Method for locating irradiated areas

Abstract

Method for locating irradiating points, with a measuring device, comprising: a detector (10), a measuring circuit (12), configured to determine a number of pulses detected by the detector; the method comprising: acquisition of measurements () facing the object, each measurement corresponding to a measurement position () and an orientation of the detector (); formation of an observation vector () from the count rates extracted from the measurements; selection of a number of irradiating points () in the object; initialization of a parameter vector (), comprising a position () of at least one irradiating point; updating of a direct matrix model, relating an estimate of the observation vector () to an intensity vector (); inversion of the direct model and updating of the parameter vector () and the intensity vector (); repetition of the last two steps.

Description

Title of the invention: Method for locating irradiated areas technical field

[0001] The technical field of the invention is spectrometry applied to the detection of ionizing radiation and the localization of irradiated areas emitting ionizing radiation. It essentially involves X-ray or γ-spectrum spectrometry. PRIOR ART

[0002] In nuclear facility equipment, radiological activity is not evenly distributed. It is generally concentrated in areas commonly referred to as "hot spots." The intensity and location of these hot spots are generally unknown, as they depend on the operating history of the nuclear facility. However, when conducting a radiological inventory of a nuclear facility, it is useful to know, as accurately as possible, the location of the hot spots and their respective activities.

[0003] Since the 1990s, gamma cameras have been developed, inspired by imagers used in the medical field. These devices produce images that can be used to create maps within nuclear facilities. The objective is to remotely locate and identify the main radiation sources present in a facility. The development and uses of gamma cameras have been extensively described in the literature. Since the early 2000s, spectrometric gamma cameras have been developed. These cameras are based on a pixelated imager, with each pixel providing a spectrum of the radiation it detects. This represents a considerable improvement in the localization of radiation sources.Indeed, the spectrometric function allows the selection of energy bands of interest, corresponding to unscattered photons, that is to say, photons that have not been deflected since their emission by the irradiation source.

[0004] These are high-performance but rather expensive devices. Their sensitivity may be insufficient when the activity is due to weakly γ-emitting isotopes, for example, plutonium isotopes. Thus, gamma cameras may have insufficient sensitivity for performing checks aimed at accurate nuclear material accounting or criticality risk assessment. A typical example is the quantification of nuclear material accumulation in a glove box, for example, in nuclear fuel fabrication facilities.

[0005] Currently, gamma cameras allow for an estimation of the dose generated by each detected hotspot. However, if it is desired to estimate the activity of the detected hotspots, it is necessary to use modeling methods. This It requires certain modeling assumptions, as well as a certain level of expertise. It is understood that estimating hotspot activity relies heavily on user experience.

[0006] The invention described below makes it possible to locate and quantify the activity of hotspots using a simple measuring device. It is particularly suited to installations with low irradiation from gamma emitters with low emission intensity. It is also suitable for environments with constrained access, particularly cluttered environments. Beyond the nuclear sector, the invention can also be applied to hotspot detection for other types of applications, for example, in the medical field. Description of the invention

[0007] A first object of the invention is a method for locating irradiating points in an object, each irradiating point emitting gamma photons at least one emission energy, the method employing a measuring device, the measuring device comprising: - a detector, configured to detect gamma photons, and to generate a pulse upon each detection; - a measurement circuit, configured to determine a number of pulses detected;

[0008] the process comprising the following steps: a. acquisition of measurements facing the object, each measurement corresponding to a measurement position and an orientation of the detector, the measurements being acquired by placing the detector in different measurement positions and / or different orientations; b. processing of measurements, by the measurement circuit, in order to extract counting rates; c. formation of an observation vector from the count rates extracted during step b); d. selection of a number of radiating points in the object; e. initialization of a parameter vector, including a position of at least one radiating point located in the object; f. from the initialized parameter vector resulting from e), or from the parameter vector resulting from a previous iteration, updating of a direct matrix model, linking an estimate of the observation vector to an intensity vector, the intensity vector including an estimate of the intensity of each irradiating point; g. inversion of the direct model, using an optimization algorithm, so as to update the parameter vector and the intensity vector; repeating steps f) and g) until an iteration stopping criterion is reached, so as to obtain, following the last iteration, an estimate of the parameter vector and the intensity vector corresponding to the number of irradiating points selected.

[0009]

[0010] According to one embodiment, known as spectrometric: the measurement circuit is a spectrometric measurement circuit, configured to form a spectrum, the spectrum corresponding to a number of photons detected in different channels, each channel corresponding to an energy of the detected photon; the measurement circuit includes a spectrometry unit, configured to identify at least one emission peak on the spectrum formed by the spectrometric measurement circuit, each emission peak extending around an emission energy; The process can be such that: in step a), each measurement is a spectrum; Step b) involves processing spectra, by the spectrometry unit, in order to extract count rates from each emission peak.

[0011] According to one possibility, in step g), the inversion involves a minimization of a cost function, the cost function quantifying a difference between the estimation of the observation vector obtained during step f); the observation vector formed in step c).

[0012] Step g) can be performed by a maximum likelihood algorithm.

[0013] According to one possibility: steps d) to h) are repeated taking into account, during each iteration of steps d) to h), different numbers of irradiating points; the process includes determining a validity indicator associated with each iteration of steps d) to h), the validity indicator being associated with the number of irradiating points selected during each iteration; The process involves estimating the most probable number of irradiating points based on different validity indicators respectively associated with different numbers of irradiating points.

[0014] The validity indicator can be an Akaike information criterion.

[0015] According to one possibility, the direct model comprises a response matrix, formed by a Hadamard product between at least: a distance matrix, representing the respective distances between each measurement position and the position of each radiating point, where each term comprises the square of the distance between a measurement position and a position of an irradiating point, the position of each irradiating point forming a parameter of the direct model; - an efficiency matrix, reflecting the efficiency of the detector, where each term corresponds to a detection efficiency of the detector for a position and orientation of the detector and for a position of a point irradiating at least one emission energy.

[0016] The direct model may include a response matrix, formed by a Hadamard product between at least: - a distance matrix, translating the respective distances between each measurement position and the position of each irradiating point, each term of which includes the square of the distance between a measurement position and a position of an irradiating point, the position of each irradiating point forming a parameter of the direct model; - an efficiency matrix, reflecting the efficiency of the detector, where each term corresponds to a detection efficiency of the detector for a position and orientation of the detector and for a position of an irradiating point.

[0017] The response matrix can be formed from a Hadamard product between the distance matrix, the efficiency matrix and an attenuation matrix, the attenuation matrix representing an attenuation of the photons emitted by each irradiating point in the object, each term of the attenuation matrix having an attenuation factor, at an emission energy, between a position of an irradiating point and a position of the detector, each attenuation factor forming a parameter of the direct model.

[0018] Step e) may include - el) from the observation vector resulting from c), calculation of an observation vector in the absence of attenuation in the object; - e2) estimation of the observation vector in the absence of attenuation in the object using a direct model including the distance matrix and the efficiency matrix; - e3) inversion of the direct model, so as to estimate a parameter vector initialized and an initial activity vector, taking into account the number of irradiating points considered in step d).

[0019] According to one possibility: - for the same number of irradiating points selected in the object, steps e) to h) are repeated; - the process includes a comparison of the cost functions resulting from each step g) of each iteration of steps e) to h), the parameter vector and the intensity vector, for the number of irradiating points se selected, being those corresponding to the minimum cost function.

[0020] According to one possibility, step g) comprises: - gl) application of a gradient descent algorithm to estimate the parameter vector, based on the initial activity vector or the vector resulting from a previous iteration, - g2) application of an inversion algorithm to estimate the vector of activity, using the parameter vector resulting from gl).

[0021] According to one possibility, for the same number of selected irradiating points, the method comprises: - a first series of iterations of steps e) to h), using a direct model in which the response matrix is ​​constituted by a Hadamard product of the distance matrix and the sensitivity matrix of the detector; - a second series of iterations of steps e) to h), using a direct model in which the response matrix is ​​formed by a Hadamard product of the distance matrix, the detector sensitivity matrix and the attenuation matrix; - The position and activity of the irradiating points resulting from the first series of iterations is used to initialize the inversion of the forward model in the first iteration of the second series of iterations.

[0022] According to one embodiment, step b) involves selecting at least one emission energy of a predetermined isotope. The count rates are thus extracted for each selected emission energy. Steps b) to h) can be implemented by successively selecting, in each step b), at least one emission energy of different isotopes.

[0023] Following step h), the process may include an estimation of a dose rate at at least one measurement point, from the intensity vector and the parameter vector resulting from said step h).

[0024] According to one possibility, the process comprises: - updating the distance matrix and the efficiency matrix, based on the parameter vector resulting from step h); - taking into account mass absorption coefficients at at least one emission energy; - estimation of the dose rate at each measurement point from the distance matrix, the efficiency matrix and the absorption coefficients.

[0025] In the spectrometric embodiment, the dose rate can be estimated, at each measurement point, for different emission energies corresponding respectively to different peaks on the spectrum formed at each measurement.

[0026] A second object of the invention is a device configured to estimate a position of radiating points in an object, the device comprising: - a detector, configured to detect gamma photons, and to form, at each detection, a pulse, the detector being mobile around the object, so as to be able to be arranged in several positions and / or according to different orientations with respect to the object; - a measurement circuit, configured to determine the number of pulses detected by the detector; - a processing unit, programmed to implement steps c) to h) of a process according to the first object of the invention from the number of pulses detected by the measurement circuit.

[0027] According to one possibility: - the measurement circuit is a spectrometric measurement circuit, configured to form a spectrum, the spectrum corresponding to a number of photons detected in different channels, each channel corresponding to an energy of the detected photon; - the measurement circuit includes a spectrometry unit, configured to identify emission peaks on the spectrum formed by the spectrometric measurement circuit.

[0028] A third object of the invention is a support, which can be connected to a computer, comprising instructions for implementing steps c) and e) to h), possibly d), of a method according to the first object of the invention from counting rates resulting from measurements made using a gamma photon detector around an object.

[0029] The support can be integrated into a computer or connected to a computer by a wired or wireless link.

[0030] The invention will be better understood upon reading the description of the exemplary embodiments presented later in this description, in connection with the figures listed below. FIGURES

[0031] Fig. 1A represents an example of a device enabling implementation of the invention, according to a first embodiment.

[0032] Fig. 1B shows different positions or orientations of the device, according to the first embodiment around an object studied.

[0033] Fig. 2A represents an example of a spectrum.

[0034] Fig. 2B represents the spectrum shown in Fig. 2A after energy calibration.

[0035] [Fig.2C] is a detail of [Fig.2A].

[0036] [Fig.2D] is a detail of [Fig.2B].

[0037] Figure 3A shows the main steps of a process implementing the invention.

[0038] Figure 3B shows steps according to which a vector of parameters then an activity vector, during each iteration.

[0039] Fig. 3C illustrates steps allowing initialization of each iteration, when several numbers of radiating points are successively taken into account.

[0040] Fig. 3D illustrates steps allowing estimation of a dose rate from identified irradiating points.

[0041] Fig. 4 schematically represents an efficiency curve of a detector.

[0042] Fig. 5 illustrates the performance of an estimation of a term of an observation vector, corresponding to the energy 129.3 keV, without taking into account screens in the object.

[0043] Figure 6 illustrates a second embodiment of the invention.

[0044] Figures 7A and 7B illustrate an example of application on a glove box. In [Fig.7A], the counting rates of the observation vector are shown, in an energy band, for different positions of the detector.

[0045] Fig. 7B shows an estimate of the distribution and mass of matter from different irradiating points in the glove box. PRESENTATION OF SPECIFIC IMPLEMENTATION METHODS

[0046] Figure 1A shows a device 1 for implementing the invention, according to a first embodiment, referred to as the spectrometric embodiment. The device is a measurement system comprising a detector 10, capable of interacting with ionizing radiation 5 emitted by an object 2. Object 2 is a glove box, which may contain various irradiating points (or hot spots) 3 distributed within the glove box. The activity of each irradiating point, as well as their distribution, is unknown. The invention can be applied to any type of object used in a nuclear installation, such as civil engineering structures, waste packages, and various components. The invention can also be applied outside the nuclear field, for example in the medical field, for instance, to locate and quantify the activity of a radioactive isotope administered to an individual's body.

[0047] In the example shown in Figure IA, the glove box has an area containing various components. The irradiating points 3 are located in the area 4 and at floor level of the glove box. The position of each irradiating point in an XYZ coordinate system associated with the object under study is denoted by nn. The index n is an integer, l <n< N qui permet d’identifier chaque point irradiant. A correspond au nombre de points irradiants. Généralement, N est inconnu. Un objectif de l’invention est de déterminer la position et l’activité 0n de chaque point irradiant.

[0048] It is assumed that the irradiating radionuclides likely to be present in a measured object are known beforehand. If not, they can be determined by The spectrometry unit. In particular, a list can be compiled containing 2j irradiating radionuclides potentially present in the analyzed object. The subscript j designates each irradiating radionuclide. The list of radionuclides, and their relative proportions, is assumed to be known, and forms a typical spectrum.

[0049] Failing that, and this is the option described in the following example, the process is implemented radioisotope by radioisotope.

[0050] In the example shown, the detector comprises a semiconductor material, of the Germanium (Ge) type, but it could also be another material, scintillator or semiconductor commonly used for the detection of ionizing photons, for example of the Si, CdTe, CdZnTe, LaBr3, or Nal type, or even gaseous detectors, of the ionization chamber type.

[0051] Regardless of the detector used, it allows the collection of a quantity of charges Q under the effect of an energy E released by the ionizing radiation during an interaction in the detector 10. By ionizing radiation, we mean X-ray or gamma-ray photon radiation, made up of photons whose energy is, for example, between 1 keV and 2 MeV.

[0052] The detector 10 is connected to a measuring circuit 12, configured to generate a pulse whose amplitude depends on, and is preferably proportional to, the amount of charge collected during an interaction. The amount of charge corresponds to the energy deposited by the radiation during the interaction.

[0053] The measurement circuit 12 includes a spectrometry unit 13, which aggregates all the pulses formed during an acquisition time. Each pulse corresponds to an interaction of the incident radiation with the detection material. The spectrometry unit 13 then classifies the pulses according to their amplitude Amp, to provide a histogram showing the number of detected pulses as a function of their amplitude. Such a histogram is an amplitude spectrum. It is usually obtained using a multichannel analyzer. Each amplitude is discretized into channels, with each channel assigned an amplitude band. The value of each channel in the spectrum corresponds to a number of pulses whose amplitude lies within the amplitude band assigned to the channel. Each amplitude band corresponds to an energy band, the correspondence being bijective. Thus, each channel is assigned either an energy band or an amplitude band.

[0054] The relationship between amplitude and energy can be established by irradiating the detector with a calibration source emitting radiation of known energy. In particular, this radiation must exhibit at least one discontinuity, or energy peak, at a known energy value. This operation is usually referred to as energy calibration. For example, in the context of spectrometry For gamma rays, the detector is exposed to a 152Eu calibration source, producing photons with known emission energies. Alternatively, a 137Cs source can be used, producing mostly photons with an energy of 661.6 keV. A 60Co source, producing photons with energies primarily of 1173 keV and 1332 keV, can also be used. Energy calibration can be performed as described in WO2023126509.

[0055] The spectrometry unit is configured to form an energy spectrum from the pulses generated in the processing circuit 12. The spectrometry unit is also configured to perform spectrum processing operations, for example, peak detection and determination of a spectral value at each peak. These operations are described in more detail with reference to Figures 2A to 2D.

[0056] The device includes a processing unit 14, programmed to implement algorithm steps described below, in connection with figures 3A to 3D, in order to locate each radiating point and to estimate their respective activities.

[0057] In the example shown, the detector 10 is connected to a cryostat 18, containing liquid nitrogen to maintain the detector Ge at an operating temperature. The detector 10 is surrounded by a shield 16, so as to limit the influence of radiation emitted outside an observation field Q of the detector 10. In [Fig. 1A], the limits of the observation field Q are represented by two dashed lines.

[0058] An important aspect of the invention is that the detector 10 is moved at various measurement points around the object 2 under study. In [Fig. 1A], each measurement point is marked by a cross. Each measurement point corresponds to a position occupied by a reference point of the detector 10, for example, the center.

[0059] Figure IB shows the detector 10 positioned at several measurement points around the object 2 under study. At each measurement point, the detector is oriented along one or more orientations. Subsequently, each measurement is identified by an integer m. Each measurement is performed at a position Pm and an orientation am. Each position Pm and each orientation am have three coordinates, respectively spatial and angular, in the XYZ frame associated with the object under study 2.

[0060] Figure 2A shows an example of a spectrum. The x-axis represents the amplitude, discretized into amplitude channels, and the y-axis represents the number of pulses counted at each amplitude during spectrum acquisition. Figure 2B shows the same spectrum after energy calibration. Each amplitude channel is assigned an energy value.

[0061] Some commercial software allows for automatic peak detection and estimation of the intensity of the detected peaks. Estimation of intensity refers to estimating the area of ​​each peak. Figures 2C and 2D Figures 2A and 2B illustrate the extraction of a peak surface area within a region of interest, delineated by a box. In Figures 2C and 2D, the peak surface area is extracted "above" the background noise, which is represented by a dashed line. The extracted surface area corresponds to the peak intensity at the peak's emission energy, the latter corresponding to the peak's x-coordinate. Document WO2023126508 describes a method for automatically extracting a peak surface area as an alternative to currently available commercial software.

[0062] Compared to gamma cameras, an advantage of using a non-pixelated spectrometric device is that the detection volume can be large. For example, on the order of 1 inch in diameter and 1 inch in height, or even larger for a LaBr3-type detector. The use of germanium-type detectors allows for even larger volumes. This provides good measurement sensitivity. It is thus possible to address low levels of irradiation, which is particularly suitable for low-radiating emitters, such as certain Pu isotopes. This also makes it possible to address low activity levels for strong gamma-emitting isotopes, for example, 137Cs or 60Co.

[0063] The high detection volume can be combined with the use of long acquisition times, for example several tens of seconds, or even several minutes or tens of minutes. This makes it possible to obtain very good detection sensitivity, especially since spectrometry allows the selection of peaks at certain energies, previously determined.

[0064] The main steps of a detection process are described in relation to [Fig.3A].

[0065] Step 100: Positioning the detector in a position Pm and a measurement orientation am around the object. Thus, each measurement m is associated with a position Pm and a measurement orientation am.

[0066] Step 110: Acquisition of an Sm spectrum

[0067] Steps 100 and 110 are repeated so as to obtain M measured spectra. Each measured spectrum Sm is associated with a measurement position or orientation.

[0068] Step 115: Extraction of Making peaks.

[0069] During this step, the spectrum is analyzed by the spectrometry unit so as to extract an area from each peak. A counting rate is determined for each peak, corresponding to the number of pulses detected in the peak, divided by a unit of time. This allows the formation, for each measurement m, of a vector S'm, of dimension L, each term of which is an area of ​​a peak detected by the spectrometry unit at an emission energy.

[0070] Each energy corresponds to a radioisotope, emitting a photon at said energy according to a branching ratio z' / , where / is an index denoting the energy, h is a number of photons emitted for an activity of 100 Bq of the radioisotope.

[0071] Step 120: selection of one or more isotopes and formation of the observation vector.

[0072] During this step, one or more isotopes are selected whose emission energies correspond to the energies detected by the detector. A single isotope can be selected, or all isotopes can be selected by assigning a fraction wj to each of them. This fraction can be estimated, to a first approximation, by the spectrometry unit, or result from a priori assumption, for example based on a sample or knowledge of the mining history.

[0073] From the vector of extracted surfaces S'm, for each isotope j considered, an observation vector )'m is calculated for the measurement m such that:

[0074] y = „ix|œa) •• m J'[tm

[0075] corresponds to an integration time of the Sm spectrum.

[0076] When the process is implemented for a single isotope, the vector ym is defined only for all or part of the emission energies of the isotope, detected by spectrometry, and = 1. In this case, L corresponds to a number of emission energies taken into account for the isotope in question. Advantageously, the process is carried out successively for a single isotope, successively considering each isotope identified from the detected spectra.

[0077] The M observation vectors ym for each measurement are concatenated to form an observation vector y, of dimension ML

[0078] The observation vector 1' is such that: [°079] (2) -v iW J - : ^■l)

[0080] Each term y(L) is a count rate of a peak detected during a measurement m at energy 2 / , normalized by the branching rate i[ of the isotope at energy / . Thus, each term y(L) is dimensionally equivalent to pulses detected per second for 1 photon emitted per second.

[0081] L is an integer indexing the energy, with 1 ≤ l <L.

[0082] Step 130: selection of a number of irradiating points N.

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[0092] In this step, a number N of radiating points to be located within the object is arbitrarily defined. N is a strictly positive integer. Advantageously, N can be progressively increased, as described below. The steps described below are iterative steps; k is an integer that denotes the rank of each iteration. 1 < k < K Step 140: Defining a 9k parameter vector, The parameter vector includes certain unknowns, in particular the position of each irradiating point, and, optionally, attenuation parameters. The attenuation parameter quantifies the attenuation of the radiation, at energy 2, emitted by the irradiating point n. The index n designates each irradiating point, at the position with 1 < « < N. During the first iteration, (k = 1), the parameter vector 0k is initialized arbitrarily, or based on a priori. This is the subject of step 240. The parameter vector &k can be initialized as described in connection with steps 241 and 249 described subsequently, in connection with [Fig. 3C]. Step 150: Formation of matrices to establish a direct model. During this step, several matrices are formed allowing the formation of the direct model. A distance matrix Gk translates the respective distances between the measurement position Pm of each measurement m and the position of each irradiating point, each term of which corresponds to the inverse square of the distance between a measurement position and a position of an irradiating point, the position of each irradiating point forming a parameter of the direct model. In the first iteration (k= 1 ), the position of each radiating point corresponds to an initial position, resulting from an initialization phase, described later. When (k> 1 ), the position of each radiating point corresponds to the position updated during the previous iteration.

[0093]

[0094] In the matrix each term---!—- represents the inverse of the square of the n^ir The distance between the position at iteration k and the position Pm of the detector at the measurement of rank m. This corresponds to taking into account the attenuation of the photons emitted by the irradiating point, positioned so that the photons are detected by the detector, due to the effect of distance. The irradiating point is considered as a point relative to the detector.

[0095] An efficiency matrix Hk represents the detector efficiency at the different emission energies resulting from step b), where each term corresponds to a detector detection efficiency for a given detector position and orientation and for a given position of an irradiating point. The efficiency matrix Hk can, for example, be established under the assumption that the detector's response function at an emission energy depends only on the angle of incidence α of the photons generated by each irradiating point present in the field of view. As shown in [Fig. 1B], the angle of incidence α is established with respect to an axis A normal to the detector 10, and forming an axis of symmetry of the detector. This assumes that the detector response is axisymmetric, and that each irradiating point is considered sufficiently distant so that the detected photons 5 are considered to have the same angle of incidence.

[0096] We ask

[0098] In the matrix Hk, each term corresponds to a cosine of the angle of incidence between a considered irradiating point, at the time of iteration k, at the position and the detector at the time of measurement m.

[0099] The quantity , / , \ corresponds to the detection efficiency, to the energy for \ The radiation emitted by a localized irradiating point, during iteration k, at position ^n, whose photons, detected by the detector located at point Pm, reach the latter at an angle of incidence whose cosine is . The efficiency corresponds to a ratio between the number of photons detected at energy to the number of incident photons at that energy

[0100] The case of a detector whose efficiency is axisymmetric is a simplifying assumption. When such an assumption is not verified, an efficiency can be determined by taking into account two angular variables instead of just one.

[0101] Figure 4 shows different values ​​of the detector efficiency h as a function of the energy (MeV) and the cosine of the angle of incidence α. The detector considered is a cylindrical germanium detector with a surface area of ​​38 mm² and a thickness of 30 mm. The points correspond to values ​​modeled with the MCNP particle transport code. The sheet corresponds to a product of two second-degree polynomials: a first polynomial whose variable is the energy and a second polynomial whose variable is the cosine of the angle of incidence. Figure 4 shows that, subject to the preceding assumptions, for a given detector, the detection efficiency can be considered, to a first approximation, as depending only on the energy.

[0102] Optionally, but preferably, an attenuation matrix Ak is constructed. The attenuation matrix represents the attenuation of photons emitted by each irradiating point in the object, each term of the attenuation matrix having an attenuation factor, at an emission energy, between a position of an irradiating point and a position of the detector, each attenuation factor forming a parameter of the direct model.

[0103]

[0104] Each term corresponds to an attenuation of the photons detected by the detector, located at point Pm, the photons being emitted by a localized irradiating point, during iteration P at position ^n. The Tkmfl values ​​are attenuation terms of the parameter vector Pk. Thus, the parameter vector includes each position

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[0120] and each attenuation term rLn^. The method can operate without necessarily implementing the attenuation matrix Ak, for example, for applications using low-density screens and / or high-energy gamma emitters. This is the case, for instance, with surface activity, in the absence of attenuating components in the object under study. In this case, the parameter vector only includes the position of each point radiating at iteration k. Each of the matrices Gk, Hk, and Ak is parameterized by the parameter vector. Thus, each matrix is ​​updated during each iteration. Each matrix constructed during this step has the same dimension: ML x N. Step 160: Forming the response matrix From each matrix, or only from the matrices Gk, Hk, we can construct a response matrix Rk, such that: Rk = G^O Hk O Ak (6) where 0 denotes the Hadamard product (term-by-term product). Step 170: Formation of the direct model From the response matrix Rk, we can establish a direct model such that y corresponds to an estimate of the observation vector resulting from the direct model, during iteration k. The index N denotes the fact that ÿ cst estimated by considering a number N of radiating points distributed in the object. is a vector of dimension N which includes the activity of each irradiating point taking into account the emission lines and branching rates selected during step 120. Expression (6) is equivalent to: A / , \ V'V / / ; \ y (m A 1 represents an estimate of the term of the observation vector corresponding to the measurement m and the energy Step 180: Inversion of the direct model. Solving the inverse problem posed in (6) allows us to jointly estimate the parameter vector and the vector. For this, we establish a cost function, reflecting a difference between the observation vector and its estimate ■ NJ< resulting from the direct model. The cost function can be established using a maximum likelihood algorithm. We then assume that each measure, corresponding to the vector observation 1' is a realization of a random variable Y. We assume that the measures y ( LA with and 1 i L are realizations of variables MX l independent random variables Ym^ following a Poisson distribution with parameter $ On

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[0135] This assumes that the Poisson distribution can be approximated by a normal distribution, provided a sufficiently large parameter is used, i.e., for peaks formed from at least 30 detected pulses. This corresponds to peaks which, following the extraction in step 115, have an area corresponding to 30 pulses. Sm(2 / ) > 30. For each energy A and each measurement point m, we define a likelihood function such that LW ( 3h = '1=^ (8) By taking into account the L emission energies and the M measurement points, the previous expression can be extended; we can define a likelihood function applied to the vector y, such that: T ia AI \ El2 ET17 1 ' / 1 (9) Lva ( #• = 1 ij Li-ftïï । The log likelihood of jy j is written in(LKk( eh yy L 1 ue[ iy y A / / ,\l 2 ^ / =1^31=11 L i ,\ I To optimize computation time, expression (10) is simplified by introducing y(m, Aj) instead of in the variance estimators, so as to obtain: ) » E\E m / tJ-tU L1" The first term of (11) being independent of the cost function to be minimized is (aa) _ 1 Y'2'' VM This expression can be expressed in matrix form: 3& = ~^(ynj."Ynj) ^(y^-y^ With Wk = diag(~) (14) Wk is a matrix of size ML * ML and whose diagonal has the size 1 A>Mi) The parameters to be determined are those that maximize the true- function. ¢.= argmin <K semblance; ( 0 (h}■ Maximize the function; ( g \ is equivalent to minimizing “'mvjV / A ^k) •'mv.NJcX & *k) the opposite function - ( 0k).

[0136] and can be estimated according to: "re1! r] (15)

[0137] n corresponds to the volume of the object examined, and more precisely to the positions that the irradiating points may take. In the absence of a priori assumptions, fl corresponds to the entire volume examined.

[0138] T corresponds to a range of variation of the quantities Tkm„; it can be defined beforehand.

[0139] Step 190 reiteration of steps 140 to 190

[0140] Following the acquisition of @k, steps 140 to 180 are repeated until a stopping criterion for the iterations is reached. This criterion can be a predetermined number K of iterations or a difference between two successive values ​​of the likelihood function j / f) (fa j and j ( ÿ (b 1) sufficiently small that one can assume that convergence is reached. Steps 140 to 180 of the following iteration are implemented taking into account the parameter vectors &k and ^ resulting from step 180.

[0141] After the iteration stopping criterion has been reached, we have: 0^ = dK and — 4>K- K corresponds to the rank of the last iteration.

[0142] Experience shows that convergence is generally reached in a few dozen iterations k, or for a number of iterations k on the order of a hundred.

[0143] Step 200: renewal of steps 140 to 190.

[0144] Advantageously, steps 140 to 190 are repeated Q times, taking the same number N of irradiating points, Q being an integer typically between 10 and 100. A rank el is assigned to each iteration of these steps. At each step 190, a pair of vectors 6*^, is obtained. For each pair of vectors 0NqJ cst associated a value of the cost function. / re, \ minimum, resulting from the Jmv,NJC\U^cf 'Nq) minimisation described above in connection with (15).

[0145] Step 210: selection of a 0Nq pair,

[0146] During this step, the pair 0N, pN is selected from among the pairs, allowing the minimum value to be obtained among the Q values / re , \ obtained during each renewal of steps 140 to 190.

[0147] Steps 200 and 210 are optional. They allow obtaining a number Q of minimizations. We thus obtain a parameter vector and an activity vector allowing us to minimize the difference between k' and its estimate y^K- This avoids obtaining values ​​resulting from an optimization trap, in which minimization allows us to obtain a secondary minimum of the cost function.

[0148] Step 220: modification of the number of irradiating points N

[0149] As previously stated, steps 140 to 190, as well as any steps 200 and 210, are preferably carried out successively for different values ​​of N. For example, N is progressively increased between an initial value (e.g., N = 1) and a final value. This makes it possible to obtain, for each value of N, a parameter vector 8N and an activity vector ÿv.

[0150] Step 230: Selection of the most probable value of N

[0151] In this step, an AICN validity indicator is calculated for each number N previously considered. The process includes estimating the most probable number of irradiating points based on the different validity indicators. The most probable number of irradiating points is the one for which the validity indicator is minimal.

[0152] The validity indicator may be the Akaike Information Criteria, such as: [01531 A7C(5' m )=

[0154] With kn = 4N + NM

[0155] Using (12),

[0156] 4ZC(^J- c«+^(wj+^

[0157] is a constant

[0158] Since the number of measurements M is small, the corrected Akaike information criterion Al Ce is preferably used, such that:

[0159] ««> \ - N I / \ - N I / ML-Kff 1

[0160] In view of (17), expression (18) can be written [°161] AICclyJ -cte + j + X^NJcJ Jmv,NJc\ J h ML-Kjv-1

[0162] The optimal number of irradiating points is that for which the criterion AICc yj is m in i ma 1. Thus,

[0163] argmin(A / Cc(j ,)V20^

[0164] Following this step, the activity vector retained is Similarly, the parameter vector retained is 8^.

[0165] According to one possibility, the Akaike information criterion can be replaced by another indicator, for example the BIC (Bayesian Information Criteria). Variants

[0166] The expression of the direct model, according to (6), involves the parameter vector and the activity vector. The direct model is nonlinear with respect to the parameter vector and linear with respect to the activity vector $k. In step 180 described above, during each iteration k, &k and are jointly estimated <frk.

[0167] It may be advantageous to estimate, during each iteration, &k and success sively. For this, step 180 is subdivided into a sub-step 181 and a sub-step 182. See Figure 3B. During substep 181, a A gradient descent method, for example the Broyden-Fletcher-Goldfarb-Shanno method. This amounts to calculating the gradient of the maximum likelihood with respect to the parameter vector.

[0168]

[0169] = (G t QH k O was defined in (14). •J (21) -w --

[0170] This allows an update, during iteration k, of the vector. For the implementation of the previous expression, we use r resulting from the previous iteration.

[0171] During substep 182, the direct model, made explicit in (6), is solved by a least squares type method to maximize the likelihood function (or minimize the opposite of the likelihood function), according to (13):

[0172] . { \ i / / / , x(22)

[0173] and

[0174] ) (23)

[0175] Minimization is carried out by taking into account the vector resulting from substep 181.

[0176] The advantage of estimating $k and $k separately is that it reduces the search space, which generates fewer optimization traps. It also allows us to separate the quantity $k, whose values ​​vary over a much wider range than those of the parameter vector forming the function. Use of a priori / Initialization

[0177] Preferably, during each first iteration of steps 150 to 180, it is preferable to have initial values ​​for certain parameters, or even for certain activity values. Otherwise, the parameter values ​​are drawn according to a uniform distribution. This constitutes step 240.

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192] Preconceived notions may result from knowledge of the operating history, or from examinations implementing other methods. According to one possibility, during step 240, an initialization is implemented before each first iteration of steps 150 to 180. The initialization is implemented either at each new value of N. The initialization is described in relation to steps 241 to 249 in [Fig. 3C]. In step 241, for each measurement m, a flux vector is formed such that that : <=>(25) hdet corresponds to an average of the efficiency vectors (dimension I), considering, for each energy, an average value of the efficiency extrema as a function of the angle of incidence. Each term <j>*; corresponds to a first approximation of an equivalent surface activity in the object during the measurement m (photons emitted per unit area). Step 242: This involves establishing the variation of as a function of energy, using a simple relationship, in order to estimate the value of in the absence of a screen in the object. From each term, two coefficients fi^ and fi^ are defined such that 9ue M fiim is a positive real number and fi2m is a negative real number. fi im corresponds to the value of 0^ when the energy tends towards infinity. This can be likened, as a first approximation, to an equivalent surface activity, neglecting the attenuation in the object examined. fi2„, describes the evolution of as a function of energy. This coefficient represents the capacity of the material forming a screen, in the object studied, to attenuate the radiation detected during the measurement m. Thus, fi2m corresponds to an attenuation affecting the measurement m. If we assume: (27) And the vector = ) (28) We can estimate using the expression: 'm (29)

[0193]

[0194]

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207] and W, a matrix of size ML * ML and whose diagonal contains the magnitude This step assumes that the selected isotope has several exploitable emission energies. Step 243: estimation of an equivalent activity of the object corresponding to each measurement. From this, we establish a corrected observation vector, for the measure m, of which Each term is: C'=c%«<31) eC <32> can be considered as representative of an equivalent surface activity in the object, at the measurement position m, assuming a homogeneous surface activity, and in the absence of a screen in the object, which corresponds to an infinite emission energy. Step 244: Formation of a corrected observation vector for each measurement m. y™r corresponds to a corrected observation vector for measurement m. This is an estimate of an observation vector that would correspond to an object whose activity would be y^ and can be considered, as a first approximation, as representative of a spectrum that would be measured, at position m, corresponding to the equivalent activity. Step 245: formation of a corrected observation vector for all measurements. The dimension of}'",rest i, which corresponds to the number of emission energies considered. From each vector y1^, a corrected observation vector can be formed, analogously to (2), such that: The dimension of yC(,r) is ML Figure 5 shows, for different simulated measurements (x-axis) curve a: vector 2' resulting from observations, at energy 129.3 keV; curve b: corrected vector 3', this corrected vector being obtained by modeling, by removing the screens in an object; Curve c: ycor vector obtained by implementing steps 241 to 245 from the vector shown on curve a, still at an energy of 129.3 keV. To obtain this curve, a simulated measurement scene was used, comprising three irradiating points made of 239Pu, positioned respectively within a 0.5 cm thick enclosure made of a material composed of 30% (mass fraction) Pb and 70% Si. The three irradiating points were arranged: • the first, at the center of a hollow steel sphere with a radius of 0.5 cm; • the second, behind a steel plate 0.5 cm thick; • the third one, without a screen.

[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214]

[0215]

[0216]

[0217]

[0218] Curve b) was obtained by simulation, removing the screens. It corresponds to the "ground truth". We observe that curve c) constitutes a good approximation, as it is sufficiently close to curve b). Logically, the values ​​forming curves b) and c) are greater than those forming curve a). This is due to the fact that curve a) results from measurements taking into account the actual attenuation in the object examined. Step 246: formation of a model to estimate the corrected observation vector. This is an iterative estimation, analogous to the iterations described in connection with steps 150 to 190. Each iteration corresponds to an iteration index k. ywr is a vector of dimension ML, as is ZA. From Vœr, we can write: The goal of initialization is to establish a vector of initial parameters conditioned positing the matrices Gk and Hk at each iteration k, as well as a vector THE matrices and / 7^ correspond respectively to the parameterized matrices Gk and Hk K by .° k is an estimate of the activity of the N irradiating points considered. Step 247: Maximum Likelihood Optimization This step is analogous to step 180 described previously. Using expression (13), we establish an initial likelihood function: i ( d>y\ — -~(vCOf'-v \W® (v™'' - vi ($5) WithW?= dia^}

[0219] Then, in a manner analogous to (23) [02201 ¢^^(^(¢^ GA

[0221] Expression (36) is solved as k iterations progress.

[0222] Step 248: this involves launching a new iteration as long as the stopping criterion of the iterations has not been reached (see step 190).

[0223] Step 249: This step is optional. As described in connection with steps 200 and 210, steps 246 to 248 can be repeated Q times, each iteration being indexed by the index 5. During each iteration, a pair of values ​​is obtained The likelihood is at its maximum.

[0224] Following initialization, the vectors g® are used to initialize the resolution described in connection with step 180, when the iteration index k is equal to 1. Dose estimation

[0225] According to one possibility, after step 230, a dose can be estimated at different points, generated by the identified irradiating points, and by the parameter vector The main steps of this variant are shown in [Fig.3D].

[0226] Step 250: Matrix creation

[0227] We can form 4 matrices G, A and G, A of dimension ML x fi using fi as well as the parameters resulting from step 230.

[0228] The matrix G is a distance matrix similar to the matrix Gk described in step 150, in connection with (3).

[0229]

[0230] An attenuation matrix is ​​constructed, in a manner similar to the attenuation matrix A^described in step 150, in connection with (5).

[0231]

[0232]

[0233] We establish a matrix D of absorption coefficients ¢.,)1 (42) d(A) due ¢,) d <M ^Gl) 1

[0234]

[0235]

[0236]

[0237]

[0238]

[0239]

[0240]

[0241]

[0242] Each term corresponds to a mass absorption coefficient (i.e., per unit of mass) at energy X- We also establish an energy matrix A, of dimension ML x: XJ (43) From the matrices G, H, A, and A, a dosimetric response matrix R, of dimension MLx^y, is established. R = GO HO AOA (44) Step 260: Estimating a dose rate at at least one measurement point We then calculate a vector DR, of dimension M, where each term DR(m) is an estimate of the dose rate at the measurement point m. DR= 4zr r Equation (45) allows us to estimate a dose rate at depth, under the assumption of electronic equilibrium, where the dose rate is equal to the kerma rate. The estimate is correct when the contribution of scattered photons is negligible. report on the contribution of unscattered photons.

[0243] The dose rate between measurement points m can then be estimated by interpolation, so as to estimate a dose rate at points different from the measurement points.

[0244] The dosimetric response matrix R can be established by taking into account only a part of the measurement points, or even a single measurement point. Non-spectrometric embodiment

[0245] In the embodiment described above, the detector has a spectrometric function. The input data for the algorithm described in relation to Figure 3A are spectra measured Sm at different measurements m, each measurement m corresponding to a position and orientation of the detector. Such an embodiment is suitable when the irradiated points are composed of several isotopes. This corresponds in particular to applications of the method in nuclear facilities, on waste or process equipment, or even civil engineering structures.

[0246] The algorithms described in connection with Figures 3A to 3D can be applied to a measurement modality in count rate, according to which, in each measurement, the measured quantity CRm (count rate) is a number of pulses per second resulting from the measurement circuit 12.

[0247] The detector 10 and the measuring circuit 12 can be simpler than in the spectrometric embodiment. Thus, the detector 10 can be a solid or gaseous detector, connected to a measuring circuit that allows the number of pulses detected per unit time to be determined. In one possibility, the measuring circuit determines the counting rate within a particular amplitude range, which amounts to addressing only a single spectral band.

[0248] It is understood that according to this embodiment, Σ = 1 and J = 1 there is only one spectral band, which corresponds to the pulse amplitude range in which the measuring circuit determines the counting rate. There is only one isotope, or one mixture of isotopes, for each irradiating point.

[0249] Applications of this method can be found in the nuclear field, where the emission spectrum is simple and / or dominated by a single radioisotope, without taking attenuation into account. It can also be used in the medical field, an example being the search for irradiated spots in a body that has previously been injected with a radioactive isotope. Another application could be the search for sentinel lymph nodes when the radioactive isotope is configured to bind to cancer cells. In such an application, there is only one emission energy, and the attenuation of the emitted radiation can be neglected. The user employs a compact detector that can be easily handled by hand. The detector can be coupled to a positioning unit, allowing the positions to be determined. respective detector at each measurement point. [Fig.6] represents an application for searching for irradiated areas 3, in this case sentinel lymph nodes, by placing a portable assembly, formed by the detector 10 and the measurement circuit 12, at different measurement points around a person's body 2.

[0250] The steps described in connection with Figure 3A are followed. According to this embodiment, step 115 is not implemented. During step 120, the observation vector ))„ corresponds to the count rate CRm associated with the measurement m. A branching rate may optionally be taken into account.

[0251] Thus, during step 120, )' = CRm (50) or y _ (50') •• m iL

[0252] Taking the branching factor into account is preferable if one wishes to obtain a quantification of each irradiating point. It is optional if the main objective is to locate the irradiating point, the quantification of the activity being only indicative.

[0253] We form an observation vector 2 of dimension M.

[0254] (52)

[0255] Steps 130, 140 and 150 are implemented. During step 150, it is defined the matrices Gk and Hk of dimensions such that

[0256]

[0257]

[0258]

[0259] The matrix is ​​not used.

[0260] The detector response can be assumed to be isotropic, in which case A has the same value

[0261] Steps 160, 170, 180 and 190 are implemented with F = 1, as are the steps 200 to 230. During these steps y(m. ^) = y(m) and

[0262] The variants illustrated in Figures 3B to 3D can be implemented with this embodiment. The dose rate estimation is performed by taking into account the emission energy of the radioactive isotope considered. In medical applications, this allows for dose rate estimation at each measurement position. The device makes it possible both to locate irradiated points and to provide quantitative radiation protection data. By estimating the duration of the measurements at each observation point, it is possible to estimate the integrated dose during a procedure. Thus, advantageously, when the detector is worn manually, the device includes a timer allowing for estimation of the duration of each measurement. Experimental tests

[0263] The measurement method was implemented using a high-purity germanium detector (Ge HP broad energy 3830): surface area 38 mm² and thickness 30 mm. The detector was positioned at various locations around a glove box. The 239Pu isotope was taken into account.

[0264] Figure 7A shows a photon flux map (pulses detected per second, or counts per second) measured at 413 keV. These are values ​​of the spectrum measured Sm at different measurements m, divided by the counting time. The gray level codes the number of photons detected per second at this energy. The boxed areas are inaccessible to the detector. This is, in fact, an advantage of the invention: it allows mapping of an object in a cluttered environment by manipulating a compact detector in different positions around the object. In [Fig. 7A], the mapping carried out along four faces of the glove box is shown: face A, face B, face C, and face D.

[0265] Figure 7B shows an estimation of the location and mass of material (Pu) of radiating points using the method described above. The glove box under examination contained a machining workshop, including a surface plate supporting a lathe. Implementing the invention made it possible to locate three hot spots. All three hot spots were located on the surface plate, with the most intense (point b in Figure 7B) being directly above the cutting area of ​​the lathe. A second radiating point (point c in Figure 7B) was located in an area containing a tool holder. Finally, a third radiating point (point a in Figure 7B) was located between the wall of the glove box and the lathe frame.

[0266] The sum of the activities of the detected irradiating points was consistent with a total activity given by another retention measurement method.

[0267] This test demonstrates the relevance of the method. It allows, by deploying a simple and inexpensive detector, and under field conditions, the estimation of the quantity and distribution of activity in an object.

[0268] In the preceding examples, the use of a detector exhibiting a simple shielding. The invention can be applied to a collimated detector, the only impact being a modification of the H matrix.

[0269] The invention can be applied to the control of any other object: equipment or structure of a nuclear installation, including civil engineering, localization of radioactivity in the environment, or localization and quantification of in-vivo irradiating points, the object being a part of a human or animal body.

[0270] The preceding examples described the use of a non-pixelated detector. The invention can also be applied to pixelated detectors, where each pixel forms an elementary detector. This makes it possible to multiply the number of measurement points. At each detector position, as many measurements are obtained as there are pixels.

[0271] The invention, while offering slightly lower spatial resolution than gamma imaging, provides a usable result for locating irradiating points and quantifying their respective activities in an object with a much smaller number of measurement points and with inexpensive and easy-to-use equipment. An important aspect is that it also requires no assumptions about the object's attenuation: when the attenuation matrix is ​​used, the attenuation of the irradiating points is estimated along with their position and intensity in the parameter vector.< / j>

Claims

Demands

1. A method for locating irradiating points in an object, each irradiating point emitting gamma photons at at least one emission energy, the method employing a measuring device, the measuring device comprising: - a detector (10), configured to detect gamma photons, and to form, at each detection, a pulse; - a measuring circuit (12), configured to determine a number of pulses detected; The process involves the following steps: a. acquisition of measurements (Sm) facing the object, each measurement corresponding to a measurement position (Pm) and an orientation of the detector (^K), the measurements being acquired by placing the detector (10) in different measurement positions (Pm) and / or different orientations (am); b. processing of measurements, by the measurement circuit, in order to extract counting rates; c. formation of an observation vector (?) from the count rates extracted during step b); d. selection of a number of radiating points (N) in the object; e. initialization of a parameter vector (^o), including a position (^n) of at least one radiating point located in the object; f. from the initialized parameter vector (0q) resulting from e), or from the parameter vector (¾^) resulting from a previous iteration, updating of a direct matrix model, linking an estimate of the observation vector (v) to an intensity vector (0^.), the intensity vector including an estimate of the intensity of each irradiating point; g. inversion of the direct model, by an optimization algorithm, so as to update the parameter vector (¾) and the intensity vector (^); h. Reiteration of steps f) and g) until an iteration stopping criterion is reached, so as to obtain, following the last iteration, an estimate of the parameter vector and the intensity vector corresponding to the number of points ir- selected radiant panels.

2. A method according to claim 1, wherein: - the measurement circuit (12) is a spectrometric measurement circuit, configured to form a spectrum, the spectrum corresponding to a number of photons detected in different channels, each channel corresponding to an energy of the detected photon; - the measurement circuit comprises a spectrometry unit (13), configured to identify at least one emission peak on the spectrum formed by the spectrometric measurement circuit, each emission peak extending around an emission energy; the method being such that: - in step a), each measurement is a spectrum (Sm); - step b) comprises a processing of spectra, by the spectrometry unit (13), so as to extract count rates of each emission peak.

3. A method according to claim 1 or claim 2, wherein in step g), the inversion includes a minimization of a cost function ( ; (na ), the cost function quantifying a difference between - the estimation of the observation vector obtained in step 0; - the observation vector formed in step c).

4. A method according to claim 3, wherein step g) is performed by a maximum likelihood algorithm.

5. A method according to any one of the preceding claims, wherein: - steps d) to h) are repeated taking into account, at each iteration of steps d) to h), different numbers of irradiating points (N); - the method comprises determining an indicator of validity (A / C) associated with each iteration of steps d) to h), the validity indicator being associated with the number of irradiating points selected during each iteration; The process involves estimating the most probable number of irradiating points based on different validity indicators respectively associated with different numbers of irradiating points.

6.

7.

8. A method according to claims 4 and 5, wherein, in which The validity indicator is an Akaike information criterion (AlCc, AICn). A method according to any one of the preceding claims, in in which the direct model includes a response matrix (^), formed by a Hadamard product between at least: a distance matrix (Gk), translating the respective distances between each measurement position and the position of each irradiating point, each term of which includes the square of the distance between a measurement position and a position of an irradiating point, the position of each irradiating point forming a parameter of the direct model; an efficiency matrix (Hk), translating the efficiency of the detector, where each term corresponds to a detection efficiency of the detector for a position and orientation of the detector and for a position of a point irradiating at least one emission energy. The method according to claim 7, wherein the direct model comprises a response matrix (Rk), formed by a Hadamard product between at least: a distance matrix (Gk\ translating the respective distances between each measurement position and the position of each irradiating point, each term of which includes the square of the distance between a measurement position and a position of an irradiating point, the position of each irradiating point forming a parameter of the direct model; an efficiency matrix (^), reflecting the efficiency of the detector, where each term corresponds to a detection efficiency of the detector for a position and orientation of the detector and for a position of an irradiating point.

9. A method according to claim 7, wherein the response matrix (¾) is formed from a Hadamard product between the distance matrix (^), the efficiency matrix (¾) and an attenuation matrix, the attenuation matrix representing an attenuation of the photons emitted by each irradiating point in the object, each term of the attenuation matrix comprising an attenuation factor, at an emission energy, between a position of an irradiating point and a position of the detector, each attenuation factor forming a parameter of the direct model.

10. A method according to claim 9, wherein step e) comprises: - e1) from the observation vector resulting from c), calculation of an observation vector in the absence of attenuation in the object; - e2) estimation of the observation vector in the absence of attenuation in the object using a direct model comprising the distance matrix and the efficiency matrix; - e3) inversion of the direct model, so as to estimate an initialized parameter vector and an initial activity vector, taking into account the number of irradiating points taken into account in step d).

11. A method according to any one of the preceding claims and claim 3, wherein: - for the same number of irradiating points selected in the object, steps e) to h) are repeated; - the method includes a comparison of the cost functions resulting from each step g) of each iteration of steps e) to h), the parameter vector and intensity vector, for the number of irradiating points selected, being those corresponding to the minimum cost function.

12. A method according to any one of the preceding claims, wherein step g) comprises: - gl) application of a gradient descent algorithm, to estimate the parameter vector, based on the initial activity vector or the one resulting from a previous iteration, - g2) application of an inversion algorithm, to estimate the activity vector, using the parameter vector resulting from gl).

13. A method according to claim 9, wherein, for the same number of selected irradiating points, the method comprises: - a first series of iterations of steps e) to h), using a direct model in which the response matrix is ​​formed by a Hadamard product of the distance matrix and the detector sensitivity matrix; - a second series of iterations of steps e) to h), using a direct model in which the response matrix is ​​formed by a Hadamard product of the distance matrix, the detector sensitivity matrix and the attenuation matrix; - the position and activity of the irradiating points resulting from the first series of iterations is used to initialize the inversion of the direct model in the first iteration of the second series of iterations.

14. A method according to any one of the preceding claims, wherein step b) comprises a selection of at least one emission energy of a predetermined isotope, so as to extract the count rates in each selected emission energy.

15. A method according to claim 14, wherein steps b) to h) are carried out by successively selecting, in each step b), at least one emission energy of different isotopes.

16. A method according to any one of the preceding claims comprising, following step h), an estimation of a dose rate at at least one measurement point, from the intensity vector and the parameter vector resulting from said step h).

17. A method according to claim 16 and claim 7 comprising - updating the distance matrix and the matrix efficiency, depending on the parameter vector resulting from step h); - taking into account mass absorption coefficients at at least one emission energy; - estimation of the dose rate at each measurement point from the distance matrix, the efficiency matrix and the absorption coefficients.

18. Device configured to estimate the position of irradiating points in an object, the device comprising: - a detector (10), configured to detect gamma photons, and to form, at each detection, a pulse, the detector being mobile around the object, so as to be able to be arranged in several positions and / or according to different orientations with respect to the object; - a measurement circuit (12), configured to determine a number of pulses detected by the detector; - a processing unit (14), programmed to implement steps c) to h) of a method according to any one of the preceding claims, from the number of pulses detected by the measurement circuit.

19. Device according to claim 18, wherein: - the measurement circuit is a spectrometric measurement circuit (12), configured to form a spectrum, the spectrum corresponding to a number of photons detected in different channels, each channel corresponding to an energy of the detected photon; - the measurement circuit comprises a spectrometry unit (13), configured to identify emission peaks on the spectrum formed by the spectrometric measurement circuit.

20. Support, which can be connected to a computer, comprising instructions for carrying out steps c) and e) to h) of a method according to any one of claims 1 to 17 from count rates resulting from measurements made using a gamma photon detector around an object.

Images