FR2863079A1 - Tomography image reconstruction process for use in medical field, involves reconstructing image vector from signal vectors output from detector bars, where coefficient of matrix for detector bars are constructed - Google Patents

Abstract

The process involves reconstructing an image vector from signal vectors output from detector bars (1). The reconstruction step involves constructing the signal vectors by juxtaposing signals from the bars, and dividing a plane where the bars are detected into pixels. The image vector is constructed by juxtaposing rows of the plane. Coefficient of matrix corresponding to current detector bars is constructed. An independent claim is also included for an image reconstruction device.

Description

RECONSTITUTION METHOD AND DEVICE

  IMAGE ON BARS OF DETECTORS.

GENERAL TECHNICAL FIELD.

  The present invention relates to an image recovery method acquired through sensor arrays mounted on a projectile. STATE OF THE ART.

  Projectiles can be self-guided on a moving target when the latter releases heat, for example the heat of propellers or engines - thanks to a hot spot detection device embedded on the projectile. Once the hotspot is located, the projectile adjusts its trajectory to the hotspot to reach its target.

  Figure 1 schematically shows a longitudinal section of the focal plane of a hot spot detection device of the state of the art.

  As shown in FIG. 1, the hot-spot detection device conventionally comprises four detection bars 1 of rectangular shape and placed relative to one another to form a regular Greek cross centered on the longitudinal axis 2 of the device. The bars 1 are placed in the focal plane of the detection device. Their length is equal to the field of optics, and their width approximately to the diameter of the image spot (percussive response) of the optics. The bars 1 are fixed relative to the projectile symbolized by the normal ortho mark 3 itself centered on the axis 2.

  As the bars 1 are fixed relative to the mark 3, in order to be able to observe the scene, the optical axis 6 of the device is rotated about the axis 2 along the arrow referenced by 5, the optical axis 6 being at a distance R of the axis 2. The trajectory of the axis 6 in the focal plane is represented by the circle 4.

  During this rotation 5 of the optical axis 6 around the axis 2, the bars 1 detect a hot spot. The detection and positioning of this hot spot relative to the projectile allows the projectile to move towards the hot spot and therefore the target.

  Detection devices and signal processing methods for positioning previous hot spots, however, have disadvantages.

  In fact, the prior art only makes it possible to treat a single hot spot.

  They do not allow to reconstruct an image of the scene around the projectile.

  Therefore, the reliability of projectiles incorporating such devices and operating with such signal detection and processing methods is not optimal.

  PRESENTATION OF THE INVENTION The invention proposes to overcome these disadvantages.

  One of the aims of the invention is to propose a method for reconstructing an image by means of the signals picked up on arrays of detectors mounted on a projectile.

  For this purpose, the invention proposes a method for reconstituting an image 1 acquired by means of sensor arrays mounted on a projectile, characterized in that the representative vector of the image 1 m is reconstituted from the representative vector of the images. B signals from the bars 1 by solving the linear system such that: LÉIm = B where L is the matrix taking the signals from each bar for all the pixels of the image.

  The invention is advantageously supplemented by the following features, taken alone or in any of their technically possible combination: the method comprises the steps according to which the bars are numbered and the vector B is constructed by juxtaposing the signals received from each bar (1) according to the number of 0 bar; - The pixels in which the bars are located are divided into pixels, the pixels being situated at the intersection of lines and columns, and the vector 1m is constructed by juxtaposing the lines of the plane thus divided. and - each coefficient L is constructed; of the matrix L by plotting in column for each current pixel j the intensity of the digitized signal from each strip i for a hot spot centered on the pixel j, each line of L corresponding to a bar and each column to a pixel; the resolution of the linear system uses a method of the type minimization of a functional quadratic; - the method of resolution is a least squares method and in that the functional is of the type 2, where Im, L designate the transposed of lm and L; the least squares method comprises a step of initialization according to which the image is canceled over the entire field of the bars; - definition of an initial threshold; and - looping consisting in performing: a descent by conjugate gradient, - a thresholding of the image and a zeroing of the image signals whose intensity is below the threshold; and - a lowering of the threshold; the loop stopping after a number of iterations or when the reconstructed image is sufficiently resolved to be exploited by projectile processing and guidance means; the resolution of the linear system uses a method of the type minimizing or maximizing a functional under stress; the resolution method is a maximization of the entropy of the image with the constraint L Im = B; the resolution method uses a MART multiplicative algebraic reconstruction technique; The invention also relates to an image reconstruction device comprising detection strips and processing means adapted to implement a method according to the invention.

PRESENTATION OF FIGURES

  Other characteristics, objects and advantages of the invention will emerge from the description which follows, which is purely illustrative and nonlimiting, and which should be read with reference to the accompanying drawings, in which: FIG. 1, already commented on, represents a longitudinal section of a focal plane of a detection device according to the prior art; FIG. 2 schematically represents a longitudinal section of a focal plane of a detection device according to the invention; FIG. 3 diagrammatically represents the path of a bar in front of a scene; - Figure 4 schematically shows the sampling of the frequency plane along directions perpendicular to the bars; FIG. 5A shows the influence of the number of the bars and the size of the field of the image on the sampling of the frequencies; - Figure 5B shows schematically an embodiment of a device with seven bars; FIGS. 6A and 6B schematically represent a method for constructing the vector 1m; FIGS. 7 and 8 diagrammatically show a method of constructing the matrix L; FIGS. 9A and 9D show schematically reconstituted images by a possible method, as iterations of the process; FIG. 10 represents a pattern; and FIG. 11 represents an image of the pattern of FIG. 10 reconstituted by another possible method after about ten iterations.

DETAILED DESCRIPTION.

POSITION OF THE PROBLEM.

  Throughout the rest of the description, we do not consider any scanning of the scene by the system of auto guidance and image reconstruction. The relative movement of the projectile (including the rotation on itself) during the flight is not taken into account.

  FIG. 2, whose elements similar to FIG. 1, bear identical reference numerals, schematically represents a longitudinal section of a focal plane of a device embodying a method according to the invention.

  Thus, a detection device implementing a method according to the invention comprises at least three detection bars 1 of rectangular shape and placed relative to each other in at least three directions non-collinear with each other.

  Throughout the following description, unless explicitly stated otherwise, the detectors are oriented radially towards the axis 2 of the device, and towards the vertices of a regular polygon. In FIG. 2, the bars are thus arranged together in the shape of a regular Y centered on the longitudinal axis 2 of the device.

  The bars 1 are placed in the focal plane of the detection device. Their length is equal to the field of optics, and their width approximately to the diameter of the image spot (percussive response) of the optics. The bars 1 are fixed relative to the projectile symbolized by the normal ortho mark 3 itself centered on the axis 2.

  The optical axis 6 of the device rotates about the axis 2 according to the arrow referenced 5 by a router, the optical axis 6 being at a distance R from the axis 2. The trajectory of the axis 6 in the focal plane is represented by circle 4.

  During this rotation 5 of the optical axis 6 around the axis 2, the bars 1 acquire a signal.

  In the remainder of the present description, it is assumed that the angular position of the optical axis 6 is known as and when the signal is acquired on the bars 1.

  The angles 0 of rotation are given by measuring means connected to the router.

  During the movement of the router, the optical axis 6 performs a translational movement in front of the bars 1. It is of course also possible, when changing the reference, that the bars 1 perform a translational movement circular to the optical axis 6.

  FIG. 3 shows a bar 1 passing in front of the image 30 of the scene if the axes (Ox, Oy) centered on the image 30 in a direction of displacement in translation are taken as reference. The image 30 of the scene is acquired during a step 32, that is to say all along the translation in the direction 31.

We thus obtain a signal 33.

  We denote L the operator which makes it possible from an image 30 to obtain the signals coming from the bars 1.

  We denote by lm the function of x and y in the focal plane which represents the image of the scene we are trying to obtain. The function 1m therefore represents the image 30 in FIG.

  The signals obtained on the bars 1 are denoted B. The function B thus represents the signals 33 of FIG.

  It will be recalled that it is sought to determine lm from B, that is to say to reconstitute an image of the scene from a signal received by bars.

  The equation of the problem we are trying to solve can thus be written: (1) L.Im = B.

  It can thus be seen that the resolution of equation (1) can be performed by means of a numerical calculation.

  The fact of integrating the entire length of the bar 1 is similar to a measurement acquisition technique used in tomography. Tomography is used in the medical field in particular.

  This measurement acquisition characteristic makes it possible to use a tomographic image reconstruction method.

  First, equation (1) highlights the linear aspect of the problem and assumes the linearity of the bars.

  In addition, the numerical resolution of this problem requires a discretization of the focal plane. We need a discrete method of tomographic reconstruction, which relies by definition and contrary to analytical methods, on a discrete modeling of the image to reconstruct and measurements.

  Finally, it will be seen in the remainder of the present description that the intrinsic separating power of the signal processing during the implementation of a method is limited by the number and the size of the bars.

  SAMPLING IN FREQUENCY SPACE.

  From a theoretical point of view, the signals coming from the bars are directly related to the Fourier transform of the analyzed image.

  Due to the linearity of equation (1), a method according to the invention can use a step that is similar to a Radon transform.

  In effect, it is recalled that, in a method according to the invention, an integration 32 of the intensity of the signal acquired on the strips is performed, and this over the entire length of each strip 1 during its translation. reconstitution of an image corresponding to such acquired signal 33.

  If we apply to this signal 33 a Fourier transform 34 to a dimension denoted TF, in the remainder of the present description, then we substantially obtain a sampling of the frequency space 300 on a line 310. The frequency space fx and fy represents the two-dimensional Fourier transform of the image - noted TF2 in the following description.

  More precisely, in the hypothesis of bars 1 of infinite length, one can write, without taking into account the characteristics of the bars 1 represented usually by the gains and the offsets or offsets according to the terminology of the person skilled in the art: (2) TF , (Sk) = TF2 (I) (n (Bk)) x TF, (Det) with the following notations: I (image) designates the illumination (W / m2) of the focal plane; TF, denotes the one-dimensional Fourier transform; TF2 denotes the two-dimensional Fourier transform; Sk denotes the signal from the detector k as a function of. moving the image; n (Bk) is the direction perpendicular to the long side of the detector k, namely the direction 31 in the case of the bar 1 of Figure 3; and Det denotes the transfer function of the detector shape, typically a rectangle function whose width is the width of the detector.

  The calculation parameter is the displacement of the next image n (Bk). FIG. 4 shows that the image 300 in the Fourier space of an image acquired by arrays in real space is all the better sampled as the number of arrays in the real space is important.

  It is recalled that the direction of sampling in the frequency space is perpendicular to the direction of extension of the bar in real space.

  It is understood from Figure 4 that it is preferable to have a large number of bars to have a better reconstruction.

  In the example of FIG. 4, there are five sampling directions 41, 42, 43, 44 and 45. This means that five bars are placed in the focal plane.

  FIG. 4 also shows that the width D of the bars acts as a convolution of the image in the frequency space by a disk 50 whose diameter is YD.

  The influence of the width of the bars 1 on the number of bars to be arranged in the focal plane is detailed in the following description.

  The device for implementing the method according to the invention generally comprises, in general, seven bars.

PRINCIPLE OF RESOLUTION.

  Remember that in order to solve equation (1), it is necessary to perform a discretization of the focal plane.

  FIG. 6A thus schematically shows that the image 60 acquired by the bars 1 is divided into pixels referenced by 600. Thus, lines 61, 62, 63 and 64 are defined in FIG. 6A. .

  In addition, a numbering of each pixel of the image 60 is performed. Each pixel 600 of the image 60 thus bears a number.

  FIG. 6B shows that the image 600 is then represented as a vector 65 by putting lines 61 to 64 one after the other, for example.

  Similarly, a vector B representative of B of equation (1) is constructed by juxtaposing the signals received from each strip 1 after numbering the bars. The juxtaposition of the signals in the vector B is performed according to the numbers of the bars.

  Figure 7 shows that the operator L of equation (1) is represented by its matrix.

  Figure 7 shows that each line of the matrix L corresponds to a current bar i of the focal plane. Each column of the matrix L corresponds to a pixel j.

  The intensity of the digitized signal from each strip i for a hot spot centered on the pixel j during a router turn is then transferred in column and for each current pixel j of the focal plane. The evolution of this intensity on a bar i during a router revolution is shown schematically in Figure 8.

  The matrix of L is then obtained. It is recalled that equation (1) can be written: (1) LeIm = B It is then understood that with the knowledge of the matrix of L and the vector of B, the problem of reconstitution image is reduced to the resolution of a linear system representative of equation (1).

  In general, the system of equation (1) is not invertible and admits an infinity of solutions, because the matrix L is rectangular.

  Several resolution methods are possible to facilitate the resolution of this equation.

  The performances of a device implementing a method according to the invention will then be conditioned, in addition to the physical characteristics of the device, by the resolution steps used for the linear system, as well as by the relevance of the problem setting for the resolution.

  In all the numerical simulations which follow, the dimensions of the bars are (in μm) 700 × 100 and the represented plane is a square of 750 μm side. These dimensions are given as a non-limiting indication and depend on the field size of the optical system. FIRST EXAMPLE OF PROCESS

  A first possible embodiment of a method according to the invention consists in minimizing a quadratic functional instead of directly solving equation (1).

  Preferably, the quadratic error between the measurements and the expected image is minimized. This method is called least squares method by the skilled person.

  Several different functionalities can be used in a least squares method.

  Preferably, it is sought to minimize the functional defined by: (3)! ImImLeelim ImELEB where Imt, L denote transpose of lm and L. Thus, according to the possible method, it is defined during an initialization step 20 that the starting image is null in the whole field of the detectors.

  We define an initial threshold. The threshold depends on the applications and the acquisition modules. In our example, it can be set to '/ 2. The following sequence is then repeated in loop: conjugate gradient descent known to those skilled in the art, image thresholding and zeroing of the image signals whose intensity is below the threshold lowering threshold.

  The loop stops after a certain number of iterations or when the reconstituted image is sufficiently resolved to be exploited by the means for processing and guiding the projectile.

  Of course, other gradient descent steps can be used in a method according to the invention. It may especially be a method of descent gradients simple or optimal step for example.

  Performing a thresholding of the image makes it possible to avoid the formation of parasitic signals on the image and to ensure a better convergence of the calculation.

  Lowering the threshold at each iteration of the calculation makes it possible to control the limit of the iterations.

  We can thus define the threshold s by (4) s = 1 / 2n where n is the number of the iteration.

  Figures 9A to 9D show the results of the first four iterations of a least squares method.

  In this example, the image is divided into 1600 pixels. The focal plane comprises two hot spots 91 and 92 of the same intensity and visible in particular in Figure 9D. The calculation takes into account signal processing, including the elimination of a low frequency component.

  Figure 9A is the reconstructed image after an iteration with a threshold equal to 1/2.

  Figure 9B is the reconstituted image after two iterations with a threshold equal to /.

  Figure 9C is the reconstituted image after three iterations with a threshold equal to 1/6.

  Figure 9D is the reconstructed image after four iterations with a threshold equal to 1/8.

  It can thus be seen that the calculation method allows a rapid convergence towards a reconstructed image of the scene.

SECOND EXAMPLE OF PROCESS.

  A second possible embodiment of a method according to the invention consists in using a resolution method of the maximization or minimization type of a functional under stress.

  This constraint makes it possible to choose an acceptable solution among an infinity of possible solutions to equation (1).

  There can indeed be an infinity of solutions during an underdetermination in the measurements.

  Such under-determination may occur when the measurements are of a limited number, ie when the bars are rapidly acquiring the scene, or when the measurements under certain incidences are not accessible or exploitable.

  A method of maximizing or minimizing a constrained functional can of course be used in all cases of acquisition.

  In a method of resolution under stress, one preferably uses a method of resolution of the type Algebraic Reconstruction Technique algebraic reconstruction technique or Multiplicative Algebraic Reconstruction Technique (MART) multiplicative algebraic reconstruction technique according to the terminology generally used by the man of career.

  Preferably, a method of the MART type is used.

  This method of resolution can be interpreted as a minimization or a maximization under stress with an entropic criterion.

  A method according to the invention converges the solution to a maximum entropy of the image with the constraint given by equation (1).

  In a method of the MART type, a set of measurements is corrected at each iteration to obtain a solution quickly.

  However, this set of measurements is only located at a given bar. Therefore, it is not corrected for each iteration of all the measurements on the image defined in FIG. 6A, which ensures the speed of the convergence.

  The set of measurements to be corrected is then moved at each iteration according to the displacement of the bar considered with respect to the scene.

  Of course, the steps of the previously described method for each of the bars are renewed.

  The principles of the MART method are described below.

  For each pixel k included in the strip considered, the correction of the image during the iteration n + 1 of the method is substantially performed by a multiplication of the image jn obtained at the pixel k after correction during an iteration n by the ratio of the signal Bn received by a given bar in this pixel k during the iteration n on the one hand to the signal Rn reconstituted over the entire bar given during the iteration n on the other hand. We therefore have an expression of the form: t / (k) _ (k) (5) 1 n + 1 j, nBn Rn where jn + is the image at pixel k at the iteration n + 1; 10 j (k) is the image at pixel k at the iteration nn L ,,, is an operator equal to 0 in the calculations involving coefficients of the matrix L not relating to a pixel included in the bar considered, and 1 in the calculations involving coefficients of the matrix L concerning a pixel included in the bar considered; Ânk is a coefficient for adjusting the convergence of the iterations by distributing the correction over all the pixels of the bar considered; and R. is defined by a relation of the type: 6) R = I Lnj I ,, l in which the index j of the summation indicates that we sum the Ln] on all the pixels j of the considered bar . Rn represents the signal that gives the image reconstituted on the bar considered.

  It is understood that when n denotes a matrix index, it describes the indices of each matrix cyclically, modulo the size of the matrix. The index n is thus not limited by the size of the matrices in the iterations.

  According to (6), equation (5) can also be written: (7) n + +1 = j (k). Bn Lnj'InJ) J / Znk makes it possible to carry out an averaging of the correction on all the pixels of the bar. This ensures a conservation of energy during the different iterations and the convergence of the iterative process is allowed. One can define / lnk by the expression: The iterations are stopped when a number of iterations is reached or when the reconstituted image is sufficiently resolved to be exploited by the means for processing and guiding the projectile.

  FIG. 10 thus shows the image of a pattern comprising remarkable patterns 100.

  Figure 11 shows the reconstructed image of the pattern of Figure 10 after about ten iterations of the process. It clearly distinguishes the reconstituted images 110 of the patterns 100.

  Other methods of solving the system of equation (1) are of course possible.

  NUMBER OF BARRETTES IN THE FOCAL PLAN.

  It is recalled that because of the limited size of the field of the image, and if we call D the diameter of the circular field in real space, the images undergo a convolution by a disk 50 whose diameter is 1 / D in the frequency space.

  Let us take the example of a sinusoid in real space, this sinusoid being seen by the disk of diameter D. Then the image of this truncated sinusoid is a disk of diameter 11D in the space of the frequencies.

  However, Figure 4 clearly shows that the high frequencies are less likely to be perceived by the sampling given by the lines 41 to 45 for example, since they are away from the center of the marker (Ofx, Ofy).

  Thus, the higher the frequencies, the less the convolution disk 50 is likely to be perceived by the sampling.

  With reference to FIG. 5A, the disk 50 is detected, in the worst case, when it is tangent to two straight lines at the same time.

  As a first approximation, we have the relation: (8) tan (-) 2D 1 f 1 ax where O is the angle between two successive bars; and f max is the maximum frequency that is detected.

  We have, by approximating the tangent at its angle: (9) 0 = 1 We want to have: (10) fmaxD to be able to observe more than one period of the sinusoid in real space. 1 must therefore be less than 1.

  f max.D Now, as we have by definition: (11) 0 = 2z, where n is the number of bars. n According to (10) and (11), 2 must be less than 1. n Therefore, n is preferably greater than or equal to 7.

  The device for implementing a method according to the invention thus preferably comprises seven strips 1 equally distributed, as shown in FIG. 5B.

f max D

Claims (1)

CLAIMS.   1. A method of reconstituting an image (1m) acquired by means of arrays (1) of detectors mounted on a projectile, characterized in that the vector representative of the image (1m) is reconstituted from the vector representative of signals (B) from the arrays (1) by solving the linear system such that: ImIm = B where L is the matrix taking the signals from each bar for all the pixels of the image.   2. Method according to claim 1, characterized in that it comprises the steps according to which: - the bars are numbered and the vector B is constructed by juxtaposing the signals received from each bar (1) according to the bar number; dividing in pixels the plane in which the bars are located, the pixels being situated at the intersection of lines and columns, and constructing the vector 1m by juxtaposing the lines of the plane thus divided; and each coefficient L, 1 of the matrix L is constructed by reporting in column for each current pixel the intensity of the digitized signal coming from each strip i for a hot spot centered on the pixel j, each line of L corresponding to one bar and each column to a pixel.   3. Method according to one of claims 1 or 2, characterized in that the resolution of the linear system uses a method of the type minimization of a functional quadratic.   4. Method according to claim 3, characterized in that the resolution method is a least squares method and in that the functional is of the type I Imel ELEIM ImEL.B where Im, L denote the transpose of lm and L 5. Method according to claim 4, characterized in that the least squares method comprises a step of: initialization according to which the image is canceled over the entire field of the bars; - definition of an initial threshold; and - looping consisting of performing: - a conjugate gradient descent, a thresholding of the image and a zeroing of the image signals whose intensity is below the threshold; and - a lowering of the threshold; the loop stopping after a certain number of iterations or when the reconstructed image is sufficiently resolved to be exploited by means for processing and guiding the projectile.   6. Method according to one of claims 1 or 2, characterized in that the resolution of the linear system uses a method of the type minimizing or maximizing a functional under stress.   7. Method according to claim 6, characterized in that the resolution method is a maximization of the entropy of the image with the constraint L É Im = B. 8. Process according to claim 7, characterized in that the method Resolution uses a MART multiplicative algebraic reconstruction technique.   9. Image recovery device, characterized in that it comprises detection strips and processing means adapted to implement the method according to one of claims there 8.   10. Device according to claim 9, characterized in that it comprises seven bars arranged radially relative to the axis of the device and not collinear with each other.