JP2013005840A - Image reconstructing apparatus and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an image reconstructing apparatus and program capable of easily corresponding to imaging embodiments of various projecting images and improving applicability.SOLUTION: The image reconstructing apparatus receives image data related to a plurality of projecting images transmitted through an observation object obtained from mutually different directions to the observation object, and based on a distribution function expressing the presence of a predetermined correlation among the pixels of the images of the observation object and a condition related on the process until the projection image is obtained based on the observation object, forms a calculation equation expressing a probability model for forming the projection image, and using a Bayesian inference, estimates the sectional image of the observation object from the calculation equation expressing the probability model and the image data.

Description

  The present invention relates to an image reconstruction device and a program, and more particularly to improvement of image quality.

  A technique is known in which an X-ray captured image of an observation target is captured from various angles θ from the outside of the observation target, and an image inside the observation target is reconstructed using a plurality of images obtained by the imaging. . This technique is called CT (Computed Tomography) and is used in various scenes such as medical treatment and product manufacturing.

  The CT technique is classified into an analytical method and a successive approximation method according to a method of reconstructing the image, and the successive approximation method is further classified into an algebraic method and a statistical method.

  FIG. 7 is an explanatory diagram illustrating an example of an image reconstruction method in the conventional CT technique. A projection image y obtained by photographing the observation object x by CT is obtained as a result of Radon transformation (Radon transformation) W of the original image x. That is, y = Wx. Theoretically, the original image can be obtained by performing inverse Radon transform on the projection image y (x = Wty). However, in reality, since the shooting angle θ is discrete, the sampling interval between the projected images increases (A) and the image becomes blurred (B) as it goes outward from the center of the observation target.

  In view of this, a method has been proposed in which the filter f is first applied to the projection image y and then f * y and inverse transformation Wt are performed. As such a filter f, there is, for example, a so-called Ramachandran-Lakshminarayanan filter. Since this method is widely known, detailed description thereof is omitted, but the image obtained after the inverse transformation is relatively close to the original image.

  Patent Document 1 discloses a technique for performing super-resolution processing on a CT image.

JP 2005-095329 A

  However, the above conventional method does not take into account the effects of noise from the detector, rotational axis shift during imaging or reconstruction, fluctuations in the amount of rotation, and the like, and various artifacts (artifact: actual) It is known that a non-existent image) occurs.

  In addition, in the inverse Radon transform, an integration operation is performed over the entire reconstructed image. Therefore, when a part of information is missing, a fatal artifact may occur. For example, in an electron microscope CT or the like, there is a limit on the angle at which an image can be captured due to structural limitations of the imaging target, and information cannot be captured in the range of the angle related to the limitation. In addition, if there is a part of the observation target that has a greatly different radiation absorption rate from the other part, a radial artifact is generated.

  On the other hand, there is also a method in which the estimated image xk of the original image is sequentially approximated as xk = xk-1 + αkqk using a predetermined update vector q_k and a weight αk without using the filter f. According to this method, artifacts based on other factors cannot be suppressed, although generation of artifacts can be suppressed with respect to information loss compared to a method using a filter.

  Furthermore, the method using these filters f and the method of sequentially approximating them have poor applicability because the filter f must be designed in accordance with the imaging mode of the projected image.

  The present invention has been made in view of the above circumstances, and it is an object of the present invention to provide an image reconstruction apparatus and program that can easily cope with various imaging forms of projected images and have improved applicability. .

  Another object of the present invention is to provide an image reconstruction device and program capable of improving image quality, such as suppressing artifacts caused by various factors.

  An invention for solving the problems of the above conventional example is an image reconstruction device, which accepts image data relating to a plurality of projection images obtained from different directions with respect to the observation target and transmitted through the observation target. And a projection function based on a distribution function indicating that there is a predetermined correlation between pixels of the observation target image and a condition relating to a process until a projection image is obtained based on the observation target. Means for generating an arithmetic expression that represents a probabilistic model for generating the image, an arithmetic expression that represents the probabilistic model using Bayesian estimation, and a means for estimating a cross-sectional image of the observation object from the image data. That's what it meant.

Further, in the image reconstruction device according to one aspect of the present invention, the means for generating the arithmetic expression representing the probabilistic model is a condition related to a process until a projection image is obtained based on the observation target. It is means for generating an arithmetic expression representing a condition including an unknown parameter due to disturbance, and further includes means for estimating the unknown parameter.
Furthermore, in the image reconstruction device according to another aspect of the present invention, the projection image is obtained by detecting an electromagnetic wave or a particle beam that passes through an observation target, and generates an arithmetic expression that represents the stochastic model. The means generates a projection transformation matrix, which is an arithmetic expression, using a transformation matrix that represents an effect that the wavelength-dependent energy attenuation of the electromagnetic wave or particle beam accompanying the transmission of the observation object has on the projection image. That's what it meant.

  Furthermore, a program according to another aspect of the present invention includes a computer for receiving image data relating to a plurality of projection images obtained from different directions with respect to the observation target and transmitted through the observation target, and the image of the observation target. A probabilistic model for generating the projection image based on a distribution function indicating that there is a predetermined correlation between the pixels and a condition relating to a process until a projection image is obtained based on the observation target. Means for generating an arithmetic expression to be represented, an arithmetic expression representing the probabilistic model using Bayesian estimation, and a means for estimating a cross-sectional image of the observation target from the image data. .

1 is a configuration block diagram illustrating an example of an image reconstruction device according to an embodiment of the present invention. It is a functional block diagram concerning an example of an image reconstruction device concerning an embodiment of the invention. It is explanatory drawing showing an example of the process of obtaining a projection image from a cross-sectional image. It is a flowchart figure showing the process example of the image reconstruction apparatus which concerns on embodiment of this invention. It is explanatory drawing showing the example of the image respectively reconfigure | reconstructed by the image reconstruction apparatus which concerns on embodiment of this invention, and the image structure apparatus of a prior art example. It is explanatory drawing showing the example of evaluation of the image each reconfigure | reconstructed by the image reconstruction apparatus which concerns on embodiment of this invention, and the image structure apparatus of a prior art example. It is explanatory drawing showing the example of the reconstruction method of the image in the conventional CT technique.

  Embodiments of the present invention will be described with reference to the drawings. As illustrated in FIG. 1, the image reconstruction device 1 according to the embodiment of the present invention includes a control unit 11, a storage unit 12, an input unit 13, and an output unit 14.

  Here, the control unit 11 is a program control device such as a CPU (Central Processing Unit), and operates according to a program stored in the storage unit 12. In the present embodiment, the control unit 11 accepts image data relating to a plurality of projection images obtained from different directions with respect to the observation target and transmitted through the observation target, and between the pixels of the image of the observation target. Generates an arithmetic expression that represents a probabilistic model for generating a projection image based on a distribution function that represents a predetermined correlation and a condition related to a process until a projection image is obtained based on the observation target. Then, using Bayesian estimation, a process for estimating the cross-sectional image of the observation target from the arithmetic expression representing the probabilistic model and the received image data is executed. Details of the processing of the control unit 11 will be described later.

  The storage unit 12 is a memory device, a disk device, or the like, and holds a program executed by the control unit 11. The program may be provided by being stored in a computer-readable recording medium such as a DVD-ROM and copied to the storage unit 12. The storage unit 12 also operates as a work memory for the control unit 11.

  The input unit 13 includes, for example, a serial or parallel input interface, receives image data obtained by imaging with a CT apparatus, and outputs the image data to the control unit 11. The output unit 14 is a display, a printer, or the like, and displays and outputs image data in accordance with an instruction input from the control unit 11.

  The plurality of projection images to be processed by the image reconstruction device 1 according to the present embodiment are transmitted through the observation target or scattered by the observation target from different directions with respect to the observation target. Is obtained by imaging with a detector in which a plurality of detection elements (channels) are arrayed. As an example, a plurality of observation elements on a virtual plane that cuts the observation object in a circle It is a projection image by the general CT apparatus which irradiates X-ray from the angle direction of this. That is, a plurality of projection images obtained by projecting a cross-sectional image when the observation target is cut along the plane from a plurality of angles are set as processing targets.

  The control unit 11 of the image reconstruction device 1 according to the present embodiment functionally includes an image data reception unit 21, a luminance vector extraction unit 22, a transformation matrix generation unit 23, a Bayes, as illustrated in FIG. The estimation unit 24 and the reconstruction unit 25 are included. The image data receiving unit 21 receives input (for example, K pieces) of image data of a plurality of projection images from the input unit 13 and accumulates and stores them in the storage unit 12. Here, the image data of the projected image includes data representing a plurality of pixel values (output values for each detection element). The pixel value data includes, for example, a luminance value.

  The luminance vector extraction unit 22 performs pixel value data (for example, luminance) for each of the k-th (k = 1, 2,..., K) image data stored in the storage unit 12 by the image data receiving unit 21 in a predetermined order. ) To obtain a luminance value vector y (k) (k = 1, 2,..., K). The set of K luminance value vectors D = {y (k)} corresponds to a sinogram.

と表すことができる。すなわち、

The transformation matrix generation unit 23 generates an arithmetic expression related to a prior distribution used for Bayes estimation. That is, the luminance vector representing the original image (cross-sectional image) is x, the projection transformation matrix representing the Radon transform for obtaining the projection image is W (k), and the error caused by the conditions at the time of imaging is ε (k),

It can be expressed as. That is,

を得る。ここでβは精度（分散の逆数）であり、ＩはＷ(k)と同じ次元の単位行列、Ｍはｙ(k)の次元、Ｎ（ｙ(k)｜ａ，ｂ）は平均ベクトルａ、分散行列をｂとする分布関数である。この分布関数は具体的にはガウス分布やポアソン分布など広く知られた分布関数のうちから、予め利用者が選択しておく。 Here, the likelihood function p (D | x) representing the correspondence between the cross-sectional image, which is the original image, and the projection image, that is, the probability that the sinogram D is obtained from the luminance vector x of the original image is the projection transformation matrix W. Since a portion excluding a portion uniquely determined by (k) (ε (k) = W (k) D−x) is equal to a probability p (ε (k)) in which an error (noise) ε (k) occurs,

Get. Here, β is accuracy (reciprocal of variance), I is a unit matrix of the same dimension as W (k), M is a dimension of y (k), and N (y (k) | a, b) is an average vector a , A distribution function with a variance matrix of b. Specifically, this distribution function is selected in advance by the user from widely known distribution functions such as a Gaussian distribution and a Poisson distribution.

を求める。この行列Ｆ(k)は、位置

にある画素を所定の位置に移動したうえで、θkだけ回転させ、ｒ（ｒ＝Ｍ／Ｎ）倍して、

を当該ｒ倍した位置まで再度移動することを意味する。これにより、次のように画素ベクトルの要素ｖjを変換すれば、投影像上の画素値ｕj(k)が得られる。

Further, the transformation matrix generation unit 23 uses the projection transformation matrix W (k) as a matrix representing at least one affine transformation (matrix representing translation, rotation, reduction / enlargement, etc.) or a product (in the case of a plurality thereof), for example, It is determined as follows. That is, as conditions relating to the process until the projection image is obtained from the observation object, the angle when the kth projection image is obtained is θk, the size of the projection image (dimension of the luminance vector) is M, and the original image of the observation object The size of the image (the dimension of the luminance vector) is N, and the width of the disk image, that is, the size of the point spread function, indicates what size disk image is projected on the projected image by imaging. First, the matrix R (θk) representing the rotation of θk, T (ξ) representing the translation by ξ, and M (r) representing the r-fold enlargement / reduction are represented by M (r).

Ask for. This matrix F (k) is the position

Is moved to a predetermined position, rotated by θk, multiplied by r (r = M / N),

Means to move again to the position multiplied by r. Thus, the pixel value uj (k) on the projected image can be obtained by converting the element vj of the pixel vector as follows.

により、投影変換行列Ｗ(k)の要素を次のように表すことができる。

And this uj (k) was used

Thus, the elements of the projection transformation matrix W (k) can be expressed as follows.

  In addition, the transformation matrix generation unit 23 generates an arithmetic expression p (x) that represents a prior distribution (that is, an evaluation function of the cross-sectional image itself that is the original image) based on the constraint condition regarding the image to be observed. Specifically, this distribution is determined as follows. That is, in the image to be observed (image to be reconstructed), there is a correlation between pixels, and it is assumed that the difference in luminance does not exceed a predetermined threshold value between adjacent pixels. As such p (x), for example, there is a Gaussian distribution (the following equation).

であり、ここにｖiは位置ｉにある画素値（ここでは輝度の値）、ｒは画素間の距離、Ａは経験的に定められる係数である。変換行列生成部２３は、これら生成したｐ（Ｄ｜ｘ）、及びｐ（ｘ）に係る演算式（２），（４）式を、確率的モデルを表す演算式として出力する。また、このｐ（ｘ）としては、ポアソン分布等、他の分布を用いてもよい。 The fixed matrix Zx representing the variance is

Where vi is the pixel value at the position i (in this case, the luminance value), r is the distance between the pixels, and A is a coefficient determined empirically. The transformation matrix generation unit 23 outputs the generated equations (2) and (4) relating to p (D | x) and p (x) as equations representing the probabilistic model. As this p (x), other distributions such as Poisson distribution may be used.

であり、このうち分母のｐ（Ｄ）は、すべてのｘについて分子のｐ（ｘ）・ｐ（Ｄ｜ｘ）の和をとったものに他ならないから、予め規格化して「１」としておく。すると、サイノグラムＤが与えられたとき、像がｘである確率を与える事後分布ｐ（ｘ｜Ｄ）は結局、

となる。ここにμは平均のベクトルである。ベイズ推定部２４は、この（７）式に含まれる平均ベクトルμを演算する。この平均ベクトルμは、

である。ここに、Σは分散行列であり、

と表される。再構成部２５は、平均のベクトルμを像の輝度のベクトルとして演算し、出力する。 The Bayesian estimation unit 24 calculates the posterior distribution p (x | D) using Bayesian estimation. This is an estimation of a cross-sectional image that maximizes the evaluation function of the cross-sectional image itself, which is the original image to be reconstructed, and the evaluation function based on the relationship between the cross-sectional image and the projected image. It corresponds to searching as a result. Specifically, from Bayes' theorem,

Of these, p (D) of the denominator is nothing but the sum of p (x) · p (D | x) of the numerator for all x, so it is normalized in advance and set to “1”. . Then, given a sinogram D, the posterior distribution p (x | D) giving the probability that the image is x is

It becomes. Here, μ is an average vector. The Bayesian estimation unit 24 calculates the average vector μ included in the equation (7). This mean vector μ is

It is. Where Σ is the variance matrix,

It is expressed. The reconstruction unit 25 calculates and outputs the average vector μ as a vector of image brightness.

  The image reconstruction apparatus 1 according to the present embodiment has the above-described configuration and operates as follows. That is, with respect to a known 64 × 64 pixel two-dimensional image S, along a scanning direction inclined by an angle θk (k = 1, 2,..., K) from a predetermined angle around the center thereof, A plurality of images each having n pixels (in this case, a plurality of one-dimensional images) Y1, Y2,..., YK projected onto a line segment perpendicular to the scanning direction are obtained (FIG. 3).

  The image reconstruction device 1 according to the present embodiment performs the processing shown in FIG. 4 and accepts a plurality of one-dimensional images for n pixels. Then, a plurality of n-dimensional vectors y 1, y 2,. Here, the luminance value is used, but in the case of color, a vector of values in a predetermined color space (for example, R, G, and B values) may be used.

  Further, the image reconstruction device 1 has a condition related to a process until a projection image is obtained from the observation target, an angle when obtaining the k-th projection image is θk, and a size of the projection image (dimension of the luminance vector) is M. , The size of the original image to be observed (dimension of the luminance vector) is N, the width of the disk image representing the size of the disk image projected in the projected image, that is, the point spread function A matrix R (θk) that represents the rotation of the θk using a magnitude γ of (point spread function), and a matrix that represents a translation by ξ is T (ξ), and a matrix represented by the equation (3) F (k) is obtained (S2).

  Then, the image reconstruction device 1 converts the pixel vector element vj by this F (k) to obtain a pixel value uj (k) on the projection image, and uses this uj (k) to determine the element. A transformation matrix W (k) is obtained (S3). Then, using this matrix, a likelihood function used for Bayesian estimation, p (D | x), is obtained as in equation (2) (S4).

  Further, the image reconstruction device 1 generates an arithmetic expression p (x) representing a prior distribution based on the constraint condition regarding the image to be observed (expression (4)) (S5), and the generated p (D | x), And the arithmetic expressions (2) and (4) relating to p (x) are arithmetic expressions representing a probabilistic model, and an average vector μ that is a result of the posterior estimation using the Bayesian estimation expression (Equation (6)) Is calculated by equation (8) (S6). The image reconstruction device 1 outputs the image represented by the average vector μ as a reconstructed image (S7).

  Here, since the average vector μ is a vector obtained by arranging the luminance values (pixel values) of pixels to be included in the reconstructed image in a predetermined order, the value of each pixel of the original image according to the order. Is determined from the value of the corresponding component in the average vector μ (for example, the value itself), thereby obtaining the original image.

  According to this embodiment, the process of obtaining a projection image from a cross-sectional image of the original observation object is described as it is as a probabilistic model for generating an observation image. The maximum likelihood cross-sectional image (observation target image) is directly estimated from the image. Further, by setting the projection transformation matrix based on the conditions related to the process until the projection image is obtained from the observation target, various types such as a helical scan, a cone beam, a multi-CT, a phase CT, and a three-dimensional CT are available. A reconstructed image can be obtained for a projected image obtained by the above projection process.

としてもよい。 Furthermore, the image reconstruction apparatus 1 according to the present embodiment calculates a projection transformation matrix W (k) representing Radon transformation as an arithmetic expression representing a condition related to a process until a projection image is obtained from an observation target. 3) Instead of the matrix F (k) defined in the equation, the following matrix F (k) may be used. That is, the angle when obtaining the k-th projection image is θk, the size of the projection image (dimension of the luminance vector) is M, the size of the original image to be observed (dimension of the luminance vector) is N, and the point image by imaging Is a matrix R (θk) representing the rotation of the θk, using the width of the disc image, that is, the size γ of the point spread function, representing what size disc image is projected in the projected image ), Including a matrix T (ξ) representing a translation by ξ, and a translation T (Sk) by a shift vector Sk representing a positional shift when the kth projection image is obtained,

It is good.

  This matrix F (k) is obtained by assuming that a positional deviation of only Sk occurs when the k-th projected image is picked up. Actually, this positional deviation amount Sk is measured because it is a disturbance. Is difficult. In addition, θk and γ may be deviated from predetermined values during actual photographing due to disturbance. That is, Sk, θk, γ can be said to be unknown parameters.

とおく。これにより、最終的に求めたい確率的モデルを表す演算式の一つの対数値

を考え、この期待値を最大化する。 Therefore, the image reconstruction device 1 according to the present embodiment estimates these unknown parameters using a so-called EM algorithm (expected value maximization method) or a direct estimation method. When using the EM algorithm, the set of unknown parameters

far. As a result, one logarithmic value of the arithmetic expression that represents the probabilistic model to be finally obtained

This expectation is maximized.

  That is, the image reconstruction device 1 initially determines the initial value αt = α0 of this unknown parameter set. Initially, Sk and γ may be set to 0, and θk may be set to an angle representing the X-ray track direction when the k-th projection image is obtained, that is, a set angle at the time of imaging, or may be determined at random.

を演算する。以下この（１２）式を最大化することを考える。そしてこの（１２）式の期待値を最大化するステップ（Ｍステップ）として、（１２）式を最大化するαを求め、これを次の未知パラメータのセットαt+1とする。すなわち、

とする。 In the step (E step) of evaluating the expected value when the unknown parameter set is αt, the image reconstruction device 1 is a term related to αt in the equation (11).

Is calculated. Hereinafter, it is considered to maximize the expression (12). As a step (M step) for maximizing the expected value of the equation (12), α that maximizes the equation (12) is obtained, and this is set as the next set of unknown parameters αt + 1. That is,

And

  The image reconstruction device 1 repeatedly executes the E step and the M step alternately until this α converges, that is, until the magnitude of the vector αt + 1−αt falls below a predetermined threshold value. If α after convergence is obtained, the value of the unknown parameter included in α is used to obtain the matrix F (k), further the projection transformation matrix W (k), and the likelihood function p (D | X).

として、これを最大化するαを求める

こととしてもよい。 As a method for estimating this unknown parameter, the image reconstruction device may directly obtain α that maximizes the marginal likelihood. That is, the marginal likelihood

Find α to maximize this

It is good as well.

  In CT imaging, when a projection image of a living tissue containing metal is obtained, a region where data is lost may occur in the projection image due to a high X-ray absorption rate of the metal. This may be the case, for example, when an image of the oral cavity containing a metal crown (a covering used in dentistry) is used, but the conventional method cannot avoid the artifacts (so-called metal artifacts) caused by the missing area. . In the image reconstruction apparatus 1 according to the present embodiment, an Ising model or the like that expresses an edge of an estimated image including the missing region is used as the prior distribution p (x) based on the constraint condition regarding the image to be observed. This can reduce this metal artifact.

  In addition, as an unknown parameter that can be included in the matrix F (k) when calculating the projection transformation matrix W (k), there are characteristics (sensitivity, etc.) of the image sensor used for capturing the projected image, and the observation target When determining the prior distribution p (x) based on the constraint condition on the image, various information such as information indicating the property of the substance such as the X-ray absorption rate of the object to be included in the estimated cross section can be used. Thereby, it is possible to reconstruct the cross-sectional image by effectively using the information related to the observation target image (cross-sectional image). Further, since the matrix F (k) for obtaining the projection transformation matrix W (k) includes parameters related to the resolution of the image obtained, so-called super-resolution processing for reconstructing an image having a higher resolution than the projection image is performed. It is also possible to do.

  Furthermore, when the imaging angle is limited, or when there is an electromagnetic wave or particle beam source detected by the detection element inside the imaging target (when there is a phosphor), the electromagnetic wave or particle beam detected by these detection elements When a substance that scatters or absorbs is included in the imaging target, each condition is determined when generating a matrix F (k) that represents a condition related to a process from the observation target until a projection image is obtained. May be generated as a product of a matrix representing

Further, when nonlinear scattering occurs, such as when a zone plate is used at the time of imaging, a matrix L that approximates the nonlinear scattering linearly is created. Then, the matrix F (k) is obtained by the product of the matrix including the matrix L in the same manner as shown in the equation (3) or (10). Further, even when there is a correlation in output value between adjacent detection elements, a matrix F (k) is obtained by the product of a plurality of matrices including a matrix representing that effect.
Furthermore, in this embodiment, if the process until obtaining the projection image is known, an image reconstructed from the CT data obtained so far can be obtained.

Furthermore, CT using electron beams or X-rays has an effect of beam hardening artifacts. Electromagnetic waves and particle beams detected by these detection elements are not generally single wavelengths but include electromagnetic waves and substance waves (de Broglie waves) of various wavelengths from components having relatively long wavelengths to components having relatively short wavelengths. This beam hardening is a phenomenon in which, while these X-rays or the like pass through the object to be imaged, a component having a relatively long wavelength is absorbed more, and a component having a short wavelength increases as a result of transmission, resulting in higher energy. .
If this phenomenon occurs when CT is used for medical purposes, it may appear that there is a low absorption region that does not actually exist in the body.
Therefore, a matrix representing a change in CT data due to beam hardening (attenuation of energy such as X-ray) is included in the matrix F (k) as shown in the expression (3) or (10). include.

More specifically, the matrix A includes the matrix F (k) as an unknown parameter that includes the attenuation amount of the wavelength-dependent electromagnetic wave or particle beam energy in each part of the projection target that occurs during the imaging process of the k-th projection image. It may be expressed by a product of (a _{λ 1} , a _{λ 2} ...) And other matrices M (r), T (Sk), and the like representing conversion in the imaging process. Here, a _λn may be determined by selecting a plurality of predetermined wavelengths (for example, by selecting at least one representative wavelength from each frequency band considered to have different absorption rates) λ1, λ2,. It means the absorption coefficient for each component of λn (the attenuation ratio of the component of wavelength λi (i = 1, 2,...)). That is, the matrix F (k) represented by the product of a plurality of matrices including this matrix represents the pixel value that is the output value for each detection element with a multidimensional absorption coefficient. Thereby, the absorptance for each wavelength band is estimated, and artifacts and the like generated due to the difference in the absorptance for each wavelength band are reduced.
In this way, by generating the matrix F (k) representing various conditions related to the process until the projection image is obtained from the observation target, it is possible to reproduce the image reflecting various imaging modes and the characteristics of the imaging target. Configuration can be performed.

  As an embodiment of the present invention, an example in which the image reconstruction device 1 is realized by using a computer adopting Intel Xeno 2.66 GHz (4 cores) as a CPU as the control unit 11 will be described below.

FIG. 5 shows the 32 × 8, 32 × 16, 32 × 32, and 32 × 64 pixel sinograms (R) obtained for the original 64 × 64 pixel two-dimensional image (A). Reconstructed image (B) obtained by performing transformation, reconstructed image (C) using a filter, reconstructed image (D) by the successive approximation method, reconstructed image obtained by the image reconstruction device 1 of this embodiment (E) is contrasted.
In FIG. 5, each reconstructed image (B, C, D, E) represents a reconstructed image obtained from a sinogram of 32 × 8, 32 × 16, 32 × 32, and 32 × 64 pixels in order from the top.

を得た結果を、図６に示す。図６において、横軸はサイノグラムのサイズ、縦軸はＩＳＮＲ値を示す。 In the example of FIG. 5, a vector representing the reconstructed images C, D, E (hat is attached to x), the original image x, and a reconstructed image obtained by simply performing an inverse Radon transform. Reproducibility evaluation value ISNR calculated using a vector representing an image (x is a tilde (~)) (Expression (16))

The results obtained are shown in FIG. In FIG. 6, the horizontal axis represents the sinogram size, and the vertical axis represents the ISNR value.

  As illustrated in FIG. 6, according to the method of the present embodiment, reproducibility can be greatly improved as compared with an example using a filter and an example using successive approximation.

  DESCRIPTION OF SYMBOLS 1 Image reconstruction apparatus, 11 Control part, 12 Storage part, 13 Input part, 14 Output part, 21 Image data reception part, 22 Luminance vector extraction part, 23 Transformation matrix production | generation part, 24 Bayes estimation part, 25 Reconstruction part

Claims (4)

Means for accepting image data related to a plurality of projection images obtained from different directions with respect to the observation target and transmitted through the observation target;
The projection image is generated based on a distribution function indicating that there is a predetermined correlation between pixels of the observation target image and a condition relating to a process until a projection image is obtained based on the observation target. Means for generating an arithmetic expression representing a probabilistic model to be
Means for estimating a cross-sectional image of an observation object from the arithmetic expression representing the probabilistic model and the image data using Bayesian estimation;
An image reconstruction device. The image reconstruction device according to claim 1,
The means for generating an arithmetic expression representing the probabilistic model generates an arithmetic expression representing a condition including an unknown parameter due to disturbance at the time of photographing as a condition relating to a process until a projection image is obtained based on the observation target. Means,
An image reconstruction device further comprising means for estimating the unknown parameter. The image reconstruction device according to claim 1 or 2,
The projected image is obtained by detecting electromagnetic waves or particle beams that pass through the observation target,
The means for generating an arithmetic expression representing the probabilistic model uses a transformation matrix that represents the influence of the wavelength-dependent energy attenuation of the electromagnetic wave or particle beam caused by the transmission of the observation target on the projected image. An image reconstruction device that generates a projection transformation matrix that is an arithmetic expression. Computer
Means for accepting image data related to a plurality of projection images obtained from different directions with respect to the observation target and transmitted through the observation target;
The projection image is generated based on a distribution function indicating that there is a predetermined correlation between pixels of the observation target image and a condition relating to a process until a projection image is obtained based on the observation target. Means for generating an arithmetic expression representing a probabilistic model to be
Means for estimating a cross-sectional image of an observation object from the arithmetic expression representing the probabilistic model and the image data using Bayesian estimation;
Program to function as.

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