JPH01229380A - Data processor - Google Patents

Abstract

PURPOSE:To effectively compress projection data, and to attain high compression ratio, and simultaneously, to restore a high quality picture by providing a reconstituting part consisting of a redundancy realizing means and a reconstituting means, and a compression restoring part consisting of an encoding means, etc. CONSTITUTION:In a course that the projection data of a body P to be inspected from many directions are collected by an X-ray CT scanner of an external device 1 and fetched in the reconstituting part 5, and a two-dimensional picture is reconstituted, the essential redundancy of the projection data is realized. Namely, the projection data is orthogonal-polynominal-series-developed by the redundancy realizing means 7, and thus, the essential redundancy of the projection data is realized. The processed result of the means 7 is sent to the encoding means 8 and encoded, and the redundancy of the projection data is deleted by this encoding. Then, the restoration of compressed data is performed by a decoding means 10, and the result of it is fetched in the reconstituting means 11, and here, the two-dimensional picture is reconstituted. Thus, the effective compression of the projection data becomes possible, and the high compression ratio is attained, and simultaneously, the high quality picture can be restored.

Description

DETAILED DESCRIPTION OF THE INVENTION [Object of the Invention] (Industrial Application Field) The present invention relates to a data processing device, and particularly to one that performs compression processing of projection data.

(Prior art) CT (CT) is an image processing technology that images and observes the internal structure of a subject using measurement data called projection data.
Computed tomography) is known. There are various methods for reconstructing images from projection data, but the currently mainstream method is the filtered back projection method (FBP algorithm: Filtered B algorithm).
ackprojection Method).

This filtered back projection method transforms the data by applying a special filter to the projection data in the Fourier domain, and then obtains a reconstructed image by projecting the projection data in reverse and overlapping it. It is considered the most effective method because it can obtain high-quality reconstructed images with a relatively small amount of calculation.

Incidentally, attempts have been made to compress CT data using various methods, but most of them involve compressing images reconstructed using the FBP algorithm using existing still image encoding techniques. For this reason, in medical images where the correlation of raw data is limited to an extremely narrow range, it is difficult to achieve a high compression ratio even in lossy compression, for example.

In addition, a method for compressing raw data (projection data) in a CT device capable of high-speed processing has also been proposed (Japanese Unexamined Patent Publication No. 62-1
00875). In this method, raw data collected at a certain rotation angle or an initial rotation angle of Skillena is stored as is as standard view data, and for view data that is continuously collected thereafter, the difference from the previous view data for all channels is stored as is. Data is compressed by calculating values and storing them in a fixed number of bit ranges. According to this method, the amount of raw data per frame can be reduced, and the storage capacity of the external storage device can be saved, compared to the method using the above-mentioned still image encoding technology. However, since it does not utilize the essential correlation that exists between each piece of projection data, it cannot be said that effective data compression of one-dimensional projection data is performed.

(Problem to be solved by the invention) As mentioned above, F
It is difficult to achieve a high compression rate with the method of compressing reconstructed images using the BP algorithm, and it is difficult to achieve a high compression ratio with the method of compressing reconstructed images using the BP algorithm, and it is difficult to achieve effective data compression of one-dimensional projection data with the above raw data compression method. hard.

SUMMARY OF THE INVENTION The present invention aims to eliminate the above-mentioned drawbacks, and its purpose is to enable effective compression of projection data, achieve a high compression ratio, and obtain high-quality restored images. Our goal is to provide a data processing device that can.

[Structure of the Invention] (Means for Solving the Problem) In order to achieve the above object, the data processing device according to the present invention embodies the redundancy of projection data in the process of image reconstruction based on the projection data. and a second processing means that performs a compression process on the projection data by removing the embodied redundancy through high-efficiency encoding, and a second process unit that performs a restoration process on the compressed data. ing.

(Function) In the present invention, the redundancy of projection data is realized in the process of image reconstruction based on the projection data, and the embodied redundancy is removed by high-efficiency encoding, thereby compressing the projection data. This process achieves a high compression ratio.

(Example) Hereinafter, the present invention will be specifically explained with reference to Examples.

First, the principle of the present invention will be explained in detail.

The operator that associates the target image with its projection data is mathematically called Radon transformation. The image reconstruction problem in CT can be considered as an inversion problem of Radon transform.

As shown in Figure 2, the target image existing within a circle with radius a is represented by f(x, y), and a parallel beam
Let us consider a projection system based on l Beam Geometry. At this time, projection data CI (r, θ) is defined by the following equation.

+ C7(2-,) Given q(r, θ) at O≦θ≦2π, f(x, y
) is the problem of image reconstruction from projection.

Now, let C1 and f be elements of inner product spaces G and H, respectively,
The H→G linear operator that associates 9 with f is called Radon transformation, and is denoted by R.

cx=Rf (2-2)g(r,
A system in which g) can be measured continuously with −a≦r≦a and O≦θ≦2π is called an ideal measurement system (see FIG. 3). In a reconstruction problem in an ideal measurement system, the operator R is a half-pair, and the inverse operator R-1 of R exists. In other words, f is uniquely determined for a given q. However, a measurement system that discretizes the projection direction (fourth
(see figure), the operator R is not a half-pair, and there are an infinite number of fs with a given q. At this time, the operator R is said to have ambiguity (Amb i gtj i ty), and some evaluation criteria are set and one of them is reconstructed as an approximate image. This will be discussed later.

The reconstruction problem in an ideal measurement system can be said to be a problem of finding an inverse system R-1 of an operator R.

f=R-1q (2-3> There is a method using spectral decomposition to find the inverse system of a certain operator. If we consider the operator R as an operator from inner product space H to inner product space G, we can reconstruct the image by its spectral decomposition. It can represent solutions to construction problems.

When the conjugate operator of operator R is R''', the inverse action system R-1 of R can be written as follows.

f=R-1g=R'(RR'')' CI (
2-4> Therefore, to find R-1, R8 and (RR
``t)-1'' should be investigated.

The conjugate operator R''' (G-+H) is a backprojection operator (Backprojection 0p) in CT reconstruction.
called an ``erator''. Its specific form can be determined from the following equation.

(Rf, Q)CM= (f, R'''Q>+ (2-
5> Also, the operator (RR''>-1 (G→G) is an operator (Pr
injection 5pace Filtering
0perator).

Its concrete form can be expressed as follows using the eigenfunction φn and eigenvalue λn of RR.

(RR''+)-1=Σλn-'<φn,φn>n
(2-6> However, <> is a symbol called a dialad and has the following meaning.

〈φn, φn > Q= (g, φn)φn (2-
The specific forms of 7>R'' and (RR'')-1 differ depending on the definition of the internal bond space. -For example, FBP
Let's try to derive the algorithm using spectral decomposition.

First, the inside investigation of spaces H and G is defined by the following equation.

(Left below) (fl, f2) H= f, /' fIT2 dx
dV Based on the definition of this inner product, the concrete form of the conjugate operator R'' is determined from the definition of equation (2-5) as follows.

f(x, V)=R' Q(r, θ) Next, solving the eigenvalue problem of operator RR″′, RR″′
The eigenfunction φU and the two eigenvalue laws are determined as follows.

2π λω, 11! ”=□ 1° (2-10) This φω, α
, λω, α, the filtering operator (RR″
')-1 is expressed by the following equation.

h(r, θ)=(RR″')−1q(r, Eri=f
fλ吋−1〈φu, d+φw, a>g(r, θ)dωd
α°″ 0 However, F and F−1 are operators representing one-dimensional Fourier transform and inverse transform regarding r, respectively.

The filtering operator (RR')-1 of the FBP algorithm can be realized by applying a correction filter H(ω) having a characteristic proportional to the absolute value of the frequency expressed by the following equation in the Fourier domain.

In the FBP algorithm, the projection data transformed by the correction filter is converted to the backprojection operator R of equation (2-9>).
A reconstructed image is obtained by inversely projecting the images with ``l'' and superimposing them.

However, if a filter with diverging frequency characteristics expressed by equation (2-12) is used, the high frequency components of noise contained in the projection data will be emphasized, resulting in a degraded reconstructed image. Therefore, a correction filter having frequency characteristics as shown in FIG. 5 is actually used.

Now, the target image is a finite area within a circle with radius a (a<OO)
Assume that it exists in . At this time, projection data q(r, f1') (-a≦r≦a
, O≦θ≦2π) is known to essentially satisfy the following two conditions.

Condition 1 g(r, θ+π)=g(-r, θ) (2-13
) Condition 2 Condition 1 is a condition regarding the symmetry of g(r, θ), and indicates that the independent projection information is only half of O≦θ≦π. This is taken into account in all image reconstruction algorithms, including the FBP algorithm. Also condition 2
is called the condition of HelgaSOn-LudWi(],
This is a mathematical expression that expresses the redundancy in the θ direction that projection inherently has. Although this property has been known theoretically for a long time, it has never been taken into account in practical reconstruction algorithms. The meaning is g(r, M is r
When expanded by the polynomial, the next expansion coefficient does not have a frequency component of +1 order or higher with respect to θ.

These two conditions are cons 1sten of the projection data.
This is called cyCondition (condition for no contradiction).

When an image is observed indirectly in the form of projection data, information about a certain point is redundantly included in the projection data in all directions. From this, it can be intuitively understood that redundancy occurs in the projection data. Con5iste
ncy Condition is a mathematical expression of this property.

Now, if we consider data compression at the projection data stage,
Traditional image reconstruction methods have an unclear structure of projection redundancy;
This is not a format that can be used effectively. Therefore, in order to make effective use of projection redundancy, Con5isten
We will derive a reconstruction formula that actively incorporates the concept of cy Condition.

A reconstruction formula that explicitly incorporates the concept of consistency condition is derived based on spectral decomposition. Consi 吋ency Conditi
The polynomial of r has an important meaning in condition 2 of on. Therefore, the eigenfunction φ of the operator RR' (G-+G)
So that (r, θ) satisfies one basic requirement,
The operator R is spectrally decomposed.

(1) The eigenfunction φ(r, θ) of the operator RR″′ is the radius r
and the angle θ are variable-separable.

(2) φ(r, The r-direction component of ω is composed of an orthogonal polynomial of r.

It is thought that a reconstruction equation using an eigenfunction that satisfies such conditions can express the Consistency Condition in an explicit form.

First, consider the weighted inner product spaces H, G, and Wl (X,
V), W2 (r, Define the weighted inner product of the following equation where Eh is the weighting function.

(fl, f2)H −ffxt+te≦1f1〒2 Wl (X, y)dx
dy((11,(J2)c) The weighting functions W1 (X, V), W2 (r, θ) are defined by the following equations so that the basic requirements are satisfied.

Wl (X, V) = 1 W2 (r, El) = V'h (r) = □ET: Lower 7 The concrete form of the conjugate operator R''' (G→H) of the operator R is given by the formula (2-5> Based on the definition, it becomes as follows.

f(x, y) -R″' CI(r, g) = W1 (X, V)-' fg(X cosθ+y
sinθ1g)-W2 (X CO'Sθshiy sin
θ) dθ (2-17) Now, the weight function is expressed as (2-
16), the following function system φtp(r, 6
)) becomes a completely orthonormal system and becomes an eigenfunction of the operator RR'.

(+-0,1,2,・,(X) : 1 =-h,-,
-fe group-A: even) However, U%(r) is a Tiebishiev polynomial of the second kind and is defined by the following equation.

U moxibustion (r) - moxibustion + tCtr r' -4 + IC3
r'-2(1-"" +b+cs rth-4(
1-r2) ”5in((k+1) cos-1r
) Also, the eigenvalue λU of RR' is given as follows, and this φ2. Using λ, the filtering operator (RR
″′)−1 is expressed by the following formula.

k(r, 0) = (RR''')'g(r, θ) Equation (2-21) is the expression form of the filtering operator (RR')'''1 using orthogonal polynomial series expansion.

In formula (2-1a), l = - committee, ..., review; committee -
The Consistency Condition of the projection data appears at the point where completeness is established even as 1:even. It is thought that by using this reconstruction formula, projection redundancy can be used effectively.

So far, we have dealt with reconstruction problems in an ideal measurement system, in which projection data is obtained continuously all around the target image.

However, in reality, projection data is measured discretely, so if a reconstruction method targeting an ideal measurement system is used approximately, a reconstruction error will occur. The FBP method is the most typical example of this.

Here, the idea of the reconstruction method using the Tievisiev polynomial of the second kind described above is extended to a measurement system in which the projection direction is discretized. By discretizing the projection direction, it becomes impossible to perform exact reconstruction mathematically, resulting in approximation errors.However, we consider an approximate reconstruction operator using the HoorePenrose generalized inverse operator, and reconstruct from this operator. Let us derive the formula.

Now, as shown in Figure 6, the projection data is measured continuously in the radial direction at 1≦r≦1, and in the angular direction at 2M+1 points per 180° on discrete points equally spaced at θ. Consider models of possible systems.

In such a measurement system, the projection data q is the following 4M
It is given in the form of a set of +2 r functions.

The reconstruction problem is a problem of estimating a function f from Ω discretely obtained for θ in the form of equation <2-22).

The reconstruction equation derived here is an extension of the reconstruction equation using the Tievisiev polynomial of the second kind described above. The weighted inner product is defined by the following equation, except that the projection directions are discrete.

(fl, f2) H=ffx items y2≦lfl and 2 dxd
y However, θm is the angle at which the projection data is measured, and is defined by the following equation.

(When 1≦m≦2M+1) (When 2M+2≦m≦4M+2) Also, the weighting function W2(r) is defined by the following equation similarly to equation (2-16).

The concrete form of the conjugate operator R' (G→H) of the operator R is determined from the definition of equation (2-5>) as follows.

f' (x, y) = R' C1 (r, θ> 48÷2 = ΣCl (r, θm> -W2 (X CO5θm
+ysinθm)m=1 The eigenfunction φ and the eigenvalue λ of the operator RR″′ are given by the following equations.

” (?<=0.1.2.-, 2M!!=-ty,-,
+: 1-J! :even) (Table=2M+1...., String λ=0.1.2....2M>(&=0.1.2.・
, 2M: J = 7-, + discussion-1: ever+) 2 (
4M+2) Scan λ Table +1 (+=2M+1. ・, oO: J=0.1, 2. ・
, 2M> However, bn is defined by the following equation.

Inspect again! and Wnl are matrix A(C
M) are the non-zero eigenvalues and eigenvectors of M).

(l p-ql = mx (2M+1), m=0.1.
−,oo(7) (other times) Discretizing the projection direction causes ambiguity in the mapping, and f cannot be uniquely determined for a given q.
I get tired. Therefore, consider an operator that sets some evaluation criteria and reconstructs one of them as the optimal estimated image. Now, if we take 11ftlH'' as the evaluation standard, the f (minimum norm solution) that minimizes this is MOQrQ Pen
rO3e generalized inverse operator () loore Penros
e Generalized Inverse 0pe
rator) is given by the following equation.

f=R"cI =R'(RR"'> g(2-30) operator (R
R''' ) ten The specific form of (G-+G) is the formula (2-27)
Using , the following equation is obtained.

(Left below) (k-, j: even) After transforming the projection data with the operator (RR″′) defined by equation (2-31), backprojection defined by equation (2-26) A reconstructed image can be obtained by projecting inversely with the operator R' and superimposing them.The redundancy of projection data can be effectively used, and the reconstruction formula assumes a system with discrete projection directions. Conceivable.

As described above, we have derived a reconstruction method using orthogonal polynomial series expansion in order to perform data compression that effectively utilizes the redundancy of projection data. Now, using φU expressed by equation (2-27), the projection data Q (r , θ) is expanded into an orthogonal polynomial series as follows.

kJ: eVen 2M + Σ Σ alφ Table 2 (r, θ) 1: 28+1
10 This expansion coefficient a4u! If data is compressed using , the inherent redundancy of the projection can be effectively utilized, and by roughly applying adaptive coding to this, it is thought that the statistical redundancy can be compressed.

The expansion coefficient atp obtained when the projection data g(r,6)> is expanded to an orthogonal polynomial class is encoded using adaptive encoding. Specifically, for each frequency component kl, 0 is given to the quantization width and the number of quantization bits No. is given from the statistical properties of the projection data, and encoding is performed using these.

Now, assuming that the distribution of each frequency component of various projection data can be approximated by a normal distribution, the bit allocation that minimizes the root mean square error is given by the following equation.

Here, σ2f1.2 is obtained by examining the dispersion of aB from various projection data, and δ is the correction bias. By changing this δ, the total number of bits can be increased or decreased.

Further, the quantization width ΔU is expressed by the following equation using the standard width difference δ of aB.

That is, for each al, the next range is quantized with Nu bits.

μu−2σs≦L≦μfttJ+ 2 ON (3
-4> However, μLR is the average of 8 Table 2.

FIG. 7 shows an example of bit allocation Nxp. The part to the right of the diagonal line in the figure is O bit due to the inherent redundancy of the projection data, and the part to the left of the diagonal line is O bit due to statistical redundancy. In general, adaptive coding involves changing the quantization characteristics for each piece of data; for example, if the data is different, the quantization characteristics will naturally differ. Therefore, information necessary for decoding must also be stored as side information.

However, in the compression in this embodiment, the quantization characteristics do not change for any data, so although it may be a bit of a misnomer to call it adaptive encoding, the quantization characteristics are changed by using the statistical properties of the data. It is called adaptive coding in the sense that it is determined. Since no auxiliary information is required, it is advantageous in terms of storage capacity.

FIG. 8 shows the flow of projection data compression processing. This flow is a combination of the above-mentioned reconstruction formula using orthogonal polynomial series expansion and adaptive orthogonal transform coding.

The expansion coefficient ag is calculated using equation (3-1), which is
In the operator (RR')÷ expressed by equation (2-30), this is nothing but the part that calculates the internal equation of the projection data Ω and the orthogonal polynomial φtp. Therefore, it is considered that the above-mentioned reconstruction formula and encoding method can be easily combined. Note that instead of directly encoding the expansion coefficient at2,
It is encoded after multiplying by the eigenvalue.

Next, the configuration of the apparatus of this embodiment based on the above principle will be explained.

FIG. 1 shows an embodiment of a data processing device according to the present invention. Incidentally, since the image reconstruction and compression algorithms have been explained in detail in the above principle, detailed explanation thereof will be omitted here.

In the figure, the data processing device consists of a reconstruction section 5 and a compression/decompression section 6.

The reconstruction unit 5 reconstructs a two-dimensional image based on the one-dimensional projection data transferred from the external device @1, and includes a redundancy implementation means 7 and a reconstruction means 11. The redundancy realization means 7 has a function of realizing the redundancy of the projection data in the process of image reconstruction based on the projection data. In the device of this embodiment, this redundancy implementation means 7 is as follows:
The redundancy of the projection data is realized by the orthogonal polynomial series expansion using the above polynomial (Equation (3-1)
reference).

Furthermore, the reconstructing means 11 obtains a reconstructed image based on the processing result by the redundancy embodying means 7. Here, this reconstruction unit 5 is an example of the first processing means in the present invention.

Further, as the external device 1, an X-ray CT scanner is applied. This X-ray CT scanner consists of an X-ray tube 2 that emits X-rays in a fan-like manner toward a subject P;
an X-ray detector 3 that faces the X-ray tube 2 and rotates around the subject P in the same direction at the same angular speed;
The apparatus includes a projection data collection section 4 that collects projection data of the subject P from multiple directions via the X-ray detector 3.

Further, the compression/decompression unit 6 performs compression processing of the projection data and restoration processing of the compressed data, and the encoding unit 8
and a decoding means 10.

The encoding means 8 has a function of compressing the projection data by removing the redundancy realized by the reconstruction transformation means 7 by high-efficiency encoding.

In the apparatus of this embodiment, the above-mentioned adaptive orthogonal transform coding is applied as high-efficiency coding by the coding means 8 (see equations (3-2> to (3-4)). The encoded output of the means 8 is transferred to the decoding means 1Q via a file device 9 disposed at a subsequent stage or via a data communication path. ), and the decoded data is sent to the reconstruction means 11.Here, the compression/decompression section 6 is an example of the second processing means in the present invention. be.

The image 12 reconstructed by this reconstruction means 11
is transferred to the display 13 and visualized there.

Next, the operation of the embodiment device configured as described above will be explained.

Projection data (one-dimensional projection data in this case) of the subject P from multiple directions is collected by an external device or an X-ray scanner, and the data is taken into the reconstruction unit 5. Then, in the reconstruction unit 5, a two-dimensional image (in this case, a tomographic image of the subject P) is reconstructed based on the captured projection data, but in the process of this reconstruction, the essential Redundancy is embodied. That is, the redundancy embodying means 7 expands the projection data into an orthogonal polynomial series, thereby embodying the essential redundancy of the projection data (steps S1 and 82 in FIG. 8). The processing result is sent to the encoding means 8 and encoded there (step S3 in FIG. 8). Redundancy of the projection data is removed by this encoding (data compression).

The compressed data is restored by decoding the compressed data in the decoding means 10 (step 84 in FIG. 8). Then, this decoding processing result is transmitted to the reconstruction means 11.
The two-dimensional image is then reconstructed (steps S5 and S6 in FIG. 8).

Note that when reconstructing a two-dimensional image based on projection data without data compression, a path from the redundancy embodying means 7 to the reconstruction means 11 is passed as shown by 14 in FIG. become.

The obtained reconstructed image is transferred to the display 13 for visualization, and is further stored in a storage device (not shown) as necessary.

In this way, the device of this embodiment combines and optimizes the processing that embodies the inherent redundancy of projection data with the existing statistical redundancy compression processing, thereby improving the efficiency of conventional compression. Compared to conventional methods, it is possible to obtain restored reconstructed images with a much higher compression ratio and higher quality.

Although one embodiment of the present invention has been described above, the present invention is not limited to the above embodiment, and it goes without saying that various modified embodiments are possible.

For example, in the above embodiment, an X-ray scanner is applied as the external device 1, and one-dimensional projection data of the subject P is collected,
Although we have explained the case where a two-dimensional image is reconstructed based on this one-dimensional projection data, in general, an n-dimensional image is reconstructed based on (n-1)-dimensional projection data collected at different projection angles. The present invention can be applied to such cases. Note that n here means a positive integer. Furthermore, the compression processing according to the present invention is not limited to medical use, but can also be applied to, for example, industrial CT used for non-destructive testing, split 1 to telescopes, three-dimensional image reproduction in microscopes, tree ring measurement, etc. .

[Effects of the Invention] As described in detail above, according to the present invention, it is possible to provide a data processing device that can achieve a high compression ratio and can obtain a high-quality restored image.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing an embodiment of a data processing device according to the present invention, FIGS. 2 to 8 are for explaining the principle of the present invention, and FIG. Relationship explanatory diagrams, FIGS. 3 and 4 are illustrations of mapping forms in each measurement system, FIG. 5 is a characteristic diagram of a correction filter in the FBP algorithm, FIG. 6 is an explanatory diagram of a measurement system in which the projection direction is discretized, FIG. 7 is an explanatory diagram of the number of bits for matrix conversion of the expansion coefficient aU, and FIG. 8 is a flowchart of projection data compression. ] . . 1 part) device; 5. Reconstruction section (first processing means); 6. Compression/decompression section (second processing means). Figure 5

Claims (3)

[Claims] (1) In a data processing device that processes projection data collected by an external device, a first processing means for realizing redundancy of the projection data in the process of image reconstruction based on the projection data; 1. A data processing device comprising: a second processing means that performs compression processing of projection data by removing redundancy that has been encoded by high-efficiency encoding, and a second processing means that performs restoration processing of this compressed data. (2) The data processing device according to claim 1, wherein the first processing means embodies the redundancy of the projection data by expanding the projection data into an orthogonal polynomial series. (3) As high efficiency encoding by the second processing means,
The data processing device according to claim 1 or 2, to which adaptive orthogonal transform encoding is applied.