Method for locating irradiating 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 counting 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, linking an estimate of the observation vector () to an intensity vector (); inversion of the direct model and updating the parameter vector () and the intensity vector (); reiteration of the last two steps.

Description

Title of the invention: Method for locating irradiating zones Technical field

[0001] The technical field of the invention is spectrometry applied to the detection of ionizing radiation and to the location of irradiating zones emitting ionizing radiation. This essentially involves X or y spectrometry. PRIOR ART

[0002] In nuclear facility equipment, radiological activity is not distributed homogeneously. It is generally concentrated in areas, usually referred to as "hot spots". Generally, the intensity and location of hot spots are not known, as they depend on the operating history of the nuclear facility. However, when carrying out a radiological inventory of a nuclear facility, it is useful to know, as best as possible, the location of hot spots and their respective activities.

[0003] Since the 1990s, gamma cameras have been developed, inspired by imagers used in the medical field. These are devices that allow an image to be formed to establish a map in nuclear installations. The objective is to locate and identify, remotely, the main irradiating sources present in a facility. The developments and uses of gamma cameras have been extensively described in the literature. Since the early 2000s, we have seen the development of spectrometric gamma cameras. These cameras are based on a pixelated imager, each pixel making it possible to obtain a spectrum of the irradiation it detects. This represents a considerable gain in the localization of irradiating sources.In fact, the spectrometric function makes it possible to select energy bands of interest, corresponding to non-diffused photons, i.e. photons which have not been deflected since their emission by the irradiation source.

[0004] These are high-performance but fairly expensive devices. Their sensitivity may be insufficient when the activity is due to low-y-emitting isotopes, for example Pu isotopes. Thus, gamma cameras may have insufficient sensitivity to carry out checks aimed at achieving accurate nuclear material accounting, or assessing the risk of criticality. A typical example is the quantification of nuclear material accumulation in a glove box, for example in nuclear fuel manufacturing facilities.

[0005] Currently, gamma cameras allow an estimation of the dose generated by each detected hot spot. However, if one wishes to estimate the activity of the detected hot spots, it is necessary to resort to modeling means. This requires certain modeling assumptions, as well as some 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 hot spots, using a simple measuring device. It is particularly suitable for installations with low irradiation, and originating from gamma emitters with low emission intensity. It is also suitable for environments in which access conditions are restricted, in particular cluttered environments. Beyond nuclear power, the invention can also be applied to a search for hot spots for other types of application, for example medical. Presentation 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 at least one emission energy, the method implementing a measuring device, the measuring device comprising: - a detector, configured to detect gamma photons, and to form, at each detection, a pulse; - a measuring circuit, configured to determine a number of detected pulses;

[0008] the method 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 the measurements, by the measuring circuit, so as 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, comprising 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 a direct matrix model, linking an estimate of the observation vector to an intensity vector, the intensity vector comprising 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 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, called spectrometric: the measuring circuit is a spectrometric measuring 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 measuring circuit comprises a spectrometry unit, configured to identify at least one emission peak on the spectrum formed by the spectrometric measuring 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) comprises processing of spectra, by the spectrometry unit, so as to extract counting rates from each emission peak.

[0011] According to one possibility, during step g), the inversion comprises a minimization of a cost function, the cost function quantifying a difference between the estimation of the observation vector obtained in 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 method comprises 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 method includes an estimation of the most probable number of irradiating points based on the different validity indicators respectively associated with different numbers of irradiating points.

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

[0015] According to one possibility, the direct model comprises a response matrix, formed from 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 a radiating point, the position of each radiating point forming a parameter of the direct model; - an efficiency matrix, reflecting the efficiency of the detector, each term of which corresponds to a detection efficiency of the detector for a position and an orientation of the detector and for a position of a point irradiating at at least one emission energy.

[0016] The direct model may comprise a response matrix, formed from 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 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, each term of which corresponds to a detection efficiency of the detector for a position and an orientation of the detector and for a position of an irradiating point.

[0017] The response matrix may be formed from a Hadamard product between the distance matrix, the efficiency matrix and an attenuation matrix, the attenuation matrix translating 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.

[0018] Step e) may comprise - 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 comprising the distance matrix and the efficiency matrix; - e3) inversion of the direct model, in order to estimate a vector of parameters initialized and an initial activity vector, taking into account the number of irradiating points taken into account in step d).

[0019] According to one possibility: - for the same number of radiating points selected in the object, steps e) to h) are repeated; - the method comprises 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 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 one resulting from a previous iteration, - g2) application of an inversion algorithm, to estimate the vector 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) comprises a selection of at least one emission energy of a predetermined isotope. The counting rates are thus extracted in 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 method may comprise 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 method 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 movable around the object, so as to be able to be arranged in several positions and / or according to different orientations relative to the object; - a measuring circuit, configured to determine a number of pulses detected by the detector; - a processing unit, programmed to implement steps c) to h) of a method according to the first subject of the invention from the number of pulses detected by the measuring circuit.

[0027] According to one possibility: - the measuring circuit is a spectrometric measuring 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 measuring circuit comprises a spectrometry unit, configured to identify emission peaks on the spectrum formed by the spectrometric measuring circuit.

[0028] A third object of the invention is a support, connectable to a computer, comprising instructions for implementing step c) and e) to h), optionally d), of a method according to the first object of the invention from counting rates resulting from measurements carried out using a gamma photon detector around an object.

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

[0030] 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

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

[0032] [Fig.lB] 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] [Fig.3A] shows the main steps of a method implementing the invention.

[0038] [Fig.3B] shows steps in 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 irradiating points are successively taken into account.

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

[0041] [Fig.4] shows a diagram of 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] [Fig.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], 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 material from different irradiating points in the glove box. PRESENTATION OF SPECIAL METHODS OF IMPLEMENTATION

[0046] [Fig.1A] shows a device 1 enabling the implementation of the invention, according to a first embodiment, called a spectrometric embodiment. The device is a measuring system, comprising a detector 10, capable of interacting with ionizing radiation 5 emitted by an object 2. The object 2 is here a glove box, which may comprise different irradiating points (or hot spots) 3, distributed in 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 equipping a nuclear installation, such as a civil engineering structure, waste package, or various components. The invention can also be applied outside the nuclear field, for example in the medical field, for example to locate and quantify the activity of a radioactive isotope administered into an individual's body.

[0047] In the example shown in Figure 1A, the glove box comprises an area containing different equipment. The irradiating points 3 are arranged in the area 4 and at the floor level of the glove box. We designate by nn the position of each irradiating point in an XYZ frame associated with the object studied. 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 previously known. Failing this, they can be determined by the spectrometry unit. In particular, a list can be drawn up containing irradiating radionuclides 2j potentially present in the object being analyzed. The index 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 this, and this is the option described in the following example, the method 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] Whatever the detector used, it allows a 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 photonic radiation of type X or gamma, formed 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 quantity of charge collected during an interaction. The quantity of charge corresponds to the energy deposited by the radiation during the interaction.

[0053] The measuring circuit 12 comprises a spectrometry unit 13, which makes it possible to gather all the pulses formed during an acquisition duration. Each pulse corresponds to an interaction of the incident radiation in the detection material. The spectrometry unit 13 then classifies the pulses according to their amplitude Amp, to provide a histogram comprising the number of pulses detected according to their amplitude. Such a histogram is an amplitude spectrum. It is usually obtained using a multichannel analyzer. Each amplitude is discretized according to channels, each channel being assigned an amplitude band. The value of each channel of the spectrum corresponds to a number of pulses whose amplitude is located in the amplitude band assigned to the channel. Each amplitude band corresponds to an energy band, the correspondence being bijective. Thus, each channel is assigned an energy band or an amplitude band.

[0054] The relationship between amplitude and energy can be achieved by irradiating the detector using a calibration source, emitting radiation of known energy. This is in particular radiation having 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 gamma, the detector is exposed to a 152Eu type calibration source, producing photons at known emission energies. Alternatively, a 137Cs type source can be used, producing mainly photons with an energy of 661.6 keV. Alternatively, a 60Co source can be used, producing photons with an energy of mainly 1173 keV and 1332 keV. Energy calibration can be performed as described in WO2023126509.

[0055] The spectrometry unit is configured to form an energy spectrum from the pulses formed 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 in connection with FIGS. 2A to 2D.

[0056] The device comprises a processing unit 14, programmed to implement steps of algorithms described below, in connection with FIGS. 3A to 3D, so as to locate each irradiating point and to estimate the respective activities.

[0057] In the example shown, the detector 10 is connected to a cryostat 18, comprising 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.lA], the limits of the observation field Q are represented by two dotted lines.

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

[0059] In Figure 1B, the detector 10 is shown arranged at several measurement points around the object 2 studied. At each measurement point, the detector is oriented according to one or more orientations. Subsequently, each measurement is identified by an integer m. Each measurement is carried out at a position Pm and an orientation am-Each position Pm and each orientation a»' comprise three coordinates, respectively spatial and angular, in the XYZ frame associated with the object studied 2.

[0060] [Fig.2A] represents an example of a spectrum. The abscissa axis corresponds to the amplitude, discretized into amplitude channels, and the ordinate axis represents a number of pulses counted at each amplitude during the acquisition of the spectrum. [Fig.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. By intensity estimation, we mean the estimation of the area of ​​each peak. Figures 2C and 2D schematize an extraction of a surface of a peak, in a region of interest materialized by a frame in Figures 2A and 2B. In Figures 2C and 2D, the surface of a peak is extracted "above" the background noise, the latter being materialized by a dotted line. The extracted surface corresponds to an intensity of the peak at the emission energy of the peak, the latter corresponding to the abscissa of said peak. Document WO2023126508 describes a method for automatically extracting a surface of a peak, as an alternative to the commercial software currently available.

[0062] Compared to gamma cameras, an advantage of using a non-pixelated spectrometry device is that the detection volume can be large. For example, of the order of 1 inch in diameter and 1 inch in height, or even more for a LaBr3 type detector. The use of Germanium type detectors allows for larger volumes. This provides good measurement sensitivity. This allows low irradiation levels to be addressed, which is particularly appropriate for weakly irradiating emitters, such as certain Pu isotopes. This also allows for low activity levels to be addressed for strongly 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 a selection of peaks at certain energies, previously determined.

[0064] The main steps of a detection method are described in connection with [Fig.3A].

[0065] Step 100: arrangement of the detector at 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 have 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 a surface area of ​​each peak. A counting rate is determined, in each peak, which corresponds to a number of pulses detected, in the peak, divided by unit of time. This makes it possible to form, for each measurement m, 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 rate z' / , where / is an index designating 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. One can select a single isotope or select all the isotopes by assigning, to each of them, a fraction wj. The latter can be estimated, to the first order, by the spectrometry unit, or result from an a priori, for example on the basis of a sample or knowledge of the exploitation history.

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

[0074] y = „ix|œa) •• m I[tm

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

[0076] When the method 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 considered. Advantageously, the method is implemented successively for a single isotope, successively considering each isotope identified in view of 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 Ù.) is homogeneous 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 in 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 some 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 denotes 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 an 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 later, in connection with [Fig.3C]. Step 150: Formation of matrices to establish a direct model. During this step, several matrices are formed to enable 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 of 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. In the first iteration (k= 1 ), the position of each radiating point corresponds to an initial position, resulting from an initialization phase, described below. 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 distance between the position during iteration k, and the position Pm of the detector during the measurement of rank m. This corresponds to taking into account the attenuation of the photons 5 emitted by the irradiating point, positioned in the photons being detected by the detector, under the effect of the distance. The irradiating point is considered as punctual with respect to the detector.

[0095] An efficiency matrix Hk translates the efficiency of the detector at the different emission energies resulting from step b), each term of which corresponds to a detection efficiency of the detector for a position and an orientation of the detector and for a position of an irradiating point. The efficiency matrix Hk can for example be established according to the hypothesis that the response function of the detector, at an emission energy depends only on the angle of incidence a of the photons generated by each irradiating point present in the observation field. As shown in [Fig.lB], the angle of incidence a 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 response of the detector is axisymmetric, and that each irradiating point is considered to be sufficiently distant so that the detected photons 5 are considered to have the same angle of incidence.

[0096] We pose

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

[0099] The magnitude , / , \ 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 the energy on the number of incident photons at this energy

[0100] The case of a detector whose efficiency is axisymmetric is a simplifying hypothesis. 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 represents different values ​​of a detector efficiency h as a function of the energy (MeV) and the cosine of the angle of incidence a. 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 polynomials of degree 2: 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 as depending, as a first approximation, only on and on the energy

[0102] Optionally, but preferably, an attenuation matrix Ak is constructed. The attenuation matrix translates 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.

[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 the iteration P at position ^n, The values ​​Tkmfl 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 work without necessarily implementing the attenuation matrix Ak, for example for applications using low-density screens, and / or high-energy gamma emitters. This is for example the case of surface activity, in the absence of attenuating components in the object studied. In this case, the parameter vector only includes the position 77 of each irradiating point 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 formed 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 constitute 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: Training 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 designates the fact that ÿ is estimated by considering a number N of irradiating 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 the branching rates selected during step 120. Expression (6) amounts to the following: A / , \ V'V / / ; \ y (m) to 1 represents an estimate of the term of the observation vector corresponding to the measurement m and to the energy Step 180: Inversion of the direct model. Solving the inverse problem posed in (6) allows us to jointly estimate the parameter vector as well as 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 measurement, 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 Ym^ following a Poisson distribution of parameter $ On

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[0135] assumes that the Poisson distribution can be approximated by a normal distribution subject to a sufficiently large parameter, i.e. for peaks formed from at least 30 detected pulses. This corresponds to peaks, which, following the extraction of step 115, have an area corresponding to 30 pulses. Sm(2 / ) > 30. We define, for each energy A; and each measurement point m, a likelihood function such that LW ( 3h = '1=^ (8) Taking into account the L emission energies, and the M measurement points, the previous expression can be extended and 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 as in(LKk( eh yy L 1 ue[ iy y A / / ,\l 2 ^ / =1^31=11 L i ,\ I In order to optimize the 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 and are those maximizing the truth function- ¢.= argmin <K semblance ; ( 0 (h}■ Maximizing 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 likely to be taken by the irradiating points. In the absence of a priori, 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 repetition of steps 140 to 190

[0140] Following the obtaining of @k and steps 140 to 180 are repeated, until an iteration stopping criterion is reached. The latter can be a number K of predetermined iterations or a difference between two successive values ​​of the likelihood function j / f) (fa j and j ( ÿ (b 1 sufficiently small so that one can consider that convergence is reached. The following iteration steps 140 to 180 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 achieved in a few tens of iterations k, or for a number of iterations k of 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 radiating points, Q being an integer typically between 10 and 100. A rank el is assigned to each iteration of these steps. During each step 190, a pair of vectors 6*^, is obtained. For each pair of vectors 0NqJ cst associated a value of the cost function . / d , \ minimal, resulting from the Jmv,NJC\U^cf 'Nq) minimization described above in connection with (15).

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

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

[0147] Steps 200 and 210 are optional. They make it possible to obtain a number Q of minimizations. We thus obtain a vector of parameters and an activity vector allowing us to minimize the difference between k' and its estimate y^K- This avoids obtaining values ​​and resulting from an optimization trap, in which the 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 indicated, steps 140 to 190, as well as possible steps 200 and 210, are preferably carried out successively for different values ​​of N. For example, N is progressively increased between an initial value (for example 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] During this step, a validity indicator AICN is calculated associated with each number N previously taken into account. The method comprises an estimation of the most probable number of irradiating points as a function of the different validity indicators. The most probable number of irradiating points is that for which the validity indicator is minimal.

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

[0154] With kn = 4N + NM

[0155] Using (12),

[0156] 4ZC(^J- c«+^(wj+^

[0157] is a constant

[0158] The number of measurements M being small, we preferably use the corrected Akaike information criterion Al Ce, such that:

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

[0160] Given (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 min 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 non-linear with respect to the parameter vector and linear with respect to the activity vector $k. In step 180 previously described, during each iteration k, we jointly estimate &k and <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 sub-step 181, 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 sub-step 182, the direct model, explained 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] The minimization is carried out by taking into account the vector resulting from sub-step 181.

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

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

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192] A priori assumptions may result from knowledge of operating history, or from examinations using 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 connection with steps 241 to 249 in [Fig.3C]. During step 241, we form, for each measurement m, a flux vector such that that : <=>(25) hdet corresponds to an average of the efficiency vectors (dimension I), considering, at each energy, an average value of the extrema of the efficiency as a function of the angle of incidence. Each term <j>*; corresponds to an estimate, as a first approximation, of an equivalent surface activity in the object during measurement m (photons emitted per unit of surface). Step 242: This involves establishing the variation of as a function of energy, from a simple relationship, in order to estimate the value of in the absence of a screen in the object. From each term, we define two coefficients fi^ and fi^ such that M fiim is a positive real and fi2m is a negative real. fi im corresponds to the value of 0^ when the energy tends towards infinity. This can be compared, at first glance, 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 pose: (27) And the vector = ) (28) We can estimate according to 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 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^ 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^ we can form a corrected observation vector, in a manner analogous to (2), such that: The dimension of yC(,r is ML In [Fig.5], we have represented, for different simulated measurements (x-axis) curve a: vector 2' resulting from the observations, at energy 129.3 keV; curve b: corrected 3' vector, 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 represented on curve a, still at energy 129.3 keV. To obtain this curve, a simulated measurement scene was taken into account comprising three irradiating points formed of 239Pu, respectively positioned in a 0.5 cm thick enclosure, formed of a material composed of 30% (mass fraction) of Pb and 70% of Si. The three irradiating points were arranged: • the first, in the center of a hollow steel sphere with a radius of 0.5 cm; • the second, behind a 0.5 cm thick steel plate; • the third, without 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, because it is sufficiently close to curve b). Logically, the values ​​forming curves b) and c) are higher 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: Training a model to estimate the corrected observation vector. This is an iterative estimation, similar 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 objective of initialization is to establish a vector of initial parameters condi ting the matrices Gk and Hk during each iteration k, as well as a vector THE matrices and / 7^ correspond respectively to the K-parameterized matrices Gk and Hk by .° k is an estimate of an activity of the N irradiating points considered. Step 247: Maximum Likelihood Optimization This step is analogous to step 180 previously described. By taking 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 reiteration, a pair of values ​​is obtained likelihood is 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 the parameter vector The main steps of this variant are shown in [Fig.3D].

[0226] Step 250: constitution of matrices

[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 G matrix is ​​a distance matrix similar to the Gk matrix described in step 150, linked to (3).

[0229]

[0230] We constitute an attenuation matrix, in a similar way 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) d^û ¢,) 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 mass) to X- energy We also establish an energy matrix A, of dimension ML x: XJ (43) From the matrices G, H, A and A, we establish a dosimetric response matrix R, of dimension MLx^y R = GO HO AOA (44) Step 260: estimation of a dose rate at at least one measurement point We then calculate a vector DR, of dimension M, each term DR(m) of which is an estimate of the dose rate at the measurement point m. DR = 4zr r Expression (45) allows to estimate a dose rate in depth, according to the hypothesis of electronic equilibrium, the dose rate being equal to the kerma rate. The estimate is correct when the contribution of scattered photons is negligible by relative to 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 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 of the algorithm described in connection with FIG. 3A are spectra measured Sm in different measurements m, each measurement m corresponding to a position and an orientation of the detector. Such an embodiment is suitable when the irradiating points are formed of several isotopes. This corresponds in particular to applications of the method in nuclear installations, on waste or process equipment, or even civil engineering type structures.

[0246] The algorithms described in connection with figures 3A to 3D can be applied to a counting rate measurement modality, 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 may be simpler than in the spectrometric embodiment. Thus, the detector 10 may be a solid or gaseous detector, connected to a measuring circuit allowing a determination of the number of pulses detected per unit of time. According to one possibility, the measuring circuit determines the counting rate in a particular amplitude range, which amounts to addressing only a single spectral band.

[0248] It is understood that according to this embodiment, £ = 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 may concern nuclear energy, when the emission spectrum is simple, and / or dominated by a single radioelement, without taking attenuation into account. This may also concern medical applications, an example of an application being a search for irradiating points in a body that has previously been injected with a radioactive isotope. An application may be a 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 uses a compact detector, which can easily be handled by hand. The detector can be coupled to a positioning unit, making it possible to determine the positions respective of the detector at each measuring point. [Fig.6] represents an application for searching for irradiating zones 3, in this case sentinel lymph nodes, by placing a portable assembly, formed by the detector 10 and the measuring circuit 12, at different measuring points around a body 2 of a person.

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

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

[0252] Taking into account the branching factor 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, we define 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 carried out by taking into account the emission energy of the radioactive isotope considered. In medical applications, this allows an estimation of the dose rate at each measurement position. The device makes it possible to both locate irradiating points, while providing quantitative radiation protection data. By estimating the duration of the measurements at each observation point, it is possible to estimate the integrated dose during an intervention. Thus, advantageously, when the detector is worn manually, the device includes a stopwatch allowing an estimation of the duration of each measurement. Experimental tests

[0263] The measurement method was implemented using a hyper pure Germanium detector (Ge HP broad energy 3830): surface area 38 mm2 and thickness 30 mm. The detector was positioned in different positions around a glove box. The isotope 239Pu was taken into account.

[0264] Figure 7A shows a map of photon fluxes (pulses detected per second, or counts per second) measured at 413 keV. These are values ​​of the measured spectrum Sm in 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 areas not accessible with the detector. This is also 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 4 faces of the glove box is shown: face A, face B, face C and face D.

[0265] [Fig.7B] represents an estimation of the location and mass of material (Pu) of irradiating points by implementing the method as previously described. The glove box examined included a machining workshop, comprising a marble supporting a lathe. The implementation of the invention made it possible to locate three hot spots. The three hot spots were located at the marble, the most intense (point b in [Fig.7B]) being directly above the cutting zone of the lathe. A second irradiating point (point c in [Fig.7B]) was located at an area comprising a tool holder. Finally, a third irradiating point (point a in [Fig.7B]) was located between the wall of the glove box and the frame of the lathe.

[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 attests to the relevance of the method. It allows, by means of the deployment of a simple and inexpensive detector, and in field conditions, to estimate the quantity and distribution of activity in an object.

[0268] In the preceding examples, the use of a detector having 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 irradiating points in vivo, the object being a part of a human or animal body.

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

[0271] The invention, at the cost of a spatial resolution that is certainly less good than gamma imaging, makes it possible to obtain a usable result of locating irradiating points, and the quantification of their respective activities in an object with a much smaller number of measurement points, and with inexpensive and simple to implement equipment. An important aspect is that it also does not require any hypothesis regarding the attenuation of the object: when the attenuation matrix is ​​used, the attenuation of the irradiating points is estimated jointly with the position and the intensity of the irradiating points, in the parameter vector.< / j>

Claims

Claims

1. Method for locating irradiating points in an object, each irradiating point emitting gamma photons at at least one emission energy, the method implementing 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 detected pulses; the process comprising 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 the measurements, by the measuring circuit, so as 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), comprising 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 a direct matrix model, linking an estimate of the observation vector (v) to an intensity vector (0^.), the intensity vector comprising 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. 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 points ir- selected radiants.

2. Method according to claim 1, in which: - the measuring circuit (12) is a spectrometric measuring circuit, configured to form a spectrum, the spectrum corresponding to a number of photons detected in different channels, to each channel corresponding an energy of the detected photon; - the measuring circuit comprises a spectrometry unit (13), configured to identify at least one emission peak on the spectrum formed by the spectrometric measuring 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 counting rates from each emission peak.

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

4. The method of claim 3, wherein step g) is performed by a maximum likelihood algorithm.

5. Method according to any one of the preceding claims, in which: - steps d) to h) are repeated taking into account, during each iteration of steps d) to h), different numbers of irradiating points (N); - the method comprises a determination of 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 method includes an estimation of the most probable number of irradiating points based on the different validity indicators respectively associated with different numbers of irradiating points.

6.

7.

8. A method according to claims 4 and 5, wherein, wherein the validity indicator is an Akaike information criterion (AlCc, AICn). A method according to any preceding claim, in which the direct model includes a response matrix (^), formed from 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 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 (Hk), reflecting the efficiency of the detector, each term of which corresponds to a detection efficiency of the detector for a position and an orientation of the detector and for a position of a point irradiating at at least one emission energy. The method of claim 7 wherein the direct model comprises a response matrix (Rk), formed from 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 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, each term of which 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. Method according to claim 7, in which 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 translating 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. Method according to claim 9, in which step e) comprises: - 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 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. Method according to any one of the preceding claims and claim 3, in which: - for the same number of irradiating points selected in the object, steps e) to h) are repeated; - the method comprises 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 selected, being those corresponding to the minimum cost function.

12. A method according to any preceding claim, 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. 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 ​​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 sensitivity matrix of the detector and the attenuation matrix; - the position and the 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 preceding claim, wherein step b) comprises selecting at least one emission energy of a predetermined isotope, so as to extract the count rates in each selected emission energy.

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

16. 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. 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 a 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 movable around the object, so as to be able to be arranged in several positions and / or according to different orientations relative to the object; - a measuring 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 measuring circuit.

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

20. Support, connectable to a computer, comprising instructions for implementing step c) and e) to h) of a method according to any one of claims 1 to 17 from counting rates resulting from measurements carried out using a gamma photon detector around an object.

Images