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    • 专利摘要:
    The invention relates to a method for linearization of attenuation measurements obtained by means of a direct conversion spectrometer. The spectrometer includes a radiation source and a detector for detecting said radiation after it has passed through an object. An attenuation measurement is represented by a vector Md giving the attenuation of the radiation in a plurality Nk of energy channels of the detector, said spectrometer being characterized by a response matrix Ψ. Said method estimates, by means of an iterative process, a vector Mlin, called equivalent linear attenuation vector, giving for each energy channel an attenuation linearly dependent on the thickness of material traversed by the radiation. The method is applicable to the characterization of material as well as the reduction of artifacts in computed tomography.
    公开号:FR3019652A1
    申请号:FR1453051
    申请日:2014-04-07
    公开日:2015-10-09
    发明作者:Emil Popa；Veronique Rebuffel
    申请人:Commissariat a lEnergie Atomique CEA；Commissariat a lEnergie Atomique et aux Energies Alternatives CEA；
    IPC主号:
    专利说明:

    [0001] TECHNICAL FIELD The present invention relates to the field of spectrometric imaging in transmission as well as that of X-ray or gamma ray tomography (CT). STATE OF THE PRIOR ART Direct conversion spectrometry uses a semiconductor detector (for example in CdTe), generally discretized in the form of a bar or a matrix of elementary sensors, in which the photons of a radiation incident (X or gamma) create a cloud of electronic charges (of the order of 1000 electrons for a 60 keV X-ray photon). The charges thus generated are collected by electrodes associated with the elementary sensors and form a transient electrical signal having the form of pulses. The integral of such a pulse is generally proportional to the energy deposited by the incident photon. An electronic circuit connected to the sensor makes it possible to estimate this integral by a measurement of the amplitude of the pulse, which allows the estimation of the energy deposited by the incident photon. After digitization, the values of the measured energies are divided into energy channels or energy bands in the form of a histogram making it possible to construct the spectrum of the radiation after interaction with the irradiated object. This spectrum provides information on the density and nature of the object.
    [0002] However, the spectrum provided by such a spectrometer is deformed with respect to the actual spectrum of the incident radiation due to dispersive physical energy interactions between the radiation and the detector. Specifically, charge sharing and induction sharing phenomena lead to overestimation of low energy photons and underestimation of high energy photons in the spectrum.
    [0003] These phenomena lead to measuring artifacts depending on the thickness of the irradiated object. Indeed, the greater the thickness traversed by the radiation is important and its spectrum is shifted towards high energies. We speak of "spectrum hardening". This effect is all the more pronounced as the energy channels used by the spectrometer are wide. The spectrum hardening leads to erroneous attenuation measurements, not linearly dependent on the thickness traversed by the radiation. Similarly, spectrum hardening generates artifacts in computed tomography (CT) images, particularly so-called cupping artifacts and streaking artifacts in inhomogeneous materials. These artifacts are detrimental to the interpretation and exploitation of the images obtained. The object of the present invention is to correct the attenuation measurements taken by a direct conversion spectrometer so that these depend linearly on the thickness of the material traversed. A subsidiary object of the present invention is to reduce cupping and streaking artifacts in computed tomography. DISCLOSURE OF THE INVENTION The present invention is defined by a method of linearizing attenuation measurements obtained by means of a direct conversion spectrometer comprising a radiation source and a detector for detecting said radiation after it has passed through an object. , an attenuation measurement being represented by a vector Md giving the attenuation of the radiation in a plurality Nk of energy channels of the detector, the real attenuation of the constituent material of the object decomposing according to a characteristic basis of the attenuation in this material, p, ', n = 1, ..., N with N> _2; said spectrometer being characterized by an IF response matrix giving for a plurality Nk of energy bands the probability that a photon emitted in an energy band h = 1, ..., N h is detected in a channel of energy.
    [0004] Said method estimates a Mbri vector, said equivalent linear attenuation vector, giving for each energy channel an attenuation linearly dependent on the thickness of material traversed by the radiation, said method comprising an initialization step in which M is estimated in by the attenuation measure Md and a succession of iterations, each iteration j providing an estimate (N'Il "'(i) and comprising: (a) a step of projecting the estimate (i -1) M'in obtained at the previous iteration on a gigri image basis, n = 1, ..., N, image by said response matrix P of said characteristic basis of attenuation of the material; (b) a step of determining a nonlinear energy deformation, T, of the components of the estimate S'I` "` (j -1) to obtain a corresponding attenuation Mdr (j) in said different energy channels, according to a model non-linear spectrometer, (c) a step of deformation inverse mapping of the Md components to provide a new estimation M'In (j) of the equivalent linear attenuation Mhn of said attenuation measurement, or components of said equivalent linear attenuation Mhn in said image base. Iterations can be stopped when a predetermined number (Lx) of iterations is reached.
    [0005] Alternatively, they can be stopped when a convergence criterion of the estimate of the equivalent linear attenuation is satisfied. According to a first variant, the characteristic basis of the material is a vector base 1.1, CO ph where p, c0 gives the linear attenuation coefficient of the radiation due to the Compton effect in the different energy bands and iiph gives the coefficient of attenuation of the radiation due to the photoelectric effect in the different energy bands, the vector of the real attenuation coefficients gi of the material in these different bands being obtained as a linear combination of the vectors pco, pph.
    [0006] According to a second variant, the characteristic basis of the material is a base of itn vectors, n = N, relating to reference materials, each vector of this base giving the actual attenuation coefficients in the different energy bands for a material. reference.
    [0007] In step (a) of an iteration j, a vector of size N giving the components of 11 / 11m (j-1) in the image base fμ ,,, n = 1, ..., N is advantageously determined. We can then determine the non-linear transformation T by estimating the real attenuation in the material from 1111 (j) = 13,, where 13p is a matrix whose columns are constituted by the vectors itn, n = 1, ..., N, and calculating the diagonal matrix Wid such that WfM hn (j -1) = Mc: (j) where Mrd (j). ). In step (c) of the iteration, the new estimate M'in (j) of the equivalent linear attenuation is advantageously obtained by means of M'in (= (w 11 M d). the invention, the linearization method further provides a characterization of the material from the components "ei, ..., êN said M'in equivalent linear attenuation in said image base.This characterization may be in particular a composition of the material in BRIEF DESCRIPTION OF THE DRAWINGS Other features and advantages of the invention will become apparent upon reading a preferred embodiment of the invention with reference to the accompanying figures in which: Fig. 1 shows an experimental scheme using a direct-conversion spectrometer known from the state of the art Fig. 2 shows attenuation coefficient curves as a function of the 25 energy channels; 3 schematically represents a model of the attenuation measured by a direct conversion spectrometer; Fig. 4 shows examples of nonlinear deformation curves used in the model of FIG. 3; Fig. 5 is a flowchart of a method for linearization of attenuation measurements obtained by means of a direct conversion spectrometer, according to an embodiment of the invention; Fig. 6 shows the procedure of the attenuation mitigation method of FIG. 5 from the model of FIG. 3; Fig. 7 is an example of a spectrum of a radiation source; Fig. Figure 8 illustrates the effect of the method of linearization of mitigation measures in a particular example. DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS Before allowing a better understanding of the correction method according to the invention, we will first model the phenomenon of spectrum hardening in the context of a simple experimental scheme, illustrated in FIG. 1. This experimental scheme uses a radiation source 110, for example a source of X or gamma radiation. The photon beam emitted by the source passes through a homogeneous object, 120, the attenuation of which it is desired to measure or more precisely the linear attenuation coefficient, hereinafter simply referred to as the attenuation coefficient. After passing through the object, the beam arrives on the detector of a direct conversion spectrometer, 150. The detector, 151, is connected to the pulse integration device, 152, providing for each pulse a value of energy corresponding. The counting module, 153, distributes the energy values thus obtained in energy bands (energy channels) to give the spectrum of the radiation having passed through the object. Knowing the radiation spectrum of the source or having previously measured it in the absence of the object (so-called full flow measurement), a calculation module, 154, estimates the attenuation by the object in the different bands. If one notes / the coordinate along the beam, the thickness of the crossed material is none other than: L = f dl r where F is the intersection of the trajectory of the beam with the object 120. The energy spectrum radiation passed through the object is given by the Beer-Lambert law: ni (E) = no (E) e-ii (E) L (2) where no '(E) is the amount of radiation emitted by the source , at energy E, nt (E) is the amount of radiation that has passed through the object, at energy E and, u (E) is the attenuation coefficient of the material for energy photons E. L i indicates that the spectrum of the incident radiation on the spectrometer is considered, as opposed to the index d, used in the following to designate the spectrum actually measured by the spectrometer.
    [0008] In order to be able to carry out a vector processing of the source spectrum, we will assume that the energy axis is discretized into a plurality of indexed bands h = 1, ..., Nh of arbitrarily small width (for example of the order of 1keV). The expression (2) then translates into discrete form by: ni (h) = no (h) e-11 '(h) L (3) The term, d (h) represents the real linear attenuation coefficient of material, regardless of any measure. The physical quantity, u` (h) L represents the attenuation of the radiation, having passed through the thickness L, for the energy band h and will be denoted subsequently by Mt (h, L). In the case where the object is not homogeneous, the trajectory F can be decomposed into 6 (1) elementary segments of attenuation coefficients (h, /) and the total attenuation of the beam for the band h is then simply : ni (h) = nio (h) em '(h .1 ") with Mt (h, L) = f (h, 1) dl (4) If we have an ideal detector, we can access to ni (h) and to deduce the attenuation coefficient on the beam path: p1 (h) = - -n L flio (h) L 1 ((h) fit '(h, /) d / (5) It will be understood that the attenuation coefficient measured by an ideal detector is therefore equal to the average of the attenuation coefficients encountered, weighted by the thicknesses traversed on the path.In practice, the spectrometer is not ideal and a photon of given energy can generate a response in several adjacent energy channels The energy channels used by the detector will be indexed by k = 1,., N k with Nk "Nh and the spectral densities measured by the spectrometers. be noted nd (k), k = 1, N k It will be understood that the discretization in energy bands h = 1, ..., NI, can be made arbitrarily fine to model the theoretical spectrum while the channel discretization of energy k = 1, N k is conditioned by the spectrometer for counting the pulses. The relationships between the real densities nd (k) and the theoretical densities ri (h) are complex because of the large number of physical phenomena involved. If nonlinear phenomena such as stacking phenomena are ignored , drift or memory effect of the detector, the actual densities can be expressed linearly from the theoretical densities in the form: nd (k) = E n '(h) (13 (k, h) (6) h The equation (6) can be expressed equivalently in the following matrix form: nd = (Dili (7) where nd = (nd (1), ..., nd (NOr is the vector of the spectral densities measured by the T spectrometer, ni = (r71 (1), ..., r1 (Nh)) is the vector of the spectral densities of the source and d) is the matrix of size Aik x Aiii formed by the coefficients (13 (k, h ), k = 1, ..., AI k, n = 1, .., Ni, Expression (7) gives the spectral density measured by the detector under full flow conditions from the spectral density of the sour More precisely, the element (13 (k, h) of the matrix (1) is the average number of photons detected in the energy channel k when the source emits a photon in the energy band h. The matrix (13 therefore depends only on the detector and will be called for this reason the response matrix of the detector For an ideal detector iv k = Ni, and the matrix (/) is none other than the identity matrix.
    [0009] It is recalled that the attenuation of the measured radiation by means of an ideal detector is given by the expression (4), namely: M i (h, L) = -ln n (h, L) On the other hand, when Radiation attenuation is measured using a real detector: do (h, L) (8), 1 (13 (k, hpo (h) e Md (k, L), ln nd (A '= ln h "(k, L) (D (k, h) lo (h) h (k, h) o (h) ew (hL) Md (k, L) = ln nt (k'L) = -ln h n ((k, L) (k, h) nto (h) h is still in the more condensed form: (Md (k, L) = -ln rP (k, h) e (h, L) h (9-1) (9-2) having defined the coefficients 111 (k, h) by 111 (k, h) = (I) (k, h) nto (h) II: (k, h) nto ( h) h It is therefore understood that, in the case of a homogeneous object, if the attenuation measured with the aid of an ideal detector depends linearly on the thickness traversed by the beam (M (h, L) = (h) L), it is not the same for a real detector IN, (Md (k, L) = -ln rii (k, h) e - "'(h) L), in other words the coefficient attenuation measured h = 1 / Id (k, Lq-Ald (k, L) depends on the driver L traversed by the beam. The same conclusion is all the more true for an inhomogeneous material. The matrix tif of size Nk x Nh depends on both the source and the response of the detector, it will for this reason be called hereinafter system response matrix. An element kil (k, h) of the matrix represents, under full flux conditions (and thus in the absence of an object between the source and the detector), the probability that a photon detected in the channel k is in fact derived from a channel h of the source, in other words the coefficient (k, h), k # h, represents the probability of bad detection in the channel k knowing that the emitted photon was in the channel h. Similarly the coefficient 'I' (k, k) represents the probability of good detection of a photon in the channel k. When the system is ideal, Nk = Nh and the matrix W is, like the response matrix of the detector, equal to the identity matrix of size Nh>: Nh.
    [0010] Because of the convexity of the function -1n (x), we have the following increase: Md (k, (k, MM '(h, L) (10) h We then define the equivalent linear attenuation I (k, L) by: (k, L) i (k, h) Mi (h, L) h For a homogeneous material, we can similarly define the equivalent linear attenuation coefficient by: (k) (k, h ), ui (h) (12) h Thus, the measured attenuation, respectively the attenuation coefficient measured, is increased by the equivalent linear attenuation, respectively by the equivalent linear attenuation coefficient: Md ( The expressions (11) and (12) can be more condensed in matrix form: _) WIVII (L) and itfin = (14) where tif is the matrix Nk X Ni, consisting of the elements (k, h), M "n = Aen (1, Aen (Nk, L)) Tet glin = ( fi "n (1), ... 'u" n (Nk) Y It is important to note that the measured attenuation Md (k, L) approaches asymptotically from Mit "(k, L) and when the thickness crossed L tends to zero. Similarly, for a homogeneous material, the measured attenuation coefficient Md (Lk, L) k, L) = approaches asymptotically from, e (k) when the thickness crossed L tends to zero. Physically, the equivalent linear attenuation coefficient represents the measured attenuation coefficient of a very fine homogeneous sample of the object. On the other hand, when the object is not homogeneous, the equivalent linear attenuation coefficient represents the average of the linear attenuation coefficient on the beam path. Indeed: mlin (L) 1 L) = f gi (l) d1 = L = itiht (l) d1 (15) On the other hand, it should be noted that this linearity property is not checked for the measured attenuation coefficient dud (k, L) = -1 Md k, L). Fig. 2 represents attenuation coefficient curves measured using a direct conversion spectrometer as a function of energy. These curves relate to polyoxymethylene samples of different thicknesses. The radiation source is a tungsten-based x-ray source and the semiconductor detector a CdTe line detector with a pitch of 0.8mm and a thickness of 3mm. The energy channels of the detector have a width of 1keV.
    [0011] The curve designated by small circles corresponds to the equivalent linear attenuation coefficient jim. As predicted, it is noted that for small thicknesses the curves of the attenuation coefficients measured are almost coincident with the curve of the equivalent linear attenuation coefficient. The idea underlying the invention is, for a given attenuation measurement, to estimate the equivalent linear attenuation or the equivalent linear attenuation coefficient, by using a model of the attenuation of the material. Fig. 3 represents a modeling of an attenuation measurement by a direct conversion spectrometer from a model of the attenuation of the material. There is shown in 310 a model of the attenuation of the material. According to this model, the attenuation / the real (linear) attenuation coefficient of the material is decomposed according to a base of attenuation vectors, characteristic of the material. Thus, the real attenuation coefficient is decomposed according to a lin attenuation vector base, n = 1,..., N:, u1 (h) = E anx (h), h = 1, ..., N h (16-1) n = 1 is again, in vector form: N Ill = 1 angn (16-2) n = i where g - (xi (1), ..., / he (h)) T is the vector of the real attenuation coefficients of 'T material at energies 1, ..., N h and pin = Cun (1), ...' un (Nh)), n = 1, ..., N are the vectors of the characteristic basis of the material and an, n = 1, ..., N, are the components of p, in this base. It is important to note that the a components do not depend on energy.
    [0012] The relation (16-1) can result in particular from the discretization of the attenuation function of the material when it can be expressed according to a linear combination of elementary functions: N (17) ii (E) = Ian, a ( E) n = i where dul (E) is the attenuation function of the material as a function of the energy E of the radiation and, u, (E), n = 1, ..., N form a basis of functions. For a thickness traversed by the beam, the attenuation can decompose in a manner similar to (16-1), using the same characteristic basis: NM (h, L) = I cn (L), a (h), h = 1, ..., N h (18-1) n = 1 is again, in vector form: N (18-2) 15 M (L) - 1 in M'un n = i with cn (L) = L.an. The components cn (L) depend only on the thickness L and not on the energy h. They physically represent equal attenuation lengths for the different vectors of the characteristic base. According to a first variant, the vectors of the characteristic base relate to distinct physical mechanisms. Thus, it is known that X-rays are essentially attenuated due to the Compton effect, on the one hand, and the photoelectric effect, on the other hand. In this case, the relation (16-2) can be expressed in the following form: 12 = acol-tco + aphil ph (19) where lico is the vector of attenuation coefficients due to the Compton effect and is the vector of attenuation coefficients due to the photoelectric effect. The coefficients aco and aPh do not depend on the energy. On the other hand, the vectors p, co and 1.1, ph and, more generally, the attenuation functions pc, (E) and uph (E) each depend on the energy E according to distinct dependence laws. According to a second variant, the vectors of the characteristic base are relative to different reference materials. Indeed, it is known that an attenuation coefficient of a material can be considered as the linear combination of two attenuation coefficients of two known materials, or even more, and that in a range of energy varying between 10 keV and 200 keV. For example, if the material of the object is a mixture of elementary materials X, Y, Z, the relation (16-2) can be written in the following form: Ili = axl-tx + aylly + azilz (20) ) gx, p, y, i..tz are respectively the vectors of the attenuation coefficients of the elementary materials X, Y, Z.
    [0013] Whatever the chosen characteristic base μn, n = 1, ..., N, the coefficients, uh (h), h = 1, ..., Nh, constituting the vectors of the base, are supposed to be known by means a calibration or pre-simulation phase. In a general way, the base consists of N vectors. In particular, each vector is representative of a property of a given material as a function of energy. In the examples described in this description, the vectors are attenuation coefficients, in particular linear attenuation coefficients. It could of course be mass attenuation coefficients.
    [0014] Block 320 represents a linearized model of the direct conversion spectrometer, represented by the system response matrix, P. Using the attenuation model, 310, and the linearized model of the spectrometer, 320, the equivalent linear attenuation coefficient is expressed by means of relations (12) and (16-1): Nh N (21- 1) duhn (k) = EE ang (k, h), a (h) h = 1 n = 1 Similarly, the equivalent linear attenuation is expressed using relations (12) and (18) 1): Nh NI (k, L) = Icn (L) 111 (k, h) / in (h) (21-2) Expressions (21-1) and (21-2) can more simply be formulated from matric way: en = 1PB a (22-1) and Mlin = LIPBea = WB / 2c (22-2) where qi is the response matrix of the system, Bi, is the matrix of size Ni, x N whose columns are the vectors if, n = 1, ..., N of the characteristic base, a = ..., aN) T and c = LaN) T Expressions (22-1) and (22-2) mean that the coefficient equivalent linear attenuation / equivalent linear attenuation can decompose in a second base, image of the characteristic base by the linearized response of the system, r represented by the matrix y. In other words, the image base consists of the column vectors of the matrix A = IFB of size NkX N with the same components as those of the attenuation coefficient / the real attenuation in the characteristic base. Expressions (22-1) and (22-2) provide a linear model of mitigation measures since the components of Win do not depend on L and those of M "" are proportional to L. Block 330 represents a model of the attenuation measurements using the real spectrometer. A decomposition of the real attenuation coefficient in the base B is associated with a measurement M d of attenuation of the spectrometer. More precisely, to a decomposition a = (a ,, ..., aN) T of this base, one associates the attenuation measure: Md (L) = ln (Ilie-LB "a) = -1n (life -Bec) (23) where the expressions ex and ln (X), X being a vector, respectively represent vectors of the same size as X whose elements are respectively ex (m) and ln (X (m)) where X (m) are the elements of X. The vector M = B c, M = Mc (Nh)) represents the measure that would be obtained if the detector were ideal, the matrix 111 being equal to the identity, with Nk = Nh - The transformation between 320 and 330 makes it possible to go directly from the linear model to the non-linear model of the real spectrometer This transformation is in fact a dispersion function operating on the components of the equivalent linear attenuation vector Mb "in the image of the characteristic base. More precisely, to a vector Mlin = Arc = cnμn, we associate the vector T (mlin) _Md with Md = IcnWdllign where n = 1 n = 1 Wd = Diag (Wd (1, L), ..., Wd (Nk , L)) is a diagonal matrix of size NkX Nk whose elements are given by: (24) (Nh -11-1rP (k, h) e-m '(") 1 Wd (k, 0 = __LNh- / 1) 115 (k, h) / 14, (h) 1,1 It will be understood that the transformation T corresponds to a scalar cn, applying identically to all the energy components of a vector Iin, a matrix T (cn) = cnWid of size Nk whose diagonal coefficients may differ, thus the transformation T represents a mechanism of dispersion in energy and can be seen as a deformation of each coefficient C ,, as a function of the energy component to which it applies or, in the same way, as a deformation of the vectors Wiln, n = 1, ..., N the matrix Wd differently weighting the energy components of these vectors, It will be noted that when the thickness crossed L is low, the values are such that cnitn (h) "1 and the matrix Wd is close to the identity matrix. Due to the convexity of the function -1n (x) the elements Wd (k, L) are strictly included between the values 0 and 1. FIG. 4 represents the dispersion of the coefficients C, as a function of the thickness traversed L. More precisely, this figure represents the strain function Nh -ln r P (k, h) e-m '(") 1 (Wd (k, L) = 21.71 of each of the Nk components of vector No. 115 (k, h) A / 1, (h) n = 1 in the image base, as a function of the thickness traversed L. It is clearly seen that, for low values of L, the weighting coefficients Wd (k, L) are close to 1 and therefore the components are not deformed, whereas the M lin deformation becomes larger for higher thickness values, especially in Fig. 5 shows a method of linearization of attenuation measurements obtained by means of a direct conversion spectrometer, according to an embodiment of the invention. at least one attenuation measure in a plurality of energy bands, k = 1, ..., Nk, by means of of said spectrometer This measurement is represented by a vector M d = (Md (1), ..., Md (Nk) where Md (k) is obtained as the natural logarithm of the ratio between the number of photons detected in the channel k with and without the object. It is assumed that the response matrix of the system, qi, is also known by means of calibration or pre-simulation. It is recalled that this matrix of size Nkx Ni gives, under full flux conditions, the probability that a photon is detected in a channel k of the spectrometer when it has been emitted in a band of energy h. Finally, we assume that we know a base of vectors, B characteristic of the attenuation of the material, in other words a plurality N of vectors on which we can decompose the real attenuation coefficient of the material, as explained above. At step 510, the estimation of the equivalent linear attenuation vector, M n, is initialized by the measured attenuation vector M d, ie M lin (0) = Md. It can indeed be considered, as a first approximation, that the measured attenuation vector is an estimate of the equivalent linear attenuation vector. The iteration counter j is initialized to 1. The method of linearization of the attenuation measures then operates by successive iterations, refining progressively the estimation of Miin. We denote M lin (j), the estimation of M lin at the iteration j.
    [0015] In step 520, the estimate of M end obtained at the preceding iteration is projected, namely Kilin (i, on the basis Ai, = 1nμ, image of the characteristic base 13 ", by the response of the system, otherwise known as determines the coefficients' eh (j), n = 1, .., N, such that: ellin Ci -1) = riri (j) 1111.4 = Aeê (j) (25) n = 1 where ((I), CN (j)) Given that we generally have N "Nk, the system of Nk equations with N unknowns (25) is overdetermined and we solve it by a least squares criterion .The vector ê (j) is for example determined by: = end (j -1) (26) where At = AT (AA ') 1 is the pseudo-inverse of the matrix A. At step 530, the nonlinear deformation to be applied to the components of Miln is calculated ( j-1) in the image base, Witn, to obtain the attenuation measured by the spectrometer: (Nh -ln Itlf (k, Me-wu / xi))) Wd (k) = N 11-1 .11- 5 (k, h) / 14, (j) (h) h = 1 (27) where Mc (j) = 13, that is, each component ôn (j) is dispersed in energy and gives Instead, at a plurality of coefficients for the different energies: i '(i) W d (1), i) 147 d (Nk) In step 540, the equivalent linear attenuation vector is estimated from the vector of M d attenuation: M./dr md (28) d that is to say A ^ 411n (i) (k) = M (k) ^ k = 1, ..., Nk. Y ') In step 550, it is checked whether a stop criterion is satisfied. According to a first variant, the stopping criterion is a predetermined maximum number of iterations j ..
    [0016] According to a second variant, the stopping criterion is a convergence condition. For example, we can decide to stop the iterations as long as: 11Miln (i) -Miln (i 11Miln (j) 1 <e (29) where en, is a predetermined threshold and 11I designates the Euclidean norm. stopping criterion is checked, the linearization method continues at step 560. If not, the iteration index j is incremented at 555 and step 520 is returned to a new iteration. step 560, the estimation of the equivalent linear attenuation M fin = (ein (1), ..., ein (Nk)) T for the different energy channels of the spectrometer is provided.
    [0017] The linearization method can alternatively provide the vector of the components δ = (,..., NN) of the equivalent linear attenuation in the image of the characteristic base 11/131. These components make it possible to characterize the material of the object, and if necessary, when the vectors of the characteristic base are relative to reference materials, to determine their composition. It is shown in FIG. 6 in the form of a graph, the implementation of the method of linearization of attenuation measurements from the model of FIG. 3. It contains the model 310 of the attenuation of the material using the characteristic base Bp, the linear model of the attenuation measurements, 320, using the image of the characteristic base by the response of the system, 111134, and the model nonlinear mitigation measures 330, associated with the spectrometer. The initialization operation, 610, consists of an approximation of the equivalent linear attenuation by the attenuation measurement M d. This first estimate amounts to supposing that the deformation matrix Wod is equal to the unit matrix.
    [0018] The first operation, 620, is a projection of the estimate of the linear equivalent attenuation M fin (j -1) on the basis of the linear model. It makes it possible to obtain the components of M d in this base, represented by êj. From this projection, one can go back in 631 to an estimate of the attenuation of the material, expressed in the characteristic base, that is 1-N / 1 (j) = 13,, ê1. Operation 632 consists in obtaining the measurement of the attenuation by means of the spectrometer, assuming that the attenuation of the material is equal to Mi (j). This measure of attenuation is calculated by the expression (23): Meir (j) = - ln (Ite-Beêi (30) where Md, (j) is the mitigation measure reconstructed from components.
    [0019] From the reconstructed measure Md (j) and from the estimation of the equivalent linear attenuation obtained at the previous iteration, - U 1), one determines at 633 the transformation T making it possible to pass from the linear model to the non-linear model. linear, i.e. the diagonal matrix Wd as operations 631 to 633 are performed in step 530 of FIG. As previously described. The matrix Wd (the transformation T ') is then used to obtain a new estimate of the equivalent linear attenuation at 640 by means of the expression (28), namely M' lin (i) (w di) 1 Md.
    [0020] Operations 620 to 640 are iterated until the estimate converges or until a predetermined maximum number of iterations is reached. We will illustrate below with an example the corrective effect of the linearization of attenuation measurements obtained by means of a spectrometer.
    [0021] The source of the spectrometer is here an X-ray source using a tungsten cathode. The spectrum of the source is shown in FIG. 7. The detector of the spectrometer is a pixelated CdTe sensor in 16 pixels (elementary sensors) with a pitch of 0.8 mm and a thickness of 3mm, polarized at -1kV.
    [0022] The object to be analyzed is polymethylmethacrylate (PMMA or Plexiglas Tm). The characteristic base used is a base relating to two reference materials namely polyethylene (PE) and polyoxymethylene (POM / Delrin Tm). Fig. 8 shows the corrective effect provided by the linearization method in the context of a so-called "full-spectral" measurement, that is to say when the number of energy channels is equal to the number of bands, Nk = Nh (here 256 channels of width 1keV). The acquisition of attenuation measurements (Md) is performed with a POM object whose thickness is L = 25cm Mh (_1) = (i) We see in Figure 8 that the gross measurement (curve in broken lines 810) shows a distortion with respect to the real equivalent linear attenuation coefficients (curve in solid line 820). This distortion is more visible for low energies. Note that the correction obtained by the linearization method according to the invention (curve in broken lines 830) almost completely restore the theoretical measurements (ideal spectrometer). Figs. 9 and 10 show the independence of the attenuation coefficient measurements as a function of the material thickness traversed, after linearization by the method according to the invention (- mhn). -7, The number of energy channels of the spectrometer is 2 (Nk = 2). Figs. 9 and 10 respectively relate to the first energy channel (20-49 keV) and the second energy channel. The attenuation coefficient curves before correction, by 920 and 1020, the attenuation coefficient curves after an iteration, and 930, 1040 the attenuation coefficient curves after 20 iterations, respectively, have been designated by 910 and 1010 respectively. Distortion curves 950 and 1050 also show the theoretical measurements (ideal spectrometer). It is noted that after 20 iterations the equivalent linear attenuation coefficient is quasi-constant and coincides with the theoretical value.
    权利要求:
    Claims (10)
    [0001]
    REVENDICATIONS1. A method of linearizing attenuation measurements obtained by means of a direct conversion spectrometer comprising a radiation source and a detector for detecting said radiation after it has passed through an object, an attenuation measurement being represented by an Md vector giving the attenuation of the radiation in a plurality Nk of energy channels of the detector, the real attenuation of the constituent material of the object decomposing according to a characteristic basis of the attenuation in this material, p,, n = 1, ..., N with 2; said spectrometer being characterized by a response matrix% giving for a plurality Nk of energy bands the probability that a photon emitted in a energy band h = 1, ..., Nh is detected in a channel of energy, said method being characterized in that it estimates a vector Mil '', said equivalent linear attenuation vector, giving for each energy channel an attenuation linearly dependent on the thickness of material traversed by the radiation, said method comprising an initialization step (510, 610) in which Nihn is estimated by the attenuation measure Md and a succession of iterations, each iteration j providing an estimate 1N / 1 / m (j) and comprising: (a) a projection step (520, 620) of the estimate 1/1 / m (j -1) of Nihn obtained at the previous iteration on an image basis' Fg., n = 1,. . . , N, image by said response matrix 'P of said characteristic base of attenuation of the material; (b) a step of determining a nonlinear energy deformation, T, (530, 631-633) of the components of the estimation 1/1 / m (j-1) to obtain a corresponding attenuation Md, (j ) in said different energy channels, in accordance with a non-linear model of the spectrometer; (c) a step of inverse deformation (540, 640) of the Md components to provide a new estimate Énihn (j) of the equivalent linear attenuation Mlin deladite attenuation measure, or "C ,,, components of said attenuation linear equivalent Mbri in said image base.
    [0002]
    A method of linearizing mitigation measures according to claim 1, characterized in that the iterations are stopped (550) when a predetermined number (jm ') of iterations is reached.
    [0003]
    A method of linearizing mitigation measures according to claim 1, characterized in that the iterations are stopped (550) when a convergence criterion of the estimate of the equivalent linear attenuation is satisfied.
    [0004]
    4. A method of linearization of attenuation measurements according to one of the preceding claims, characterized in that the characteristic base of the material is a vector base pco, pph OÙ gco gives the linear attenuation coefficient of the radiation due to the Compton effect in the different energy bands and gph gives the attenuation coefficient of the radiation due to the photoelectric effect in the different energy bands, the vector of the real attenuation coefficients gi of the material in these different bands being obtained as a linear combination of the vectors pco, JtPh-
    [0005]
    A method of linearization of attenuation measurements according to one of claims 1 to 3, characterized in that the characteristic basis of the material is a base of vectors 1.1, n, n = 1, ..., N, relating to reference materials, each vector of this base giving the actual attenuation coefficients in the different energy bands for a reference material.
    [0006]
    6. The method of linearization of attenuation measurements according to one of the preceding claims, characterized in that in step (a) of an iteration j, undetermines a vector of size Nj describing the components of M fin (j -1) in the image base n = 1, ..., N.
    [0007]
    7. A method of linearization of attenuation measurements according to claim 6, characterized in that the non-linear transformation T is determined by estimating (631) the real attenuation in the material from M 1 (j) B1 ô1 , where 13p is a matrix whose columns are constituted by the vectors gn, n = 1, ..., N, and calculating (633) the diagonal matrix Wid such that WjdM end (j 1) mach where mar _ ln ( 1Pe Beê)).
    [0008]
    8. A method of linearization of attenuation measures according to claim 7, characterized in that in step (c) of the iteration J is obtained (540, 640) the new estimate M lin (j) of the equivalent linear attenuation by means of Mlin (j) _ (mi1 md
    [0009]
    9. A method of linearization of attenuation measures according to one of the preceding claims, characterized in that it further provides a characterization of the material from the componentsc ,, ..., cNde said equivalent linear attenuation M'in in said image base.
    [0010]
    10. A method of linearization of attenuation measures according to claims 5 and 9, characterized in that said characterization is a composition of the material into said reference materials.
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    JP6594643B2|2019-10-23|
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    优先权:
    申请号 | 申请日 | 专利标题
    FR1453051A|FR3019652B1|2014-04-07|2014-04-07|METHOD FOR LINEARIZING MEASUREMENTS OF ATTENUATION TAKEN BY A SPECTROMETRIC SENSOR|FR1453051A| FR3019652B1|2014-04-07|2014-04-07|METHOD FOR LINEARIZING MEASUREMENTS OF ATTENUATION TAKEN BY A SPECTROMETRIC SENSOR|
    JP2015074890A| JP6594643B2|2014-04-07|2015-04-01|A method for linearizing attenuation measurements taken by a spectroscopic sensor|
    US14/677,293| US10162069B2|2014-04-07|2015-04-02|Method for linearizing attenuation measurements taken by a spectrometry sensor|
    EP15248025.7A| EP2930540B1|2014-04-07|2015-04-03|Method for linearisation of attenuation measurements taken by a spectrometric sensor|
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