Unsupervised calibration process of a detector

Abstract

A method for determining parameters governing the transport properties of charge carriers in an ionizing radiation detector. The method involves irradiating the detector and simulating a propagation of charge carrier clouds toward electrodes of the detector, so as to compare the signal resulting from the simulation and the measured signal. This makes it possible to define an error, which is backpropagated to the location of the interaction in the detector. During the backpropagation, the charge carrier transport parameters are updated, so as to minimize the error. The propagation / backpropagation operation is iterative and continues until an iteration stopping criterion is reached.

Description

Title of the invention: Unsupervised calibration method for a detector Technical field

[0001] The technical field of the invention is the calibration of ionizing radiation detectors, for example X or gamma radiation, and in particular for spectrometric imaging. PREVIOUS ART

[0002] Gamma cameras are devices for forming an image to establish a map of irradiating sources in a given environment, and in particular in nuclear installations, for medical diagnostic applications, or for non-destructive testing applications, for example baggage control.

[0003] Some gamma cameras consist of a two-dimensional matrix of pixels, connected to a detector material. The detector material is generally a semiconductor material, for example CdTe or CdZnTe. Under the effect of an interaction of ionizing radiation in the detector material, one or more pixels generate an electrical pulse, the amplitude of which is correlated with the energy released by the radiation during the interaction. Each pixel is connected to an electronic circuit for processing the pulses.

[0004] Each pixel is formed by an electrode, which usually acts as an anode. When incident radiation interacts in the detector material, electrons are released in the detector material. The electrons are collected by an anode. The latter generates a pulse whose amplitude depends on the number of electrons collected by the anode, this number generally being proportional to an energy lost by the ionizing radiation in the detector material.

[0005] Each detector extends over a few hundred millimeters on each side. For reasons of compactness, the pixel matrix generally comprises one hundred, or a few hundred, pixels per row and per column.

[0006] CdZnTe, or CZT, is often used as a detection material in gamma cameras. Indeed, this material combines many advantages for use in imaging high-energy X-rays or gamma rays: - a high atomic number Z and density for an interesting absorption power of incident photons.; - a band gap width, wide enough to be used at room temperature, while being limited to keep the electron-hole pair creation energy Epaire fairly low. - interesting charge transport properties (lifetime r and carrier mobility p) in order to have the highest possible mean free path pr.

[0007] Much work has been done over the years to improve the composition, crystal growth, geometry and processing electronics around these detectors in order to optimize their performance.

[0008] Nevertheless, the use of CZT presents a main difficulty, which is the presence of different types of defects in the crystal lattice which modify the properties of the material and thus impact the output signals of the detector. These defects can be of different natures and sizes: Cd vacancies at the atomic scale, or sub-grain boundaries which can measure several cm in length. These defects, which appear during the growth of CZT crystals, hinder the development of larger volume detectors and generally degrade their performance, by producing a non-uniform response, varying from one pixel to another.

[0009] These defects cause intermediate energy states to appear in the band gap. When a carrier finds itself in one of these new energy states, it can either recombine or return to its initial state. The trapped carriers create space charges, which modify the electric field inside the detector. Trapping is non-uniform and has an impact on the uniformity of the electric field.

[0010] Indeed, these defects cause an error in the signals induced by the charge carriers and therefore in the signals collected on the electrodes which disturb the current measured at the output which is used as data making it possible to locate the source with the most precise resolutions possible.

[0011] Until now, the detector responses can be learned by implementing supervised algorithms, such as maximum likelihood or neural networks. But this requires having accurate data for each detector taken individually. Indeed, defects affect each detector differently. Thus, the implementation of a supervised algorithm requires having reliable data regarding the position of interactions in the detector and the energy deposited during each interaction. This assumes, for example, scanning a detector using a thin beam of photons, preferably monoenergetic. Such scanning is hardly feasible for systematically characterizing detectors during their manufacture.

[0012] The inventors propose a solution for performing unsupervised learning, so as to learn the response function of a detector, from of a less restrictive irradiation of the latter. By non-constraining irradiation, we mean an irradiation which is not necessarily collimated. The entire detector can be irradiated, in order to learn the response of the assembly formed by the detector material and the electrodes. This is to enable precise simulations of signals detected by the detector to be carried out, taking into account defects inherent in the use of a CdZnTe type detection material. Statement of the invention

[0013] A first object of the invention is a method for estimating a signal measured in a pixel of a detector, the detector comprising several electrodes, forming pixels, connected to a detector material, the detector material being a semiconductor, each electrode being configured to collect charge carriers moving, through the detector material, under the effect of an electric field, following an interaction of an X or gamma photon in the detector material, the method comprising: - irradiation of the detector with X or gamma photons, so as to generate interactions in the detector material, each interaction forming a detection signal measured by at least one electrode; - for different detected interactions, association of a state vector, comprising at least one position, one charge, and each detection signal, the state vector passing from an initial state when the interaction occurs, to a final state, when the electrons, generated by the interaction, are collected by at least one electrode;

[0014] the method being characterized in that it comprises, for each detected interaction: - (i) initialization of the initial state vector; - (ii) from the initial state vector, or from an initial state resulting from a previous iteration, implementing a model of propagation of the charge carriers in the semiconductor material, to estimate the final state vector, the propagation model being based on a vector of parameters, parameterizing at least one property of transport of the charge carriers through the detector material, towards the electrodes; - (iii) calculation of an error, representative of a difference between the detection signal estimated in the final state vector and the measured detection signal; - (iv) backpropagation of a gradient of the error from the final state to the initial state, the gradient of the error being calculated with respect to at least one term of the state vector, and with respect to several parameters of the parameter vector; - (v) updating the state vector, at the initial instant, and the vector of parameter, and repeating steps (ii) to (v) until a criterion for stopping the iterations is reached;

[0015] the method being such that steps (i) to (v) are implemented by a processing unit connected to the detector.

[0016] According to one possibility, the detector material is discretized into voxels, and the parameter vector comprises, for each voxel, a transport property of the charge carriers in the detector.

[0017] According to one possibility, the charge carrier transport property includes: - a value of the electric field; - and / or a gradient of the electric field in at least one direction; - and / or a value of a divergence of the electric field; - and / or a probability of trapping in the voxel.

[0018] According to one possibility, - steps (i) to (v) are implemented for different interactions, so as to update the parameter vector at each implementation of steps (i) to (v); - the parameter vector is then updated by combining the parameter vectors updated during each interaction.

[0019] According to one possibility, - for each interaction, the time between the initial state and the final state is discretized into time steps - step (ii) comprises a numerical integration of an evolution function (fg), the evolution function translating a temporal evolution of the position and the charge of the charge carriers, as well as an evolution of each detection signal, the numerical integration being carried out successively between each time step, between the initial state and the final state.

[0020] Step (iv) may comprise a numerical integration of an adjoint propagation equation, reflecting a time evolution of the error gradient, the numerical integration being carried out successively between each time step, between the final state and the initial state.

[0021] A second subject of the invention is a method for learning a supervised artificial intelligence algorithm, intended to simulate a response of a detector, the detector comprising several electrodes, forming pixels, connected to a semiconductor material, each pixel being configured to collect charge carriers moving, through the semiconductor material, under the effect of an electric field, following an interaction of an X or gamma photon in the semiconductor material, the method comprising the following steps: - a) definition of a position of an interaction in the detector and of an energy released during said interaction; - b) estimation of a detection signal measured by at least one electrode of the detector, by implementing the steps of a method according to the first subject of the invention; - c) repeating steps a) and b) so as to form a database linking, for each defined interaction, the signal measured in at least one pixel; - d) use of the database to perform supervised learning of the artificial intelligence algorithm.

[0022] The artificial intelligence algorithm can be of the multi-layer perceptron type.

[0023] A third object of the invention is a detector, comprising several electrodes, forming pixels, connected to a semiconductor material, each pixel being configured to collect charge carriers moving, through the semiconductor material, under the effect of an electric field, following an interaction of an X or gamma photon in the semiconductor material, the detector being connected to a processing unit, configured to implement steps (i) to (v) of a method according to the first object of the invention.

[0024] A fourth object of the invention is a detector, comprising several electrodes, forming pixels, connected to a semiconductor material, each pixel being configured to collect charge carriers moving, through the semiconductor material, under the effect of an electric field, following an interaction of an X or gamma photon in the semiconductor material, the detector being connected to a processing unit, configured to estimate an energy released by the interaction and / or a position of the interaction, the processing unit implementing a supervised artificial intelligence algorithm whose learning is carried out according to the second object of the invention.

[0025] The invention will be better understood upon reading the description of the exemplary embodiments presented in the remainder of the description, in conjunction with the figures listed below. FIGURES

[0026] [Fig.l] shows a diagram of a detector.

[0027] [Fig.2A] shows the main steps of a method for determining a response of a detector.

[0028] [Fig.2B] illustrates the steps discussed in connection with [Fig.2A].

[0029] Figures 2C and 2D show consideration of five or nine anodes in determining a collected charge.

[0030] [Fig.3] details certain operations described in connection with Figure 2.

[0031] Figures 4A to 4H show the performance of estimating the interaction depth by implementing the invention, during successive iterations.

[0032] [Fig.5A] shows a comparison between an estimation of interaction positions by implementing the invention, and the measured interaction positions.

[0033] [Fig.5B] shows a comparison between an estimation of interaction depths by implementing the invention, and the measured interaction depths.

[0034] Figures 5C and 5D correspond respectively to Figures 5A and 5B, with noise taken into account.

[0035] [Fig.6A] represents a measured mapping of a “CIE” quantity, which corresponds to a ratio between the collected charge and the deposited charge.

[0036] [Fig.6B] shows an estimated mapping of the CIE by implementing the method. PRESENTATION OF SPECIAL METHODS OF IMPLEMENTATION

[0037] [Fig.l] shows a diagram of a structure of a detector 1. The detector comprises a detector material 2, polarized between a cathode 3 and different anodes 4. The anodes are connected to a reading circuit 5, allowing the analysis of each detection signal formed at each anode.

[0038] Under the effect of an interaction in the detector material, charge carriers are created: electrons migrate towards the anodes, while holes migrate towards the cathode. In a semiconductor such as CZT, the differences in transport properties between electrons and holes make the exploitation of the electron signal much more interesting from the point of view of the detector's performance. Subsequently, only the transport of electrons through the detector is taken into account, knowing that the invention can also be applied to other types of charge carriers, for example holes. Each interaction gives rise to the formation of an electron cloud, migrating towards one or more anodes.

[0039] Each anode forms a pixel, allowing a measurement, following each interaction, of a detection signal. During an interaction, one or more anodes detect a pulse. From each pulse, a detection signal Sa is formed, which makes it possible to locate the interaction in the detector material. The detection signal may comprise one or more characteristics of the detected pulse, as described in US9322937. The index “ designates each anode having received a usable detection signal. The number of anodes having received a usable detection signal may vary between 1 and 9, or even more, as described below. For each interaction, an initial instant to is distinguished, which corresponds to the occurrence of the interaction, and an instant tb which corresponds to the collection of electrons by one or more anodes.

[0040]

[0041]

[0042]

[0043]

[0044] The collected charge Qb reaching the anodes allows to estimate the charge Qo deposited in the detector material during the interaction. We can assign, to each interaction, a state X of the charge carriers generated by the interaction, which varies between an initial state Xo, when the interaction occurs, and a final state Xb corresponding to the collection of charges by the anodes. The initial state Xo is characterized by the quantities (Qo ,x0, yo ,z0 , Sao), corresponding to the charge released by the photon in the detector, to the position of the interaction and to the signal induced at the electrodes during the interaction. The final state Xi is characterized by the quantities (Qi zi Xi, yi 5^9, corresponding to the charge collected at the anodes and the position of a centroid of the cloud of charge carriers reaching the electrodes, as well as to the signal induced on each electrode, the latter being able to be measured. Figure 1 shows field lines along which the charge carriers generated during the interaction propagate between the initial state Xo, an intermediate state X(t) and the final state Xb. For each interaction, one or more signals Sa are detected. Each charge carrier propagates through the detector according to transport properties p(r) that characterize the detector. In this example, the detector is made of CdZnTe: the charge carriers are therefore electrons. Alternatively, the charge carriers can be holes. Each voxel is assigned a coordinate (x' Z). Each voxel can result from a discretization of the volume of the detector material at a spatial step of 100 pm in each direction. Each voxel is associated with at least one transport property p^r), for example a value of the electric field and / or a trapping probability Hr)- or a characteristic representative of a spatial variation of the electric field, for example gradient or divergence. For example, each voxel r is assigned a property p(r), corresponding to the couple The spatial distribution of transport properties p(r), in each voxel, is parameterized by 6n parameters, forming a parameter vector 6. According to a first approach, each voxelr is associated with parameters Q^r)-p(r) = (w(r),r(r)), defined for each voxel. This assumes a definition of a parameter value for each voxel, which is restrictive from the memory size point of view: there are as many parameters as voxels. n is an integer between 1 and N, N corresponding to the number of parameters determined. According to another approach, the spatial distribution of parameters p(r) is parameterized by 0n parameters applied to a spatial function Fn(r) or a combination of spatial functions. For example, p(r) = V, 3tlFn(r)-

[0045] Each spatial function Fn(r) can be, for example, a sinusoidal or polynomial function. The use of spatial functions makes it possible to reduce the number of 3n parameters of the parameter vector

[0046] To summarize, each voxel is assigned at least one transport property of a charge carrier. The 0n parameters allow to define the spatial distribution of the transport properties in the voxels of the detector.

[0047] The parameter vector of a detector is unknown, in particular due to the presence of defects in the detector material, distributed randomly, which influence the transport of charges between the interactions and the electrodes which collect the charge carriers, i.e. the anodes in the case of electrons. It constitutes a signature, conditioning the response of the detector. For each detector, the values ​​of each are considered to be stable over time.

[0048] The parameter vector 0 makes it possible to establish an evolution function f making it possible to follow the state of the cloud of charge carriers generated by the interaction, from the initial state to the final state, and this for each interaction.

[0049] The reading circuit 5 is connected to a processing unit 6, configured to determine the set of parameters, from signals Sa respectively measured during each interaction, by implementing the steps described in connection with FIGS. 2A and 3. The processing unit 6 comprises in particular one or more microprocessors, programmed to implement the steps described below.

[0050] Figures 2A summarize the main steps of a method for learning the parameter set 0 governing the transport properties j / r) of the detector. The detector is exposed to an irradiation source, the emission energy or energies of which are known. Under the effect of the irradiation, interactions occur in the detector material 2. During each interaction, a detection signal Sa is measured by anodes. The index a designates each anode detecting a usable signal. The signal Sa and a vector formed by each detection signal formed by a single anode or several adjacent anodes, for example: - four anodes: these are the 4 anodes closest to the position of the electron cloud when the latter reaches the anodes; - five anodes: four electrodes around anode C having collected the highest quantity of charges, the latter being the collecting anode; - nine anodes: 8 anodes around the collecting anode.

[0051] During the irradiation, the detection signals Sa measured during the irradiation are collected. Each measured signal S, corresponds to a detected interaction. The iterative steps 100 to 150 are implemented for each detected interaction. Each interaction extends between the initial time t0 (occurrence of the interaction) and the final time ti (collection of charges by the anodes) previously defined.

[0052] Step 100: initialization: an initialized value of the initial state is estimated for each interaction. The position of the interaction can be defined randomly. The deposited energy Qo can be determined randomly, or as a function of a maximum energy defined according to the nature of the irradiation source.

[0053] Step 110: During this step, the state resulting from step 100 or from a previous iteration is propagated. This step is implemented using an evolution function / , described below, and parameterized with the parameter vector 0. The evolution function is described by a differential equation of type: 100541 ^=4x(0,t)(1)

[0055] Thus,

[0056] a _ a di m Ai— Ao+ ( A (?) )dt

[0057] The integral of expression (2) can be calculated numerically, step by step, for example according to a Runge-Kutta method.

[0058] Step 120: estimation of the final state Xi and calculation of an error, error calculation: during this step, an error function is determined between the estimated final state j) and the measured final state Xb. In the measured final state, there is an estimation of each signal measured at the electrodes, as well as a measurement of this signal.

[0059] _ II / ç l|2(3): error norm.

[0060] and

[0061] = Sa -Sa O'): this is the deviation from the observation.

[0062] Other expressions of the error norm can be considered.

[0063] Step 130: Backpropagation. From the deviation AXh, a deep learning algorithm of the N-ODE type is implemented, as previously mentioned, to obtain an error AX0 with respect to the initial state taken into account during step 100, and to update the latter. This phase, called backpropagation, involves a calculation of gradients of the error with respect to each component of the parameter vector, as well as with respect to the components of the state vector (spatial components x, etz, charges Q, signal or signals Sa). Backpropagation is carried out from the final state (instant ti) to the initial state (instant to), knowing that these instants are known.

[0064] Step 140: Calculation of deviation.

[0065] During this step, we calculate, for each interaction, a deviation AX0 to be applied to the initial state, as a correction term, so as to progressively minimize the error e. We also determine a deviation X6n for each term of the vector of parameters. Steps 100 to 140 are then repeated until an iteration stopping criterion is reached, for example a predetermined number of iterations or a threshold value of the error function below which it is considered that the parameter vector describes the behavior of the detector sufficiently well.

[0066] Step 150: Taking into account different interactions.

[0067] During this step, the parameters dn determined for different interactions are taken into account to estimate an average parameter vector 0n, or another statistical function, so as to allow a correction of the parameter vector by taking a large number of interactions.

[0068] [Fig.2B] illustrates the main steps of the process.

[0069] Steps 110 and 130, which are the bases of the method, are now described in detail. Step 110 is a propagation phase, aiming to estimate the state from a state estimated by successive integration of the evolution function f according to predetermined time steps.

[0070] In the final state: A _ / A aaacx / A ^0- yCtQ? -¾ Jp, *■()'^«-OH 7

[0071] In the final state: A / A aaa to e\(5)

[0072] Among the modeling hypotheses, we consider that: - the spatial distribution of electrons in the detector volume follows a spherical Gaussian distribution whose broadening is due to diffusion and Coulomb repulsion. The temporal evolution of the variance of this distribution is known., as described in the publication G. Montemont, S. Lux, O. Monnet, S. Stanchina, and L. Verger, “Studying Spatial Resolution of CZT Detectors Using Sub-Pixel Positioning for SPECT,” IEEE Transactions on Nuclear Science, vol. 61, no. 5, pp. 2559-2566, Oct. 2014, and more specifically in connection with Figure 2 of this publication - each primary photon will generate a certain number of secondary electrons depending on its energy, which can themselves generate secondary photons and so on. We can then schematize the interaction of a photon as being a series of very localized deposits separated by a large distance. Each of these deposition positions will generate an electronic cloud which will expand under the effect of thermal diffusion and Coulomb repulsion.

[0073] The evolution function is such that:

[0074]

[0075] Where: - r is the position of the centroid of the carrier cloud. It depends on time r - r(i) ■ the different terms / ( / ) represent a trajectory of the charge carrier cloud. - y — fiE corresponds to the velocity of electrons in the detector material and E is the electric field; " and E are voxelized data: y — ; - T is the lifetime of the electrons in the detector material: this is a quantity distributed spatially in the detector, therefore T = ; - Q is the total charge of the electron cloud: this is the charge integral of the charge carrier cloud at a time t, Q — This charge evolves as a function of the trapping of the carriers. - Sa is the signal of each anode of rank a; - 1 = index of spatial coordinates J = 1, 2 and 3 correspond respectively at the spatial coordinates x' y and ' - w is the weighting field of the detector, which corresponds to the gradient of the weighting potential, w is discretized at each anode, to each anode corresponding a vector Wa whose values ​​are defined for each voxel of the detector. In [Fig.l], the weighting field of an anode is schematized. Each dotted curve corresponds to identical values ​​of the weighting field.

[0076] The weighting potential is used to calculate the signal collected by an anode under the effect of a moving charge in the detector material. The weighting potential has no physical unit and represents the influence that an anode has on the signal induction as a function of the distance from the moving charged particle. The weighting potential is significant near each anode: near each anode, the electrons are subjected to the weighting potential, by which a detection signal is formed under the effect of the electrons moving. The weighting potential is considered to be invariant from one anode to another anode: it depends on the size of each anode, the space between two adjacent anodes and the thickness and permittivity of the detector material.

[0077] The spatial gradient of the weighting potential forms a weighting field in the vicinity of an anode. The value of the current collected at the anode depends on the product scalar of the weighting field and the electric field extending through the detector material.

[0078] Thus, at a time t, when the electron cloud extends according to a coordinate r(0 - (x y- z) in the detector, it induces, on each anode a, a signal 5a(t) such that:

[0079] Equation (6) corresponds to the time transport equation, allowing to simulate the drift of the electron cloud in the detector, so as to estimate from f is the time evolution function (or propagation function). The drift of the electron cloud is obtained by predetermined time increments, for example 1 ns or a few ns, knowing that given the usual dimensions of a detector, the duration of the propagation between the interaction and the detection is a few tens of ps

[0080] The propagation step consists of a numerical integration, from near to far of kind :

[0081] rT+dt (9) X(T + dt) = X(r)+J r fjÿdt

[0082] It is thus possible to estimate the evolution of the state of the electronic cloud between the initial and final instants A) and h, knowing that the latter are known. The integration can for example implement a Runge-Kutta integration method.

[0083] This allows us to obtain an estimate of y - an estimate of the position - an estimate of the load Q - an estimate of the detected detection signal knowing that the signal of measured detection Sa is known. Backpropagation

[0084] Backpropagation is the subject of sub-steps 131 to 133 of step 130.

[0085] Step 130 corresponds to a backpropagation of the term %* _ for each î)X interaction, between the final state (X = resulting from the measurements of Sa, and the initial state (X = Xo). This involves carrying out a backpropagation, from near to far of the errors q* _ and g* —relating to the position of the electron cloud and the charge respectively, between r= rA ,r = r» cl Q- QQ— Qq respectively. The backpropagation of the charge g* is carried out according to the expression (20)

[0086] The backpropagation of the error r* is carried out according to expressions (30) to (32).

[0087] Backpropagation of the error Q* relative to the parameter vector is performed according to expression (40).

[0088]

[0089]

[0090] = X(T) Generally speaking, if = , with £ = Il AX||2 3g of dr of dQ 4 T 0 0 0 u.^ U.W2 U.W3 U.W4 0 3¾ dx dUy dx du, d7 dfïlH'1) Q~^r diuw2) Q~dT d(u.ü^) Q~dT Q-ir 0 dttr dj dtly dy du? dy d(û.W ') Q~ir Q— â(îlHr3) Q~ Q— 0 d«, dz dlly dz dti^ dz" dz & dz. dfew3) U & (^U-W4) ™ dz Qdx z2dffi dux ddl dtly 30; dd[ du Ôd^-H'1 0(7 j Qdr dux 3¾ duy dt)N du, dd^ du — te?"'1 du 0¾ (10) de dQ d£ dx d£ dy de dz de as„

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] Expression (10) is a so-called adjoint propagation function of the evolution function. Backpropagation consists of backpropagating the errors, respectively explained according to the following expressions: Evolution of the charge of the electronic cloud: (sub-step 131) IM, V (20) dt\ dQ) ~ ~ T dQ + MzdSa \U^ / Position of the electron cloud (sub-step 132) £ f de \ _ / de dg 9«, de \ de (30) dt \ dx / \ dx dx dx dy dx dz / \iL^a dx dS„ d / df 1 _ / du^ d£ duy dg dtfj \ y 9½¾^) d£ (31) A ( dy / ~ \ dy dx dy dj' dy dz / ' dy dSH d ( dg \ / dwx de dify d£ du^ g£ 1 9(¾^). (32) dt \ dz / \ dz dx dz dy dz dz / d- dS„ Parameter vector (substep 133) _ A / _ / dux de , dg , 9«; dg , ^g du , dg Qd? (40) \ dt)n / ( d()n dx "1” dOn dy d()n dz ^^adSa dd„ / + dQ r^d9„ Sub-steps 131 to 133 are implemented by successive integration, according to time steps dt as described in connection with the propagation step, according to the expressions: (r-jt) =^(T) Jr^( (21)

[0100] _ 3e fr / 9¾ 9¾ 9 g 9¾ 9e ] . nV 9 e 9x V1 ~ dx / 'h-dA dx ' 9x + 9x ' 9y + 9x * dz / + vZ-« 9X 9S„ (33)

[0101] 9g / r A . _ 9e ( T. fr / 9¾ dg 9¾ 9g 3¾ 9g \ ny 9(^) de dy -^) - dy v1 ) ^T-dA dy ' dx + dy ' dy + 9y ' dz / + V<^a dy 9SK (34)

[0102] 9e zt ,, _ 9g , T fr / 9¾ 9g 9¾ 9e 9 e ] ^y 9e 9z 11 ~at> ~ dz { / 1 'h-dA dz ' dx + 9z ' 9y + dz ' dz / dz dSa (35)

[0103] 3e / T .j / ] 3c / Ti [r / ' fK 3 e _._ 9,1 y 3ô„r '“y Ç Hr-tfA 3¾ ' 3x + 93„

[0104] On connaît A Sa = Sa-S„= — • 95« 3 g 3«; 3v ' 3#„ 3£, oy . (41) 3z + d0„ W + dQ t^Üu 'at

[0105] Les expressions (21), (33), (34), (35) et (41) permit une rétropropagation between the instants ti and t0, which are known because they are defined during propagation. These expressions can be combined with:

[0106] 9e _y 9s 95Q = y « ç 2^4 (22) dQ ~ *- <adSa dQ A ô«9g

[0107] 9e _ y 9 e 3S„ = y.„ds„ (36) dx — 9So 9x ka dx

[0108] 9e _ y 0E = y 9Sg (37) 9y — ^adsa dy dy

[0109] 9th _ y, 9th. 95« = y * ç (38) dz — ^adSa dz. a dz

[0110] 9E_y A ç A e < (42) den - A to«den A 3«90„

[0111] We thus obtain expressions allowing us to carry out backpropagations, expressing the dependence of the signals Sa on the different parameters: those of the event Q,x,y,z and those of the detector 0:

[0112] Evolution of the charge of the electronic cloud:

[0113] dSu 19^,-^(23) Position of the electron cloud

[0114] 9s“ _ / 9¾ 9^2 3¾ dSa \ ^ux^) (39) dx — \ dx dx dx dy dx dz / dx

[0115] ay / 9¾ 95“, duy dsa, 9¾ 35"), (39') dy — (dy ' dx dy dy + dy ' dz ) + dx

[0116] 95“ _ / 9¾ 95“ 9¾ as£ 9¾ 95" ) (39") dz \ dz dx dz dy dz dz / dx Parameter vector

[0117] ay_ / 9¾ asa 9¾ r A as" nda ^.a\ dsu &t (43) ■ den - V dd„ ■ dx + 93,, ■ 9y + ddn ■ dz + ^9¾ 'W / + dQ Update step

[0118] During step 140, an update of the initial state Xü is carried out. This step consists of determining deviations AQ (sub-step 141), Ar(Ar=(Ax, A / , Az)) (sub-step 142), A 0 (formed of correction terms A 0W) (sub-step 143) and this for each interaction.

[0119] The update can be carried out according to the diagonal Gauss Newton method: see expressions (50) to (54).

[0120] IM <50> y7 -

[0121] A x = y 2 (51)

[0122] Aj = SM (52)

[0123] Az = y 2 dz (53)

[0124] A (4 = they -y " (54)

[0125] When updating,

[0126] Xo= Xo+ AXo(6O)

[0127] So, in this example: *0*" x0+ Ax; jQ+ Ay0; z{)^ z0+ 9n^ 9n+ A0„(61)

[0128] During a step 150, the correction terms A 0n defined during the implementation of the method for several interactions, typically several hundred, are taken into account to form an average correction vector Ô. The average correction vector is formed from an average of the parameters 9„ defined for the interactions.

[0129] During this step, we can take criteria other than an average of the correction terms to form the correction vector Ô, for example a median.

[0130] The method previously described has been implemented. Figures 4A to 4H represent the estimation of the interaction depth in the detector, for different modeled interactions, for eight successive iterations. Each point corresponds to an interaction. The abscissa axis corresponds to the modeled depths while the ordinate axis corresponds to the depths estimated by the algorithm. The initial depths are chosen randomly (see [Fig.4A]). It is observed that after eight iterations, the estimated depths are consistent with the modeled depths.

[0131] Figures 5A and 5B respectively represent an estimate of the interaction positions along an X axis, parallel to the anodes, and along the depth (Z axis). These figures were obtained by taking into account 32768 interactions of photons with energy 122 keV on a detector comprising 2x2 anodes.

[0132] Figures 5C and 5D are equivalent to Figures 5A and 5B, but with consideration of realistic noise at energy 122 keV.

[0133] In another series of tests, the CIE (charge induction efficiency) was simulated, which represents the ratio, normalized to 1, between the charge collected and the charge deposited by a photon during an interaction. A detector formed of 2 x 2 anodes was taken into account. [Fig.6A] shows a CIE measured by scanning the detector with a collimated beam, with a beam of energy 122 keV. [Fig.6B] shows a CIE simulated by implementing the invention. It is observed that the simulation is consistent with the measurements.

[0134] The method thus allows a precise estimation of the response of a detector.

[0135] It is also possible to estimate the response of a detector using a supervised learning neural network type algorithm. The use of such an algorithm requires less computing power than the method that is the subject of the invention. However, a neural network requires a supervised learning phase. The invention cited as the subject can be used to carry out supervised learning of a neural network, replacing tedious experimental tests, because they require control of the position of the interactions in the detector material.

[0136] The invention makes it possible to generate interactions at any location of the detector and to estimate the detection signal on one or more anodes. It can therefore be used to define learning sets, associating data linked to an interaction in the detector (position in the detector and energy) and the signals induced at different anodes.

[0137] The neural network may be of the multi-layer perceptron type, comprising: - as input layer: at least one characteristic of the signal from the anode having collected the maximum signal (collecting anode) and of the anodes neighboring the latter; For example, the maximum signal from the collecting anode and the maximum signal from anodes neighboring the collecting anode may be taken into account; - as output layer: the position of the interaction in the detector, in two or three dimensions, as well as the charge released during the interaction: thus, the output layer is formed of 3 or 4 nodes.

[0138] Between the input layer and the output layer, the neural network may comprise, for example, 3 interconnected layers, with 16 nodes per layer. Such a neural network allows correct modeling of a detector

[0139] The input layer advantageously comprises, for each anode, a characteristic normalized by the same characteristic of the anode having collected the maximum signal. The characteristic can be a maximum amplitude or an amplitude of a transient signal. In this case, the output layer is multiplied by the normalization term so as to estimate the energy. An example of a neural network is for example described in Yang et al “Joint extimation of interaction position and energy deposition in semiconductor SPECT imaging sensors using fully connected neural network”. In this publication, the neural network is the subject of supervised learning, using experimental data.

[0140] Such a neural network can easily be coded on a compact electronic card, of the FPGA (Field Programmed Gated Array) type. The advantage is to use a relatively simple neural network to model the response of the detector, the implementation of which does not require a complex component. The training of the neural network is carried out simply, in particular by simulations, using the method as previously described.

[0141] Although described in connection with an X or gamma photon detector, the invention can be applied to other types of ionizing radiation, for example α, β or neutrons.

Claims

Claims

1. Method for estimating a signal measured in a pixel of a detector (1), the detector comprising several electrodes (4a), forming pixels, connected to a detector material (2), the detector material being a semiconductor, each electrode being configured to collect charge carriers moving, through the detector material, under the effect of an electric field, following an interaction of ionizing radiation in the detector material, the method comprising: - irradiation of the detector with X or gamma photons, so as to generate interactions in the detector material, each interaction forming a detection signal (Sa) measured by at least one electrode; - for different detected interactions, association of a state vector (X), comprising at least one position (x' & z), a charge (Ô), and the detection signal (Sa), the state vector passing from an initial state (Xo) when the interaction occurs, to a final state J, when the electrons, generated by the interaction, are collected by at least one electrode; the method being characterized in that it comprises, for each interaction detected: (i) initialization of the initial state vector (£ ); (ii) from the initial state vector, or from an initial state resulting as of a previous iteration, implementation of a model of propagation of charge carriers in the material semi-conductor, to estimate the final state vector (^-), the propagation model being based on a very parameter vector (#), parameterizing at least one transport property ( p(r)' w(r)' Kr)) of the charge carriers through the detector material, towards the electrodes; (iii) calculation of an error (s), representative of a difference between the 1st detection signal estimated in the final state vector (5) and the measured detection signal (Sa); - (iv) backpropagation of a gradient of the error (M , 32' dx àe te 3e j the final state towards the initial state, the gradient of 1' dy ' dz 30 / error being calculated with respect to at least one term of the state vector, and (||) with respect to several parameters of the parameter vector; - (v) updating of the state vector (xQ), at the initial instant, and of the parameter vector, and reiteration of steps (ii) to (v) until a criterion for stopping the iterations is reached; the method being such that steps (i) to (v) are implemented by a processing unit connected to the detector.

2. Method according to any one of the preceding claims, in which the detector material is discretized into voxels, and in which the parameter vector comprises, for each voxel, a property Q^r)' r(r)) of transport of charge carriers in the detector.

3. Method according to claim 2, in which the charge carrier transport property comprises: - a value of the electric field; - and / or a gradient of the electric field in at least one direction; - and / or a value of a divergence of the electric field; - and / or a probability of trapping in the voxel.

4. Method according to any one of the preceding claims, wherein - steps (i) to (v) are implemented for different interactions, so as to update the parameter vector at each implementation of steps (i) to (v); - the parameter vector is then updated by combining the parameter vectors updated during each interaction.

5. Method according to any one of the preceding claims, in which - for each interaction, the time between the initial state and the final state is discretized into time steps - step (ii) comprises a numerical integration of an evolution function (f the evolution function translating a temporal evolution of the position and the charge of the charge carriers, as well as an evolution of each selection signal, the numerical integration being carried out successively between each time step, between the initial state and the final state.

6. Method according to claim 5, in which step (iv) comprises a numerical integration of an adjoint propagation equation, reflecting a temporal evolution of the error gradient, the numerical integration being carried out successively between each time step, between the final state and the initial state.

7. A method for learning a supervised artificial intelligence algorithm, intended to simulate a response of a detector (1), the detector comprising several electrodes, forming pixels, connected to a semiconductor material, each pixel being configured to collect charge carriers moving, through the semiconductor material, under the effect of an electric field, following an interaction of ionizing radiation in the semiconductor material, the method comprising the following steps: - a) defining a position of an interaction in the detector and an energy released during said interaction; - b) estimating a detection signal measured by at least one electrode of the detector, by implementing the steps of a method according to any one of the preceding claims;- c) repeating steps a) and b) so as to form a database linking, for each defined interaction, the signal 1 measured in at least one pixel; - d) using the database to carry out supervised learning of the artificial intelligence algorithm;

8. Method according to claim 7, in which the artificial intelligence algorithm is of the multi-layer perceptron type.

9. Detector (1), comprising several electrodes, forming pixels, connected to a semiconductor material (2), each pixel being configured to collect moving charge carriers, through the semiconductor material, under the effect of an electric field, following an interaction of ionizing radiation in the semiconductor material, the detector being connected to a processing unit (6), configured to implement steps (i) to (v) of a method according to any one of claims 1 to 6.

10. Detector, comprising several electrodes, forming pixels, connected to a semiconductor material (2), each pixel being configured to collect charge carriers moving, through the semiconductor material, under the effect of an electric field, following an interaction of ionizing radiation in the semiconductor material, the detector being connected to a processing unit (6), configured to estimate an energy released by the interaction and / or a position of the interaction, the processing unit implementing a supervised artificial intelligence algorithm whose learning is carried out according to any one of claims 7 or 8.

Images