EP2405800A1

EP2405800A1 - Fluorescence image processing by non-negative matrix factorisation

Info

Publication number: EP2405800A1
Application number: EP10707297A
Authority: EP
Inventors: Anne-Sophie Montcuquet; Lionel Herve; Jérôme MARS
Original assignee: Commissariat a lEnergie Atomique CEA; Commissariat a lEnergie Atomique et aux Energies Alternatives CEA
Current assignee: Commissariat a lEnergie Atomique et aux Energies Alternatives CEA
Priority date: 2009-03-11
Filing date: 2010-03-10
Publication date: 2012-01-18
Also published as: FR2942950A1; US20120032094A1; FR2942950B1; WO2010103026A1

Abstract

The invention relates to a method for locating at least one fluorescent marker in a scattering medium, in which : a) at least one marker is inserted into said medium ; b) a fluorescence image is obtained by infrared excitation of the medium along a first axis, the image comprising a fluorescence component due to the marker and a self-fluorescence due to a portion of the medium other than the markers; c) the image is processed by factorisation into two non-negative matrices A and S; d) an image of the marker(s) distribution is determined without the self-fluorescence component.

Description

TREATMENT OF A FLUORESCENCE IMAGE BY FACTORIZATION IN NON-NEGATIVE MATRICES

DESCRIPTION

TECHNICAL FIELD AND PRIOR ART

The invention relates to the field of optical imaging applied to the medical field. This technique offers the prospect of non-invasive diagnostic systems through the use of non-ionizing, easy-to-use and inexpensive radiation. Fluorescent markers are injected into the subject and bind to certain specific molecules, for example cancerous tumors. The area of interest is illuminated at the optimal excitation wavelength of the fluorophore (the chemical substance of a molecule capable of emitting fluorescence light after excitation) and the fluorescent signal is detected. Optical diffusion imaging - without fluorescent marker injection - is already used in clinical settings, particularly in the areas of mammography and neurology. Fluorescence optical imaging (with specific fluorophore injection) is focused on "small animal" applications, due to the lack of suitable markers and injectable to humans, and the problem of tissue autofluorescence. which arises for the detection in depth. Indeed, to apply this method to the diagnosis of cancer in humans, it is essential that the specific signal located deeper under the skin than in the small animal can be detected. But the Specific signal to detect weakens with depth, mainly because of tissue absorption and diffusion, and confronts a parasitic signal that disrupts detection. This signal, called "auto-fluorescence", describes the fluorescence of tissues to which no specific chemical or fluorophore has been injected: this is the natural fluorescence of the tissue.

Various studies on the autofluorescence of tissues seem to reveal the possibility of attributing it to the presence of protoporphyrin IX in living cells. This molecule, which is involved in the transport of oxygen and especially in the composition of hemoglobin, indeed has the property of fluorescing in the wavelengths used in medical optical imaging (between 650 nm and 850 nm approximately ). Autofluorescence is therefore a known phenomenon, but it is rarely seen as a parasitic signal. In oncology in particular, autofluorescence is used to distinguish cancerous tissue from healthy tissue. It is not a matter of injecting specific markers, but simply observing the autofluorescence of specific areas and comparing different areas of the same individual. The excitation wavelength is then close to the 400 nm wavelength for which the intensity of the autofluorescence signal is maximum. In contrast, optical fluorescence spectroscopy uses near infrared excitation wavelengths, which provide less absorption, and allows better penetration of tissue. The autofluorescence of tissues is then much weaker and becomes a signal to be suppressed rather than used.

In general, there is therefore the problem of finding a new method for differentiating, in an image, the contribution of autofluorescence from that of the fluorescence sources associated with markers.

There is also the problem of finding a new device for implementing such a method.

STATEMENT OF THE INVENTION

The invention firstly relates to a method for locating at least one fluorescent marker in a scattering medium, wherein: a) at least one fluorescence image or acquisition or a series or a plurality of images or d fluorescence acquisitions, by excitation of the medium, each image or acquisition possibly comprising, on the one hand, a fluorescence component due to the marker or the markers, on the other hand an autofluorescence component due to a part of the medium other than the markers, the measured data of the image or of the acquisition or images or acquisitions that can be stored in a multidimensional array X, b) the data or table is processed by factoring this table into a product of only two non-negative multidimensional arrays, for example two non-negative matrices (if the spatial dimension is equal to 1), A and S, c) a graphical representation of the distribution of intensity or intensities of one or more sources of fluorescence, possibly of the autofluorescence which can be considered as a source of fluorescence, is determined from the data contained in Tables A and S.

The invention also relates to a method for processing an image or acquisition or a series of images or fluorescence acquisitions in a scattering medium comprising at least one fluorescent marker, each image or acquisition being obtained by excitation of this medium, this image or acquisition may comprise, on the one hand, at least one fluorescence component due to the marker, and, on the other hand, an autofluorescence component due to a part of the medium other than the markers, a method in which which, during a processing step, these data or a table X of data from the series of images or acquisitions by factorization of this table X are processed into a product of only two non-negative multidimensional arrays, by example two non-negative matrices, A and S.

It is then possible to determine a graphical representation or an image of the distribution of the intensity of a fluorescence source or the intensities of the different sources of fluorescence, each source being a fluorescent marker or an autofluorescence.

A method according to the invention may be preceded by the introduction of at least one marker in the medium. In either of the above methods, the first array of non-negative AS A product is an array whose elements a _q, _p are weighting coefficients, a _q, _p being the contribution of the spectrum represented by the ^pth line of S, at the coordinate point q. The second non-negative table S is a matrix whose lines correspond to the emission spectra of the fluorescent sources considered, the number of rows of the table S and the number of columns of the array A corresponding then to the number of fluorescence sources considered.

Table X is formed by making successive acquisitions, an acquisition being able for example to correspond to a given position of the source and to a given position of the detector. Each of these positions can be modified by a new acquisition.

The table S is, in general, a matrix, therefore an array of dimension 2, even though A and X may each be of dimension strictly greater than 2.

During the processing step of the table X of the data resulting from the acquisition or the acquisition series (it is in particular the step b) of the localization method or a step of the processing method), A is determined A and S by minimizing a cost or objective function, which function can be or

_^^ ^ _^ x _^ v, .. _^ u. _^ U _^ i _{^^ ^^} .... _^ .- _^ m _^ "X -AS I" I ² between the image

X and the product AS In addition, during the processing step, at least one row of the table S can be initialized, by a reference spectrum of the corresponding fluorescence source. This reference spectrum can be obtained empirically or from tabulated values. Table X obtained is preferably treated according to an iterative process.

For example, we carry out k iterations, the arrays Ai ₊ i and Si ₊ i, obtained during the iteration of order 1 + 1 being determined from the arrays Ai and Si obtained during the iteration of order 1. The number of iteration can be determined according to the fluctuations of the tables A and S, or automatically, according to fluctuations of the function of cost during 2 or more successive iterations. This number of iterations can also be determined empirically, depending on the experience of the user.

During the processing step, A and S can be determined by an iterative method comprising, at each iteration, the minimization of a cost function, this cost function comprising:

- a distance between table X and the product of tables A and S,

at least one distance between an array (A, S) and an initial array (A °, S °)

During the step of determining the graphical representation of the distribution of the intensities of the different sources of fluorescence (due to the marker (s), or to the autofluorescence), the position of one of the sources can be obtained by eliminating contributions from other sources in the Table S, then performing the product of A with the table S thus modified. It is also possible to replace the coefficients of the columns of Table A that do not correspond to the chosen source by a null value. It is still possible to extract the column of A and the line of S corresponding to the desired source and to produce the product of this column and this line.

The excitation of the medium may be carried out by a laser excitation source, which may possibly be focused at the interface between the scattering medium and the external medium. The excitation light will then penetrate into the scattering medium, and excite markers or sources in this medium, for example 3 cm or 5 cm deep, that is to say at a distance from the interface, in the diffusing medium. The fluorescence radiation therefore comes from a zone at depth, for example between the interface and about 3 cm or 5 cm away from the interface, or between 1 cm at a distance from the interface and 5 cm at a distance of the interface.

The excitation may occur in the infra ^¬ red or near infra-red, for example at a wavelength between about 600 and 900 nm. Fluorescence can be detected at wavelengths greater than 700 nm or 750 nm. An excitation at wavelength greater than 750 nm or at 800 nm is also possible, with, for example, a fluorescence at wavelength greater than 800 nm or 900 nm. The acquisition can be performed by an image sensor producing an image which gives, for points of the studied area, the spectral distribution of the fluorescence radiation from these points. Each acquisition can be carried out using a detector comprising a line of elementary detectors; the detector line can be moved, a fluorescence acquisition being performed for each position of the detector line.

The excitation can be performed using a laser, and the excitation line is displaced, a fluorescence image (X) can be made for each position of the excitation line. The invention also relates to a device for locating at least one fluorescent marker in a scattering medium, comprising: a) means for producing an excitation beam, and means for focusing this beam, b) means for producing a acquisition or an image or series of acquisitions or fluorescence images of points or sources of the medium, each acquisition may comprise the fluorescence components due to the different fluorescent sources present, for example on the one hand one or more markers and secondly, autofluorescence, c) means for processing a table X of the data obtained by the series of acquisitions by factorization into two non-negative tables A and S, d) means for determining a graphical representation of the distribution of intensities of the different sources of fluorescence, these different sources may be one or more fluorescent markers and one autofluorescence.

The means for carrying out an acquisition or an image or a series of acquisitions or images preferably comprise an image sensor giving, for points of the zone studied, the spectral distribution of the fluorescence radiation coming from these points. Focusing is preferably at the interface of the medium with the environment.

The means for producing a laser beam make it possible to produce a zone, called an excitation zone, focused for example at the interface of this medium with the ambient medium. The excitation light then enters the medium, diffuses there, and will excite the sources of fluorescence, markers and autofluorescence. This excitation zone may be an excitation line. As explained above, the sources of fluorescence can be located in depth, remotely under the interface.

A device according to the invention may further comprise means for modifying the position of this excitation zone, a fluorescence image being produced for each position of the excitation zone.

At least part of the means for performing a detection of the fluorescence signal from said medium may be arranged along a line, called the detection line. A device according to the invention may further comprise means for change the position of this line along two axes.

The means for processing the acquisition matrix (or multidimensional array) by factorization into two non-negative arrays A and S, implement a method according to the invention, as already described above.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 represents a device for implementing the invention,

FIG. 2 illustrates how a fluorescence acquisition is constituted,

FIG. 3 represents a fluorescence acquisition obtained, with autofluorecence and fluorescence,

FIGS. 4A and 4B respectively represent schematically a matrix S of spectra, with 2 fluorescent sources and therefore 2 lines, and a product of two arrays, whose matrix S, to obtain array X,

FIGS. 5A and 5B respectively represent a spectral model of autofluorescence and fluorescence, for initializing an S matrix in a method according to the invention; FIG. 6 represents autofluorescence and fluorescence spectra detected after treatment according to FIG. invention, and a comparison with initial models,

FIGS. 7A and 7B respectively represent an image of autofluorescence, and a image of the fluorescence, obtained after treatment according to the invention of the image of FIG.

FIG. 8 represents steps of a method according to the invention, FIGS. 9, 10A and 10B represent fluorescence images (FIGS. 9 and 10B), and an image of autofluorescence (FIG. 10A), obtained after processing, according to methods of the prior art, the image of FIG.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Figure 1 is an example of an experimental system for implementing the invention.

The illumination of an area of an object (not shown in the figure), is obtained using a continuous laser 2 whose beam, which emits for example a radiation in the infrared or even the near infrared, is focused with focusing means to reach a certain area on the surface of the scattering medium, this area may be a line. The excitation light then diffuses into an area of the scattering medium, different from the previous zone and will excite one or more fluorescent species.

Means 6 make it possible to achieve a spectral dispersion of the fluorescence radiation emitted by the scattering medium studied in the external medium. These means 6 are coupled to means 8, forming an image sensor, to produce an image which gives, for points of the studied area, the spectral distribution of the fluorescence radiation. from these points. The image sensor of these means 8 is a linear matrix (N _λ , N _xd ), where N _λ is the number of channels corresponding to the range of wavelength considered, and N _xd is the number of pixels corresponding to the number of points detected on the line.

The means 8 comprise means for digitizing the image. Data processing means 24 will make it possible to implement a processing method for analyzing the digital data thus obtained, in particular in terms of the spatial and / or spectral distribution of the fluorescent markers. These electronic means 24 comprise for example a microcomputer programmed to store and process the data acquired by the means 8. More precisely, a central unit 26 is programmed to implement a processing method according to the invention. Display or display means 27 allow, after treatment, to represent the positioning or the spatial distribution of the fluorophores in the medium under examination. The means 24 may optionally control or control other parts of the experimental device.

The medium studied is a diffusing medium, for example a biological tissue. In this type of medium, incident radiation can penetrate into the medium, the depth of penetration into the medium of up to a few cm depending on the attenuation coefficient of this medium, for example 3 cm or 5 cm. In other words, fluorophores located at a distance between 0 cm (so very close to the surface) and 3 cm or 5 cm will be detected.

The detection means 6, 8 thus detect a radiation which comes from the zone of the scattering medium excited by the laser beam, which passes through the diffusing medium towards the boundary between the scattering medium and the external medium, then which reaches the means 6 detection and spectral dispersion. The detection means are not necessarily focused on the zone or the excitation line, but can be shifted and aim for another zone or line, in particular on the surface of the medium. This embodiment is made possible due to the diffusion of light in the medium. Typically, the medium studied can be a living medium. It may be for example an area of the human or animal body. The body envelope constitutes the interface of the diffusing medium with the external medium. An excitation source is therefore focused on this interface, for example along a line. Markers injected into this scattering medium make it possible to locate areas such as tumors.

As we will see, there is also excitation of other elements of the medium, creating parasitic fluorescence, or autofluorescence. An image can be viewed on viewing means 27.

In the illustrated example, a laser source having an excitation wavelength equal to 690 nm is focused along a line on the interface and makes it possible to carry out an excitation of the fluorophores in the scattering medium, at a depth that can reach a few centimeters. The line can be fixed, and in this case one acquires only one line of the object. But we can also use translation plates to acquire line by line fluorescence image of a portion of an object or an entire object. These plates can be controlled by means such as the means 24, 26, 27 of Figure 1. By thus making several images, one can obtain a signal from all or part of an area in the object. Each image can be processed as indicated in this description.

The source 2 can be coupled to a laser fiber 3. A lens 4 makes it possible to focus the beam in the form of a laser line at the interface of the medium studied.

The laser excitation can be positioned above the object, as in FIG. 1, and it is then possible to make an observation in reflection: the fluorescence signal is detected above the object, or on the same side of the object. the object that the radiation source, by an imaging spectrometer 6 coupled to a CCD camera 8. An excitation filter is used, it allows to purify the Laser signal. A system 10 allows high-pass filtering, which cuts wavelengths below 700 nm, for example an RG9 filter system. This filtering is positioned in front of the lens, to block the parasitic excitation coming from the laser beam itself. The acquired image is then obtained using software from the manufacturer Andor or Labview, and we can control the system and translation plates by a single Labview interface.

FIG. 1 also shows an axis X _d which describes the position of the N x _d detectors aligned along a detection line in the means 8.

We find this axis X _d in Figure 2, which gives a schematic example of the type of image that can be acquired with a system as described above and information that can be found there.

The fluorescence along the detection line is detected, and a wavelength spectrum (on the abscissa) of points of the line (ie the points i _xd of the axis X _d of the ordinates of FIG. 2) is realized .

We denote by (i _xd , i _yd ) the coordinates of a point detector.

We denote (i _xs , i _ys ) the coordinates of a point source, for example a laser source. In the case of an online laser source, it can be considered that this source contains N _xs (- ^ 2) elementary sources according to the line.

A single fluorescent source is here detected along the line at the position i _xd of the source positioning point, in the wavelength range between 850 and 900 nm.

A real picture is much more complex, and mixes the contributions, both from

Autofluorescence and one or more sources of fluorescence, this fluorescence from fluorophores present in the scattering medium examined. An example of an acquisition performed for an excitation in the near infrared is illustrated in FIG. 3. Experimentally, it corresponds to the case of a capillary (glass tube filled with indocyanine green ICG) placed, in subcutaneous position, at the back of a mouse. The source excites the fluorophore present in the capillary as well as the surrounding biological tissues, which generates autofluorescence.

We see two main parts in this image: a first part A which is of the autofluorescence visible all along the acquisition line Xd whose maximum intensity is around 700 nm. The second part B is fluorescence due to the fluorophore (ICG - indocyanine green) it is spatially more localized than autofluorescence and its emission spectrum has a peak around 860 nm.

On such an image, we call source a set of points having the same emission spectrum. A fluorescent source may therefore comprise several emission zones, distributed at various positions in the scattering medium.

Such an image can be processed by a method according to the invention, in particular in order to separate the contribution of the autofluorescence on the one hand and that of the source or sources of fluorescence, on the other hand, the latter coming from fluorophores present in the medium examined.

However, for the purpose of treatment, autofluorescence is considered a fluorescent source in the same way as a fluorophore. A data processing technique is described by Lee and Seung in the article "Algorithms for Non-Negative Matrix Factorization", published in Advances in Neural Information Processing Systems, pages 556-562, 2001.

According to this technique, given a non-negative matrix X, of size N _xd * N _λ (ie N _xd rows and N _λ columns), the non-negative matrices A and S, respectively of sizes N _xd * P and P * N, are sought. _λ , which satisfy the condition:

X ≈ A S (1)

By non-negative matrix is meant a matrix whose all elements are non-negative. P is the number of fluorescence sources considered.

The matrix X corresponds to the digitized image which has been obtained by the measurement: X is the matrix expression of the image. The matrix A is called the weighting matrix and an element a _lxd , _p (> _ 0) of this matrix represents the weight of the source p at position i _xd of the measurement line X _d . It is of size N _xd * P, the number of lines N _xd representing the number of points selected along the fluorescence line, the number of columns p representing the number of sources likely to be present in the medium: fluorescent markers and possibly autofluorescence. S is the matrix of the spectra and s _p , _lλ (^

0) represents the i- ^th value of the spectrum of the ^same source. It is of size P * N _λ , the number of lines P representing the number of fluorescence sources (including autofluorescence), the number of columns N _λ representing the number of spectrum data from each source. In other words, each line of the matrix S corresponds to the emission spectrum of a fluorescent source, this spectrum being discretized along N _λ channels.

In principle, each source, except autofluorescence, has a spectrum close to that of a monochromatic source; but in practice there is some dispersion around a central frequency. The line p of the matrix S can therefore comprise several non-zero elements.

FIG. 4A gives the illustrated example of an S matrix for an acquisition with two fluorescent sources considered: the two lines represent the emission spectra of the two sources considered, one of which, the first one, has a spectral distribution more wide than the second. In the first line of the matrix S, it is rather the first elements of the sequence Si _x λ (iλ = l, .... Nχ) which are non-zero, whereas in the second line, they are rather the last elements of the sequence S ₂ iλ (iλ = l, -.Nλ)) which are non-zero.

In the case of two sources (P = 2) and

N _xd points along the line, which corresponds to Nxd detectors, so we have:

FIG. 4B shows the imaged example of the product of a matrix S (for an acquisition with two fluorescent sources) with a table in order to obtain the table XS containing information on the fluorescence spectra, while A defines their weighting. in each of the lines of X.

The solution of equation (1) above is obtained in an approximate manner, by iterations. Practically, we try to minimize an objective function. In this example, we consider the Euclidean distance between the matrix X and the product of the two matrices A and S. In other words, we try to minimize the quantity:

II "

with A≥O and S≥O.

In other words, we define a function of cost or objective, Q ^FMN , which is written:

where Xiχ _d , iλ is the element in line i _xd and in column i _λ of matrix X, and a _ixd , _p is the inline element i _xd and in column p of matrix A, and s _p , _iλ is the element in line p and in column i _λ of the matrix S. This function has the value 0 for the lower bound and vanishes if and only if X = A S.

The algorithm starts with an initialization of matrices A and S to the desired dimensions, and respecting the constraints of positivity. The columns of A are initialized randomly, while the S lines are initialized by reference spectra, representing the estimated emission spectra of the searched fluorescent sources or corresponding to these spectra. These spectra are determined empirically or according to tabulated values. The matrices are initialized, but then evolve during the algorithm. The minimization of the function Q ^FMN _S e is done in two iterative steps. First, for S fixed, the matrix A is searched. Then, for fixed A, the matrix S is computed. The formulas of update of matrices A and S are then:

These laws, once simplified, are equivalent to

- ^ {Λ ^τ X) _pJ χ

> p, i λ p, λ ^' {A vt "^{" r} yAS) _pM The objective function converges to a local minimum, and update laws ensure that the objective function decreases.

The algorithm implemented in the context of the invention is therefore an iterative algorithm that updates the matrices A and S searched according to the update functions described above which minimize as iterations the function objective (Euclidean distance between X and A. S).

The number of iteration is determined according to the fluctuations of the matrices A and S, or automatically, according to the fluctuations of the cost function, Q ^FMN , during 2 or more successive iterations, or empirically.

The initialization of the algorithm consists in principle in creating two random matrices A and S, and then updating them during iterations.

In the case of a spectrum such as that of Figure 3, this method has been tested but only a few cases on tens converge to a physically reasonable result.

For this reason, according to the invention, at least the first lines, and preferably all the lines (for more robustness), of the matrix S are chosen at initialization, which amounts to giving the approximate shape of the spectra of the corresponding sources. We therefore choose approximate spectra, one for autofluorescence, the others being those of the fluorescence source (s) due to the marker (s). For example, in the case of a Only fluorescent marker, one chooses two spectral models, one for autofluorescence and one for fluorescence of the marker, as illustrated respectively in FIGS. 5A and 5B, on the basis of a priori knowledge of the autofluorescence and the fluorescence of the fluorescence marker. marker pen .

The columns of A are initialized randomly, the initialization of the lines of S as previously described proving to be sufficient for the initialization step for a satisfactory final result.

In addition, positivity constraints are applied: positive coefficient initialization matrices are chosen, the update laws then keeping this positivity. Once the initialization matrices A and S have been determined, the algorithm makes it possible to update the matrices A and S according to the rules explained above. Thus, according to the invention: - We choose initialization matrices

A and S which respect the constraints of positivity,

- The objective function is minimized in two iterative steps:

For fixed S, the matrix A is updated. For fixed A, the matrix S is updated.

Once the matrices A and S have been found, it is possible to find the spatial distribution of the first fluorescent source by producing the product AS ', the matrix S' then being the matrix S for which the spectrum of the second source is extinguished ( therefore S ₂ , iλ = 0 for all i _λ ); and / or the second fluorescent source by producing the product AS ', the matrix S' then being the matrix S for which the spectrum of the first source is off (thus Si, _lλ = 0 for all . and / or the ^pth fluorescent source by making the product of the column p of A by the line p of S.

- and / or the p ^th fluorescent source by obtaining the product A S ^1, the matrix A 'being then the matrix A for which all the coefficients of the columns other than the pth column are set to zero.

It is therefore possible to represent the intensity distribution of each fluorescence source (markers or autofluorescence) separately from that of the other sources.

Practically this means that it is possible to obtain the spatial distribution of all or part of the fluorescence sources constituted by the markers and the autofluorescence.

A method according to the invention implements an image processing method which, applied to the image of FIG. 3, leads to the results of FIGS. 5A, 5B, 6, 7A and 7B. FIGS. 5A and 5B show the shape of the spectra chosen for the initialization of the two sources, ie the two lines of the initial matrix S.

FIG. 6 shows the final shape of the spectra of the two main sources detected in solid lines (the initialization spectra are in dotted line), for autofluorescence and fluorescence (ICG).

Figures 7A and 7B show the result in images: fluorescence (Figure 7B) can be separated from autofluorescence (Figure 7A).

One of the advantages of this method is the coherence with the data, because it is here to treat and to obtain only positive data.

Steps of a method according to the invention are represented in FIG.

in a step S1, one or more acquisitions are made by excitation of the scattering medium, by laser beam; this results, for example, in one or more images; in a step S2, the matrices A and S are initialized,

the equation X ≈ A. S can then be solved iteratively as explained above (step S 3), it is then possible to carry out a graphical representation of one or more sources of fluorescence, or a visualization of one or more sources (step S4), by selecting the desired source, for example by setting the coefficients of the other sources to zero in the matrix S.

An image corresponding to the photons produced by one or more fluorescent sources is thus constructed, for example by multiplying respectively the (the) columns of the corresponding matrix A by the line (s) of the matrix S corresponding to the selected source or sources that are searched.

A comparison with the results obtained with other methods was carried out. Thus, the same image, that of Figure 3, was first processed by the simple subtraction method, for example as explained in US 7321791 or WO 2005/040769.

The result obtained is that of FIG. 9: the iterative algorithm used makes it possible to isolate the specific fluorescence, but "streaks" remain visible on the image obtained, and the specific fluorescence intensity is lower than for the results obtained in factorization of non-negative matrices. In addition, it is possible to obtain negative values, which adapts badly to the spectral data.

The same image was then processed by the so-called singular value decomposition method, as described for example in D. Kalman, "A Singularly Valuable Decomposition: The svd of a Matrix," The College of Mathematics Journal, 27 (1), 2. - 23, 1996 or by GWStewart, "On the Early History of the Singular Value Decomposition", SIAM Review, 35 (4), 551-566, 1993.

The result obtained is shown respectively in FIG. 10A, for the auto-fluorescence portion, and in FIG. 10B, for the specific fluorescence portion. It is observed that the latter has notable defects (for example very "sliced" distributions which do not correspond not to physical realities). Moreover, this method does not only deal with positive values, and can return negative values, which is not well adapted once again to the spectral data that we handle.

Therefore processing methods such as simple model subtraction or singular value decomposition (DVS) are not suitable for spectral separation. According to the invention, positive signals are processed and only positive matrices are then found, unlike the DVS technique which can result in matrices having negative values, which does not correspond to physical reality. What has been described above implements a measurement geometry in reflection, as seen in Figure 1; in this geometry, the exciter source is located on the same side as the detector with respect to the diffusing object. It is also possible to implement a transmission geometry in which the detector is situated opposite another face of the scattering object, for example the object is disposed between the excitation source and the detector.

The acquisition and processing has previously been described along a line of N _xd detectors i _xd , not necessarily aligned with the Laser line. We will now describe how the invention can be implemented:

by moving the detector line along an axis Yd, preferably perpendicular to the axis Xd formed by the N _xd detectors i _xd . Thus, each detector will have 2 coordinates (i _xd , i _yd ) along the axes Xd and Yd respectively, with 1 <i _xd <N _xd and 1 <i _yd <N _yd . In this case, the Laser line is preferably fixed. In the preferred case, each detector is aligned along the axis Xd and one moves along the axis Yd in order to have a measurement for all the (ixd, iyd) coordinates of detectors,

and / or by moving the laser line along an axis Ys preferably perpendicular to the axis Xs of this line. In this case, the detector line remains preferentially fixed. The coordinates of an elementary source are then i _xs and i _ys . In the preferred case, the source is linear along an axis Xs and is moved along the axis Ys. In this case, ixs remains constant and only iys evolves. According to a preferred embodiment of the invention, either the on-line source or the detector is moved.

If we only move the source along the Ys axis, the coordinates (ixs, iyd) are not useful. Only the coordinates (ixd, iys, iλ) are useful so that X (and A) can be considered as (only) three-dimensional arrays.

If we only move the detector only the coordinates (ixd, iyd, iλ..are useful, and X (and A) can be considered as 3D arrays.

In the first embodiment described above, neither the source nor the detector is moved. Only the coordinates (ixd, iλ are then useful, X (and A) could in this case be considered as 2D arrays. Now we move the source and / or the detector. The device may then again be that of FIG. 1, for example. Displacements can be obtained by displacement means of the detector 8 of Figure 1 (for example by translational plates) and / or the position of the laser beam of the same figure (for example still by translation plates). These displacement means are for example controlled by the computer processing means 24.

The marks Xd, Yd and Xs, Ys can respectively be respectively associated with a reference plane, which can be the work plane on which the object to be analyzed is arranged, or the source displacement plane, or the displacement plane. of the detector.

An image or table of data obtained in each configuration can be processed independently of the images or tables obtained in other configurations, a configuration designating an acquisition with the detector and the laser line in a determined position. One can use, then, for each image obtained or each table obtained, a treatment as previously described. But the acquisition of fluorescence with a displacement of the detection line and / or the position of the source offers new possibilities that will now be described. We then take advantage of the fact that each source of fluorescence is not purely punctual but has a certain spatial extension. Also, rather than treating each acquisition independently of each other, it seems useful to make a treatment of a series of acquisitions. The treatment will then relate to the factorization of a table X including all the data measured during this series of acquisitions.

In the case where the laser line is fixed and the Nxd detectors are moved, between two successive acquisitions, along an axis Yd, we have:

X ≈A * S

where X is an array of dimensions (i _xd , i _yd , iχ), and where i _xd and i _yd are the coordinates of an elementary detector along the Xd and Yd axes.

In the case where the Laser line is moved between two successive acquisitions and the N _xd detectors are fixed:

X ≈A * S

Where X is an array of dimensions (i _x s / i _yS , iλ), and where i _xS and i _yS are the coordinates of an elementary source along the Xs and Ys axes. If the Laser line and the detectors are simultaneously moved between two successive acquisitions, we have:

X ≈A * S

X being then an array of dimensions (i _xd , iydf ixsf iys r iλ). Each of the three previous cases can be written in the form

X ≈A * S

X being an array of dimensions (q, iλ), with q = (i _xc i, iyd) when the detectors are moved and the laser line is fixed, q = (i _xs , i _γs ) when the detectors are fixed and that the laser line is moved, q = (i _xd , i _yd , i _xs , i _ys ) when the detectors and the laser line are moved.

q can be called a super index. We will then have:

^Λ q, ιλ ~ ^Λ q, p ^J p, iλ

A and S are multidimensional arrays of which all elements are positive. As previously described, A and S are initialized then determined according to a factorization algorithm in non-negative matrices. The term non-negative matrix can be replaced by "array" because A can have a dimension greater than 2.

S is said matrix spectra and s _p, _lλ (^ 0) _λ represents the i ^th value of the spectrum of the p ^th source of fluorescence. It is of size P * Nλ, the number of lines P representing the number of fluorescence sources (including autofluorescence), the number of columns Nλ representing the number of data of the spectrum of each source. In other words, each line of S corresponds to the emission spectrum of a source fluorescent, this spectrum being discretized according to Nλ channels.

The algorithm starts with an initialization of the array A and the matrix S to the desired dimensions, and respecting the constraints of positivity. Table A is initialized randomly, while the S lines are initialized by reference spectra representing the searched sources. These spectra are determined empirically or according to tabulated values.

The algorithm stems from a minimization of a function of cost or objective Q ^FMN .

In the case where this function is the Euclidean distance between X and the tensor product A * S, and placing itself in the configuration in which the laser line is fixed and the detectors are moved according to Xd and Yd, the updating laws write:

Advantageously, it is possible to consider additional spatial constraints, such as, for example, the smoothing of the coefficients of the matrix A. The function to be minimized then becomes: + WΛ ^ι ιxd, ιyd, p I

FMN

Q then representing the objective or cost function previously described, for example being the Euclidean distance between X and the tensor product A * S. α ₂ is a positive real.

In the same way, one can implement an algorithm allowing a smoothing of each spectrum of S. The function to be minimized is then:

α, 3 is a positive real.

We can also impose on S

15 constraint on the distance of each spectrum of the array S and each corresponding initial spectrum, that is to say each spectrum of the initial array S °.

The function to be minimized is then:

0.4 is a positive real

In other words, the function to minimize Q ™ ^N

25 combines a distance between X and AS (Q ^FMN ) _fe - | - _a second distance between the table S resulting from the current iteration, and the table S ° established during the initialization, or table S ° initial, this second distance that can be weighted by a real positive or strictly positive α ₄ .

According to the previous equation, the update laws _A ' ^(ι) X + a ₄ S _n write: S • <( ⁽ ! ^Ι + ⁺ ! ^Ι ) ^> = S c ( ⁽ 0 ^Λ Λ -r ^Q C ₄ J ₀

A'AS ^(ι) + a _Λ S ^(ι)

Similarly, one can impose on A a constraint on the distance of each column of Table A and each corresponding initial column, that is to say each column of the initial table A °.

The function to be minimized is then:

α ₄ 'is a real positive or strictly positive.

In other words, the function to be minimized Q ™ ^N combines a distance between X and AS ^ Q ^FMN ) _fe - (- _a second distance between the table A resulting from the current iteration, and the table A ° established during the initialization , or initial array A °, this second distance being able to be weighted by a real positive or strictly positive α _{4 '} .

According to the previous equation, the updating laws are written:

A ^(ι) SS '+ a _A , A ^(ι) It is also possible to minimize a function ^FMN _^ combining the various constraints explained above.

We obtain then: Qζ ^MN = Q ^FMN + Cc ₁ C ₁ ,

Where α _x is a positive or strictly positive real, with 1 ≤ i ≤ 4, i can also correspond to the index 4 ', α _x also being able to correspond to the index α _4.

According to one aspect of the invention, at least one marker is introduced into a diffusing medium, so that the diffusing medium contains p fluorescence sources, the autofluorescence of the medium being able to be considered as a source of fluorescence. We seek to locate this or these marker (s) fluorescent (s) in this scattering medium.

In such a method, at least one fluorescence acquisition is thus achieved by exciting the medium by a laser light source S with coordinates (i _xS , i _y s), the beam of this laser source being able to be focused, for example, in the form of a line.

The fluorescence is detected by a detector D, which may comprise a plurality of detectors (i _Xc ui _Yd ) having a spectral dispersion capacity, these detectors being for example aligned along an axis Xd and thus forming a line of N _xd elementary detectors.

The source and / or the plurality of detectors are displaced, for example in translation, the coordinates of the source and of each detector being respectively denoted (i _X d, iyd) in a reference (X _d , Y _d ) and (i _xs , i _ys ) in a reference (X ₈ , Y _s ).

A measurement pattern, or acquisition, is determined by a position of the plurality of detectors and a position of the source. At each measurement configuration, the fluorescence signal produced inside the scattering medium is measured by each detector (xd, yd) placed in (ix _d , iy _d ). Such a signal is then separated according to Nλ length 10. waves, each detector (xd, yd) measuring the intensity at each wavelength iλ.

With each measurement configuration, or acquisition, the intensity of the signal measured at each wavelength iλ is indicated in a table

Table X obtained following measurements in each configuration, then corresponding to a series of acquisitions, is then processed by factoring the product of two non-negative matrices.

A and S, such as:

V _≈ A * C ixs, iys, ixd, iyd ,, // l ^ xs, iys, ixd, iy, pp, iλ

It is therefore possible to determine an image of the distribution of the intensities of the different sources of fluorescence (markers or autofluorescence). As already explained above, one can turn off one of the sources and perform the calculation A. S which gives the distribution of the other sources.

Although, in the examples given in the

30 description the objective function is based on the calculation of the Euclidean distance between the array of X data and the tensor product A * S, other types of objective functions can be implemented within the scope of the invention, in particular an objective function based on the calculation of the divergence, including the Kullback Leibler divergence. Lee and Seung have determined for this function updating laws, which ensure the decay of the objective function in the case of a matrix X in two dimensions.

We then obtain

Claims

A method of locating at least one fluorescent marker in a scattering medium comprising such a marker, wherein: a) at least one fluorescence acquisition (X) is carried out by excitation of the medium, each acquisition comprising, on the one hand, one or more fluorescence components due to one or more markers, on the other hand an autofluorescence component due to a part of the medium other than the markers, the data measured during the acquisition or acquisitions being stored in a multidimensional array X, the acquisition being carried out by an image sensor producing an image giving the spectral distribution of the fluorescence radiation, b) the data of said Table X are processed by factorizing this table into a product of, only, two non-negative multidimensional arrays A and S, c) a graphical representation of the intensity distribution of one or more fluorescence components is determined from the given data. are contained in Tables A and S.

2. Method according to claim 1 wherein, in step b), A and S are determined by minimizing a cost function.

The method of claim 2 wherein the cost function is, or includes, the

distance W "x-AS I" I ² between the image X and the product AS

4. Method according to one of the claims

1 to 3, in which, during step b), A and S are determined by an iterative method comprising, at each iteration, the minimization of a cost function, this cost function comprising: a distance between the Table X and the product of Tables A and S,

at least one distance between an array (A, S) and an initial array (A °, S °)

5. Method according to one of the claims

1 to 4, wherein, in step b), at least one line of the array S is initialized by a reference spectrum of the corresponding fluorescence source.

6. Method according to one of claims 1 to 5, wherein step b) is performed by k iterations, tables A _{i +} i and Si ₊ i, obtained during the iteration of order 1 + 1 being determined from the tables A ₁ and Si obtained during the iteration of order 1.

7. The method of claim 6, wherein the iteration number is determined according to the fluctuations of the tables A and S, or automatically, according to fluctuations of the cost function during 2 or more successive iterations.

8. Method according to one of claims 1 to 7, wherein, in step c), the position of one of the sources is determined by eliminating the contributions of the other sources in the table S and then carrying out the product of A with the table S thus modified.

9. Method according to one of claims 1 to 8, wherein the excitation radiation has a spectrum in the infrared.

10. Method according to one of claims 1 to 9, wherein the fluorescence is detected at wavelengths greater than 600 nm.

11. Method according to one of claims 1 to 10, wherein the image is made using a detector comprising at least one line of elementary detectors, and this line of detectors is moved, an acquisition (X) fluorescence being performed for each position of the line of detectors.

12. Method according to one of claims 1 to 11, wherein the excitation is carried out in a zone, said excitation zone, the excitation light then diffusing in a zone of the medium different from the excitation zone.

13. The method of claim 12, said excitation zone being an excitation line.

14. The method of claim 13, wherein the excitation line is moved, a fluorescence acquisition being performed for each position of the excitation line.

15. A device for locating at least one fluorescent marker in a scattering medium, comprising: a) means (2, 4) for producing a fluorescence excitation beam, b) an image sensor (6, 8). ) to perform at least one fluorescence acquisition of points of said medium, this acquisition comprising the fluorescence components due to the various sources present in the medium, including the autofluorescence, and to produce an image giving the spectral distribution of the fluorescence radiation; c) means (24, 27, 28) for processing the factorization acquisition data into two non-negative tables A and S, d) means (24, 27, 28) for determining a graphical representation of the intensity distribution. different sources of fluorescence.

16. Device according to claim 15, further comprising means for modifying the position of the excitation line.

17. Device according to claim 15 or 16, at least part of the means for achieving a fluorescence acquisition of points of said medium may be arranged along a line, called a detection line, the device further comprising means for modifying the position of said detection line.