The modulator 12 can be programmed in itself to operate in a pseudo-random manner or can be controlled by the processor 50. The modulator 12 comprises, for example, a random number generator with uniform probability between 0 and 2 Pi.
[0051] The pixel matrix thus forms a mask crossed by the source light beam FS, which forms at the output of the modulator 12 (and therefore of the generator 10) the modulated beam FM and therefore the pseudo-random illuminations. Each pseudo-random illumination produced by the generator 10 is thus associated with a specific state of the modulator 12, i.e. with a particular distribution of the reflection or transmission values of the pixels. The modulator 12 comprises for example a matrix of 2048 by 1536 pixels and has a diagonal of 21,082 pm.
[0052] Alternatively, the pseudo-random illuminations may be different from speckles. For example, the illuminations of a sequence may correspond to grids of light, produced by interferences of controlled phase plane waves, which are translated and / or rotated relative to each other.
[0053] Alternatively, the modulator may be a multimode optical fiber or a diffusing medium combined with a piezoelectric actuator.
[0054] The pseudo-random illuminations produced by the generator 10 are then projected onto the sample 2 by means of the set of optical elements 30. In the example of [Fig.l], the set of optical elements 30 comprises lenses, in particular at least one lens included in a microscope objective 31.
[0055] Here, the set of optical elements 30 comprises a second lens 32 which is for example a 350 mm tube lens or an apochromatic doublet whose focal length is equal to 250 mm. The microscope objective 31 has for example a numerical aperture of between 0.7 and 1.7. The set of optical elements 30 may comprise several microscope objectives, for example mounted in rotation on a support, having different magnifications.
[0056] The set of optical elements 30 is here arranged to minimize the size of the pixels of the matrix of the modulator 12 on the sample 2. The matrix of pixels is for example positioned so that the size of a pixel of the modulator 12 projected onto sample 2, i.e. at the focal plane or image plane of the microscope objective 31, is below the diffraction limit. For this, the pixel matrix is positioned at the image plane of the microscope objective 31, here also taking into account the second lens 32.
[0057] The set of optical elements 30 also comprises a dichroic mirror 33 reflecting the modulated beam FM towards the sample 2 and transmitting a reflected beam FR coming from the sample 2 towards the image capture device 40. Each pseudo-random illumination generates a temporal portion of the reflected beam FR towards the image capture device 40.
[0058] Optionally, a quarter-wave plate 34 may be arranged between the second lens 32 and the dichroic mirror 33, as illustrated in [Fig. 1]. This quarter-wave plate 34 makes it possible to make the polarization of the FM modulated beam circular and therefore to make the statistical property of the pseudo-random illuminations isotropic and homogeneous (at the image plane of the microscope objective) in terms of contrast if the illuminations are periodic.
[0059] The set of optical elements 30 also comprises a tube lens 35.
[0060] The image capture device 40 is adapted to capture a plurality of low-resolution images. resolution of the sample 2 exposed to the pseudo-random illuminations. For this, the image capture device 40 integrates the light it receives from the reflected beam FR. By integrating the reflected beam FR (transmitted by the dichroic mirror 33) in a synchronized manner with the pseudo-random illuminations, the image capture device 40 more specifically captures a low-resolution image of the sample 2 for each pseudo-random illumination.
[0061] The image capture device 40 is for example a sCMOS (for “scientific Complementary Metal-Oxide-Semiconductor”) type sensor or a matrix detector composed of an avalanche photodiode of the SPAD type. The image capture device 40 here comprises a matrix of photosensitive pixels whose dimensions preferably correspond to twice the Nyquist criterion.
[0062] The processor 50 receives the low-resolution images captured by the image capture device 40. It comprises in particular image processing means. The imaging device 1 also comprises a memory (not shown in the figures) connected to the processor 50. The memory is a computer-readable recording medium comprising instructions which, when executed by the processor 50, make it possible to obtain a high-resolution image from several low-resolution images. The method for obtaining the high-resolution image is described in detail later. The memory and the processor 50 are, for example, part of a computer processing unit 51, as shown diagrammatically in FIGS. 1 and 4. The computer processing unit 51 is therefore suitable for implementing the obtaining of the image high resolution by the method according to the invention.
[0063] The synchronization unit 60 makes it possible to synchronize the light source 11, the modulator 12, and the image capture device 40 so that each low-resolution image corresponds to the illumination of the sample 2 by a particular pseudo-random illumination.
[0064] An alternative to the first embodiment of the imaging device 1 is shown schematically in [Fig.2]. The idea of this alternative is to have an intermediate Fourier plane Fi on the path of the modulated beam M.
[0065] For this, the set of optical elements 30 comprises two additional lenses 36 (in comparison with the example of [Fig.l]). The additional lenses 36 here have an identical focal length, for example equal to 13.5 mm. Preferably, the Fourier transform of the pixel matrix of the modulator 12 completely covers the rear pupil of the microscope objective 31. The set of optical elements 30 comprises mirrors 37 which make it possible to reduce the size. The mirrors 37 are here optical thin-film technology mirrors, insensitive to the polarization state and optimized for visible wavelengths.
[0066] Advantageously, the intermediate Fourier plane Fi makes it possible to position a physical mask to filter frequency components, for example for applications of non-diffracting beams, for example of Bessel, evanescent (TIRF), Laguerre Gauss, or Airy beam types. It is for example possible, thanks to this physical mask, to select only certain frequency components of the FM modulated beam and therefore pseudo-random illuminations. The physical mask can also be used to apodize, or attenuate the zero order, or other polluting orders, linked to the pixelization of the modulator 12.
[0067] Optionally, a rectilinear polarizer 70 is arranged at the output of the light source 11 (comprising in [Fig. 2] a single laser source 13). The imaging device 1 also comprises a dichroic cube 71 of polarization C1 as well as a half-wave plate 73 placed in front of the modulator 12 which operates here in reflection. The fast axis of the half-wave plate 73 is for example rotated by 16.5° so that the FM modulated beam is phase modulated and rotated by 90° at the output of the dichroic cube 71, which makes it possible to obtain a maximum extinction of the zero order of the modulator 12.
[0068] In the second embodiment of the imaging device 1, shown in [Fig. 3], the set of optical elements 30 comprises a galvanometric mirror 38 and relay lenses 39 ensuring the focusing of the FM modulated beam on the galvanometric mirror 38. The relay lenses 39 are used to conjugate the galvanometric mirror 38 with the pupil of the microscope objective 31. Preferably, the galvanometric mirror 38 is mounted in rotation around a single axis of rotation which is conjugated to the Fourier plane of the microscope objective 31.
[0069] Furthermore, in this second embodiment, the image capture device 40 is more specifically a rolling shutter sensor, for example of the sCMOS type, which means that its photosensitive pixel lines are acquired with a time shift relative to each other. The rotation axis of the galvanometric mirror 38 can then be aligned with the axis of the rolling shutter, i.e. aligned parallel to the pixel lines of the sensor.
[0070] As described later, this assembly makes it possible to carry out an optical sectioning of the sample 2 according to its thickness by reducing the illuminated volume of the sample 2.
[0071] The method for obtaining a high-resolution image implemented by the device 1 and shown in [Fig.4] will now be described. As shown in [Fig.4], the method comprises the following main steps: (a) generation of a sequence of successive pseudo-random illuminations, an empirical statistical property of the sequence having a predetermined value; b) exposure of sample 2 to the pseudo-random illumination sequence; c) sequentially acquiring a plurality of low-resolution images of the sample 2 by the image capture device 40, each low-resolution image being acquired while the sample 2 is exposed to one of said pseudo-random illuminations of the sequence; d) calculating a measured value of an empirical statistical property of the plurality of low-resolution images; e) determining, based on the predetermined value of the empirical statistical property of the pseudo-random illumination sequence, a model of the empirical statistical property of the plurality of low-resolution images; f) determination of the high-resolution image by minimizing, by model adjustment, a deviation between the model and the measured value.
[0072] The method thus begins with step a) of generation, by the generator 10, of the sequence of pseudo-random illuminations, that is to say of at least two pseudo-random illuminations. For example, the sequence comprises between seven and fifty pseudo-random illuminations. The sequence comprises for example less than seventy, less than sixty, less than fifty, less than forty, less than thirty or less than twenty illuminations.
[0073] The fact that the statistical property of the sequence has a predetermined value means that the sequence is produced by the generator 10 so that the statistical property is equal to said predetermined value. The predetermined value may be an input data, i.e. a control value, that the generator 10 must respect or an output data determined on the basis of output signals from the generator 10. The empirical statistical properties are subsequently simply called statistical properties.
[0074] The predetermined value is here a term referring to a set of values. Here, the predetermined value comprises for example as many values as the modulator 12 comprises pixels. For example, the average of the pseudo-random illuminations may correspond, for each pixel of the modulator 12, to an average of the transmission values for the different states of the modulator 12.
[0075] Here, the term “generate” means the act of physically producing the pseudo-random illuminations. However, the pseudo-random illuminations could be “generated” in the sense that they are designed digitally to then be produced by the generator, according to this design, during step b). Step a) can then be carried out upstream, its results recorded to then control the generator when it is desired to produce the sequence.
[0076] The method then continues to step b) during which the pseudo-random illuminations of the sequence successively illuminate the sample 2. As described previously, the pseudo-random illuminations are conducted from the generator 10 to the sample 2 by the set of optical elements 30 via the modulated beam M.
[0077] Two successive pseudo-random illuminations (i.e. illuminating the sample immediately after one another) are here spaced apart by the reading time (“read out”) necessary to collect the signal integrated by the pixels of the image capture device 40.
[0078] Step c) then comprises acquiring the plurality of low-resolution images of the sample 2. Subsequently, the plurality of low-resolution images are referred to as “the low-resolution images”. Each low-resolution image corresponds to the illumination of the sample 2 by one of the pseudo-random illuminations of the sequence. Thus, steps b) and c) are carried out in parallel since the low-resolution images are acquired progressively during the illumination of the sample 2 by the sequence.
[0079] Here, the term “low resolution” means an image whose resolution is degraded compared to the high resolution image. This means that certain details of sample 2 are not visible on the low resolution images while they are on the high resolution image. Typically, the resolution of low resolution images is limited by optical diffraction which is inversely proportional to the wavelength. The resolution limit of low resolution images is thus approximately 300 nm in the visible. This limit means that two points of the sample less than 300 nm apart are not discernible on a low resolution image.
[0080] In step c), the acquisition of the low-resolution images is synchronized with the production of each pseudo-random illumination and the exposure of the sample 2 to said pseudo-random illumination. Here, the synchronization is carried out using the synchronization unit 60, for example according to the timing diagram shown in [Fig.5].
[0081] Here, the acquisition of low-resolution images is thus sequential. The acquisition can also be simultaneous by implementing several image capture devices as is sometimes the case in ISM technology.
[0082] Each low-resolution image here takes the form of a matrix of values, each value coming from the electrical signal produced by one of the pixels of the image capture device 40. Each low-resolution image can thus be represented by a matrix whose dimensions are equal to those of the matrix of pixels of the image capture device 40.
[0083] As shown in [Fig.5], each time window for switching on the laser sources 13 (line L) corresponds to the instant when all the pixels of the image capture device (line C) are synchronized with each other, and to the instant when the pixels of the modulator 12 display a particular pattern to generate one of the pseudo-random illuminations of the sequence (line M).
[0084] Between two pseudo-random illuminations, the pixels of the image capture device 40 are read (line P), which means that the electrical signal that they have accumulated is collected to form the low-resolution image corresponding to the illumination that has just ended.
[0085] For this purpose, the synchronization unit 60 is used as master while the image sensor device 40, the modulator 12 and the light source 11 are slaves. The synchronization unit 60 is for example adapted to start processes in the slave devices and to know their state by receiving signals from them.
[0086] Initially, before the emission of the pseudo-random illumination sequence, the light source 11 is switched off. Consequently, the modulator 12 and the sample 2 are not illuminated and the image capture device 40 does not integrate light. The synchronization unit 60 then sends a start pulse, here a square pulse (line B in [Fig. 5]), to the light source 11 and the modulator 12 to form a pseudo-random illumination and to the image capture device 40 to acquire a low-resolution image. Two pulses, corresponding to two low-resolution images, are shown in [Fig. 5].
[0087] Alternatively, a shutter, for example formed from an acousto-optic intensity modulator, can be placed at the output of the light source. The light source can be left constantly on, the synchronization unit then controlling the opening of the intensity modulator. This makes it possible in particular to use lasers with slow response times.
[0088] Advantageously, the image capture device 40 can integrate, for each illu- pseudo-random mination, a positive image and a negative image.
[0089] In the second embodiment, i.e. when the imaging device 1 comprises the galvanometric mirror 38 and the rolling shutter sensor, the rotation of the galvanometric mirror 38 is synchronized with the sequential integration of the pixel lines of the image capture device 40.
[0090] For this, the image capture device 40 is for example adapted to trigger the rotation of the galvanometric mirror 38. Alternatively, the synchronization unit is master of both the galvanometric mirror and the image capture device.
[0091] As shown in [Fig.5], the galvanometric mirror 38 rotates at a constant speed, its angular position (line G) is therefore proportional to time.
[0092] The processor 50 is then programmed to implement steps d) to f). Steps d), e) and f) are here implemented for all the pixels of the low-resolution images. The high-resolution image thus has the same number of pixels as a low-resolution image. Alternatively, they are implemented for one or more predetermined groups of pixels of each low-resolution image. The high-resolution image then has a corresponding number of pixels.
[0093] In step d), it first calculates the statistical property of the plurality of low-resolution images. The statistical property of the plurality of low-resolution images may be different from that of the sequence. Thus, in the example below, the variance of the low-resolution images and the covariance of the pseudo-random illuminations are considered.
[0094] The result of the calculation of the statistical property of the plurality of low-resolution images is here a set of values, for example a matrix of values, recorded on the memory of the imaging device 40 under the name of “measured value” of the statistical property of the plurality of low-resolution images. The qualifier “measured” here refers to the fact that the set of values is calculated directly from the combination of the low-resolution images acquired by the image capture device 40.
[0095] The measured value includes as many values as the low-resolution images include pixels. For example, the average of the low-resolution images corresponds, for each pixel, to an average of the values of said pixel on the different low-resolution images.
[0096] In step e), the processor 50 constructs the model of the statistical property of the low-resolution images, i.e. a mathematical expression of this statistical property. The following mathematical expressions can be implemented by the processor 50 continuously or discretely. For this, it takes into account in particular the statistical property of the pseudo-random illumination sequence. Here, it also takes into account a point spread function of the imaging device 1 (also known by the English acronym PSF for “point spread function”).
[0097] At this stage of the presentation, we present the calculations which allow the model to be constructed, in particular on the basis of an example in which the statistical property of the illuminations (which is known from step a) is the covariance. Before this, we can introduce several variables which will be used in these calculations as well as definitions of the concepts implemented.
[0098] The “investigation domain” is the portion of space where the sample 2 to be imaged is placed. We denote “w” a point in the investigation domain. The investigation domain corresponds in practice to the portion of the sample that is imaged.
[0099] The “observation domain” is the portion of space where the measurements are made. A point in the observation domain is denoted “o”. In practice, o corresponds here to a pixel of the image capture device 40, and therefore by correspondence to a pixel of the low-resolution images.
[0100] A “sample representation” of sample 2 is denoted “X”. The sample representation is a variable which makes it possible to obtain, after the minimization of step f), the high-resolution image. The values of the representation of sample X are denoted “x”. This representation of sample X depends only on sample 2 and therefore on the investigation domain; we then denote the value x(w) at a point in the investigation domain. Here, the representation of sample X is representative of a wave-matter interaction of sample 2, for example a volume density of fluorophores of sample 2. Here, we consider a bijection between the investigation domain and the observation domain. This means that a point on the object focal plane corresponds to a point on the image focal plane. The representation of sample X therefore has as many x values as each low-resolution image has pixels.The representation of the sample X is here represented in the form of a vector or a matrix.
[0101] The “pseudo-random illuminations” are noted “im”. We then consider a number M of pseudo-random illuminations in the sequence, m is thus an integer ranging from one to M in steps of one. The pseudo-random illuminations vary spatially, they are therefore a function of the observation domain, we then note im(w) the illumination at a point in the investigation domain.
[0102] The “low resolution images” are denoted “ym”. A low resolution image ym corresponds to the signal measured by the image capture device 40 and emitted by the sample 2 in response to a pseudo-random illumination im. It is therefore a function of the point o of the observation domain. For example, ym(o) can correspond to the intensity of an electric field measured by the pixel o of the camera.
[0103] The “point spread function” is denoted h. The point spread function h depends in particular on the set of optical elements 30 and the capture device of image 40. The function h(o,w) represents the signal measured by the image capture device 40 at pixel o and emitted by a point object placed at w.
[0104] The point spread function is described as the percussion response (PSF) and represents the spatial distribution of light intensity in the image plane of an optical system, formed from an object point source. The more point-like the image of the point source is, the more "faithful" the optical system is. Even for a "perfect" optical system, free of optical aberrations, the image of the source point is not a point but a disk called an Airy spot, due to the effects of diffraction by the edges of the aperture of light waves. The Airy function is described as follows d / A _ r [ 1 with jj |a Bessel function of the first order, r being related by the numerical aperture and the wavelength as follows: r = ■ ' " has
[0105] We now detail how to construct the model of the statistical property of low-resolution images. Each low-resolution image ym can be modeled by the following equation: [Math. 2] ym^ = w) x( w) im(w)
[0106] In the formula [Math. 2] (and [Math. 4] below), the notation ^indicates that w takes all the positions of the domain of investigation.
[0107] A first moment of the low-resolution images is the average S} of the intermediate images (which notably includes the sum over the M low-resolution images) which is given by the formula: [Math. 3]
[0108] Which is rewritten: [Math. 4] 5 i [ ] ( ° ) = £ JM”, ( w ) | / M
[0109] The average Sj of the low-resolution images therefore shows the average of the pseudo-random illuminations at each point w (i.e. j
[0110] We then introduce the operator Q allowing us to carry out the following transformation consisting of calculating the square of the value of the pixel o of the camera obtained for the low resolution image number m: j(q) = y ( o ) y ( o) .
[0111] The moment S2 of the low-resolution images associated with the operator Q is obtained by the sum over all the low-resolution images according to the formula: [Math. 5] ={E^ ( ° ) ym ( ° )} / M
[0112] Which can be rewritten: [Math. 6] [y] (O) = EJLa(Wi)X(w2)h(o, wI)h(o, w2) {E^i^ JUwJ} / M
[0113] In the above formula, the notation indicates a double sum in which Wj and w2 successively take all the positions of the domain of investigation.
[0114] We then define a combination of the moments S} and S2 corresponding to the variance V of the low resolution images: [Math. 7] HylH =^(^) -SiMHsMo)
[0115] Which can be written: [Math. 8] v [ y ] ( O ) = E H E M A (W1) x (w2) T (o, w J, w2)
[0116] With: [Math. 9] T (o, Ws, w2) = h(o, W|) h(o, w2) C(vvi' w2)lM2 where C is the covariance of the pseudo-random illuminations and is given by the formula: [Math. 10] ^2) = { E^Uw^wj} / M -1 EXA< w i)}{£^ / M 1
[0117] Thus, we obtain, at the end of step e), a theoretical expression (given here by [Math. 8] in combination with [Math. 9] and [Math. 10]), that is to say a model, of a statistical property, in this example the variance, of low resolution images.
[0118] Alternatively, it is also possible to construct a model of the other statistical properties mentioned above.
[0119] As another example, it is possible to construct several models (e.g. a variance model and a mean model and then to define, in step f), a deviation taking into account the different statistical priorities (variance and mean).
[0120] In step f), the processor 50 is then programmed to compare the model of the statistical property of the low-resolution images with the measured value of the statistical property of the low-resolution images. The processor 50 more particularly compares a theoretical value, obtained using the model, with an experimental value.
[0121] As [Math. 7] clearly shows, the model depends on the representation of sample X of sample 2. The idea is therefore to refine, by iteration, the representation of sample X so that a gap (i.e. a statistical distance), between the model, and more particularly the theoretical value from the model, and the measured value is minimal. During this minimization, the representation of sample X is initialized in order to obtain an initial theoretical value to start the iteration. It is for example initialized as equal to one of the low-resolution images or to an average of the low-resolution images. Thus, the first iteration is for example based on one of the low-resolution images or on the average of the low-resolution images.
[0122] In other words, the model allows, for a given representation of the sample X, to calculate a theoretical value of the statistical property. The minimization of step f) then consists of adjusting the representation of the sample X so as to obtain the closest theoretical value, according to the chosen statistical distance, to the measured value of the statistical property. Here, adjusting the representation of the sample X means modifying one or more of its values x, which are therefore variable values here.
[0123] The statistical distance chosen is for example a Kullback Leibler statistic, a [3-divergence or a difference of squares. When the statistical distance is a difference of squares, this is for example defined as the square root of the absolute value of the difference between the square of the theoretical value (obtained using the model) and the square of the measured value.
[0124] The iterative minimization method is for example a minimization algorithm of the conjugate gradient type or a least squares method.
[0125] Once the deviation is minimized, the representation of the sample X corresponds to the high-resolution image. When the representation of the sample X is represented in the form of a vector, the processor 50 rearranges it in matrix form to obtain the high-resolution image.
[0126] The high-resolution image is referred to as “high resolution” in the sense that the values of its pixels are adjusted relative to the low-resolution images to enable details of sample 2 to be brought out that were not visible in the low-resolution images. For example, two points of sample 2 less than 300 nm apart may be discernible in the high-resolution image while they were not in the low-resolution images. In other words, the method then makes it possible to exceed the diffraction limit.
[0127] Preferably, in order to reduce the computing power required to determine the high-resolution image, it is provided that the covariance C of the pseudo-random illuminations (cf. [Math. 10]) is a circulant matrix. In practice, the imaging device 1 then keeps in memory a single line of the covariance matrix of the pseudo-random illuminations. This also improves the backward compatibility of the method of the invention with existing optical measuring devices.
[0128] Mathematically, the fact that the covariance C of the pseudo-random illuminations is a circulant matrix translates into the fact that the covariance C satisfies the following condition: [Math. 11] fv—>MA / \ '3 f _ / \ / m = qW1 - w2)+a 2 where w]r2 represents a vector of coordinates of a point in the investigation domain and in which the pseudo-random illuminations are such that: [Math. 12] {EXl^i)} / ^^
[0129] When the pseudo-random illuminations are generated by interference of plane waves whose phase is controlled, it is possible to control the phases in order to obtain such pseudo-random illuminations.
[0130] Alternatively, the computing power required can be reduced (to a lesser extent), with when the covariance matrix C is approximately a circulant matrix. The imaging device then keeps in memory only a part of the rows of the covariance matrix C of the pseudo-random illuminations. When the pseudo-random illuminations are speckles the covariance is intrinsically at least approximately a circulant matrix.
[0131] Preferably, the sequence of pseudo-random images is optimized so that the deviation, before the minimization of step f), is less than a predetermined threshold value. Thus, even before the first iteration of the minimization, the theoretical value is relatively close to the measured value. This allows the minimization algorithm to converge more quickly. This also allows, with a given number of low-resolution images, to obtain a high-resolution image of better quality.
[0132] Preferably, the sequence of pseudo-random illuminations is optimized to exhibit a statistical property close to an asymptotic value obtained with an infinite sequence of totally random illuminations corresponding to fully developed speckles. This makes it possible to reduce the number of pseudo-random illuminations in the sequence to obtain a high-resolution image of satisfactory quality.
[0133] In particular, when the statistical property of the low-resolution image sequence used to reconstruct the super-resolved image is variance, the pseudo-random illumination sequence is optimized so as to increase the uniformity of its variance. Preferably, the entropy of the illuminations is maximized under the constraint of uniformity of the empirical variance of the illuminations.
[0134] For this, the processor 50 is here programmed to implement an optimization method represented in [Fig.6]. This optimization method is implemented before the method for obtaining the high-resolution image, in particular before emitting the pseudo-random illumina-tions in step a). As shown in [Fig.6], this optimization method is preferably implemented iteratively.
[0135] First, step h) comprises recording (for example on the memory of the imaging device 1) an initial sequence of pseudo-random illuminations. This initial sequence has an initial variance value and is associated with an initial value of a global parameter representing the uniformity of the variance and the entropy of the sequence of pseudo-random illuminations.
[0136] Then, step i) comprises determining a provisional sequence of pseudo-random illuminations by randomly modifying at least one illumination of a previously recorded sequence. During the first iteration of this optimization method, the previously recorded sequence corresponds to the initial sequence.
[0137] In step j), the processor 50 then calculates a provisional value of the variance of the provisional sequence and a provisional value of the global parameter.
[0138] In step k), the processor 50 compares the provisional value of the global parameter with a previously recorded value of the global parameter. During the first iteration of this optimization method, the previously recorded value of the global parameter corresponds to the initial value of the global parameter. This comparison is here a difference.
[0139] Finally, in step 1), when this comparison indicates that the provisional value of the global parameter is greater than the previously recorded value of the global parameter, the provisional sequence and the provisional value of the global parameter are recorded in place of the previously recorded sequence and the previously recorded value of the global parameter.
[0140] Preferably, the method comprises a step m) consisting of repeating steps h) to 1).
[0141] [Fig.7] shows an example of an optimized sequence of 69 pseudorandom illuminations. [Fig.8] shows another example of an optimized sequence of 23 pseudorandom illuminations. In Figures 8 and 9, the six boxes represent, from left to right, on the top row: the mean of the illuminations, the autocorrelation of the illuminations and a particular illumination; and on the bottom row: the variance of the illuminations, the autocorrelation multiplied by the point spread function and a one-dimensional section of the function T (defined by [Math. 9]).
[0142] As shown in Figures 8 and 9, the sparse distribution of the intensity maxima of the illuminations, i.e. the sparsity of the illuminations, makes the representation of the sample of illuminations close to a totally random speckle. Indeed, the ratio between the standard deviation and the average, for these two sequences, approaches one, as in the case of totally random speckles. These sequences are thus, for example, optimized for samples which have high densities of fluorophores.
[0143] [Fig.9] shows experimental results showing a biological tissue, more specifically myosin from a fruit fly leg, labeled with a fluorescent protein (GFP). The image on the left is obtained by a SIM technique. The image on the right is obtained with the method according to the invention with a sequence of 30 pseudo-random illuminations consisting of light grids. This tissue has a relatively high degree of optical and scattering aberrations. It is observed that the method according to the invention makes it possible to significantly improve the optical resolution. In addition, the high-resolution image (on the right) has fewer artifacts.
[0144] [Fig. 10] represents two intensity profiles. A first intensity profile 101 corresponds to the intensity along segment PI of [Fig.9] (left). A second intensity profile 102 corresponds to the intensity along segment P2 of [Fig.9] (right). Each of the profiles PI, P2 intersects, with respect to sample 2, the same two membranes of two adjacent epithelial cells. As is clearly visible in [Fig.9], along segment P2, the two membranes are discernible. In practice, this results in the fact that the second intensity profile 102 has two peaks, each corresponding to a membrane. Conversely, the first intensity profile 101 has a single spread peak that does not allow the two membranes to be distinguished.
[0145] The present invention is in no way limited to the embodiments described and shown, but those skilled in the art will be able to provide any variant in accordance with the invention.
[0146] As mentioned above, remarkably, the method according to the invention is compatible with numerous optical measuring devices.
[0147] For example, the method applies to wide-field super-resolved microscopes such as structured illumination microscopes (SIM type) in which the sample is illuminated by periodically replicated light patterns, the latter being obtained by interfering coherent beams (laser beams) or by passing incoherent light (from a lamp for example) through a mask. The interference patterns can be based on 2, 3, 4 or even 6 beams. A model of the variance of the low-resolution images can be constructed, which reveals the covariance of the illuminations and the point spread function. In SIM microscopy it is possible to define the patterns so that the average of the illu minations is constant and the covariance is circulating. The calculation of the function T ([Math. 8]) is then simplified.
[0148] As another example, the method also applies to scanning microscopes in which a focused excitation beam is scanned over the sample and a wide-field image is acquired for each position of the excitation beam of a sample. This results in numerous images for each scan. The focused and translated illuminations of scanning microscopy can also be designed so that their covariance is circulating.
[0149] The method is still compatible with confocal microscopes, in particular those including a spinning disk.
[0150] In addition to the fluorescence imaging presented above, the method applies to different illumination techniques such as one- or two-photon fluorescence, with stimulation, depletion or saturated regimes.
[0151] The method also applies to white light transmission imaging. The method also applies to acoustic transmission imaging, the illuminations are then pressure waves.
Claims
Claims
1. A method for obtaining a high-resolution image of a sample (2) comprising the following steps: - a) generating a sequence of successive pseudo-random illuminations, an empirical statistical property of the sequence having a predetermined value, - b) exposing the sample (2) to the sequence of pseudo-random illuminations, - c) acquiring a plurality of low-resolution images of the sample (2) by an image capture device (40), each low-resolution image being acquired while the sample (2) is exposed to one of said pseudo-random illuminations of the sequence, - d) calculating a measured value of an empirical statistical property of the plurality of low-resolution images, - e) determining, on the basis of the predetermined value of the empirical statistical property of the sequence of pseudo-random illuminations, a model of the empirical statistical property of the plurality of low-resolution images,- f) determining the high-resolution image by minimizing, by adjusting the model, a deviation between the model of the empirical statistical property of the plurality of low-resolution images and the measured value of the empirical statistical property of the plurality of low-resolution images.,
2. The method of claim 1, wherein the model of the empirical statistical property of the plurality of low-resolution images is also based on a point spread function.
3. The method of either of claims 1 and 2, wherein the empirical statistical property of the sequence and the empirical statistical property of the plurality of low-resolution images comprise at least one of the following or a combination of at least two of the following: mean, variance, covariance, spatial correlation, standard deviation, kurtosis.
4. Method according to one of claims 1 to 3, according to which, in step f), the deviation is calculated as a difference between a theoretical value, obtained using the model, of the statistical property of the low-resolution images and the measured value of the statistical property of the plurality of low-resolution images.
5. Method according to one of claims 1 to 4, according to which each illu- pseudo-random mination of said sequence of pseudo-random illuminations comprises a light beam (FM) having a spatial intensity distribution, all of the spatial intensity distributions of the illuminations of said sequence being generated in a pseudo-random or deterministic manner.
6. A method according to one of claims 1 to 5, wherein said sequence of pseudo-random illuminations comprises a sequence of pseudo-random speckle images or a sequence of periodic patterns or a sequence of single or multiple focus spot type patterns.
7. Method according to one of claims 1 to 6, according to which the illuminations of said sequence of pseudo-random illuminations are determined so that the covariance of the sequence of pseudo-random illuminations is a circulant matrix.
8. Method according to one of claims 1 to 7, according to which said sequence of pseudo-random illuminations is optimized so as to increase the uniformity of its variance.
9. A method according to claim 8, wherein said sequence of pseudo-random illuminations optimized so as to increase the uniformity of its variance is obtained by an iterative method comprising the following steps: - h) recording an initial sequence of pseudo-random illuminations having an initial value of variance and associated with an initial value of a global parameter representing the uniformity of the variance and the entropy of the sequence of pseudo-random illuminations, - i) determining a provisional sequence of pseudo-random illuminations by randomly modifying at least one illumination of a previously recorded sequence, - j) calculating a provisional value of the variance of the provisional sequence and a provisional value of the global parameter, - k) comparing the provisional value of the global parameter with a previously recorded value of the global parameter,-1) recording the provisional sequence and the provisional value of the global parameter in place of the previously recorded sequence and the previously recorded value of the global parameter, when this comparison indicates that the provisional value of the global parameter is greater than the previously recorded value of the global parameter, - potentially, m) repetition of steps h) to 1).
10. A method according to one of claims 1 to 9, wherein the deviation is calculated as a Kullback Leibler statistical distance, a [3-divergence or a difference of squares.
11. Method according to one of claims 1 to 10, according to which the minimization of the difference is carried out using a minimization algorithm of the conjugate gradient type.
12. Method according to one of claims 1 to 11, according to which each illumination of said sequence of pseudo-random illuminations is generated by interference of controlled phase plane waves or by means of a spatial light modulator imposing a spatial intensity distribution, all of the spatial intensity distributions of the illuminations of said sequence being generated in a pseudo-random manner.
13. Method according to one of claims 1 to 12, according to which the images are acquired by a fluorescence imaging device, white light transmission imaging or acoustic transmission imaging device.
14. Method according to one of claims 1 to 13, according to which each low-resolution image is composed of a pixel matrix and according to which each step d), e) and f) is carried out for each pixel or for one or more predetermined groups of pixels of each low-resolution image.
15. Imaging device (1) comprising: - a generator (10) of a sequence of successive pseudo-random illuminations, an empirical statistical property of the sequence having a predetermined value, - a support (20) for the sample (2), - an image capture device (40) adapted to capture a plurality of low-resolution images of the sample (2) exposed to one of said pseudo-random illuminations of said sequence, - one or more processors (50) programmed to: i) calculate a measured value of an empirical statistical property of the plurality of low-resolution images, ii) determine, on the basis of the predetermined value of the empirical statistical property of the sequence of pseudo-random illuminations, a model of the empirical statistical property of the plurality of low-resolution images, iii) determine a high-resolution image by minimizing, by fitting the model,the gap between the model of the empirical statistical property, of the plurality of low-resolution images and the measured value of the empirical statistical property of the plurality of low-resolution images.
16. The imaging device (1) of claim 15, wherein the image capturing device (40) is a structured illumination microscope, a scanning microscope or a confocal microscope.