QUADRATIC OPTIMIZATION FOR IMAGE-RECONSTRUCTION .2.

被引：26

作者：

ARTZY, E

ELFVING, T

HERMAN, GT

机构：

[1] Medical Image Processing Group, Department of Computer Science, State University of New York at Buffalo, Amherst, NY 14226

来源：

COMPUTER GRAPHICS AND IMAGE PROCESSING | 1979年 / 11卷 / 03期

基金：

美国国家卫生研究院;

关键词：

D O I：

10.1016/0146-664X(79)90091-1

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We attack the problem of recovering an image (a function of two variables) from experimentally available integrals of its grayness over thin strips. This problem is of great importance in a large number or scientific areas. An important version of the problem in medicine is that of obtaining the exact density distribution within the human body from X-ray projections. A large number or methods have been proposed to solve this problem. In Part I of this paper we have shown that some methods are special cases of the same iterative quadratic optimization algorithm. In the present paper we discuss alternative iterative algorithms (conjugate gradient, nonstationary Richardson, semi-iterative) for quadratic optimization and compare their performance in image reconstruction with the previously used methods. The choice of the quadratic function to be minimized and the use of heuristic tricks to improve convergence are also discussed. The methods are illustrated by the reconstruction of a mathematically described phantom representing a cross section of the human head from simulated low-dose X-ray data. This paper is self-contained. © 1979.

引用

页码：242 / 261

页数：20

共 17 条

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[2]

Herman, Lakshminarayanan, Naparstek, Ritman, Robb, Wood, Rapid computerized tomography, Medical Data Processing, pp. 581-598, (1976)

[3]

Herman, Lent, Quadratic optimization for image reconstruction, I, Computer Graphics Image Processing, 5, pp. 319-332, (1976)

[4]

Bjorck, Elfving, Accelerated projection methods for computing pseudo inverse solutions of systems of linear equations, BIT, 19, pp. 145-163, (1979)

[5]

Shepp, Logan, The Fourier reconstruction of a head section, IEEE Transactions on Nuclear Science, 21 NS, pp. 21-43, (1974)

[6]

Herman, Lent, A computer implementation of a Bayesian analysis of image reconstruction, Inform. Contr., 31, pp. 364-384, (1976)

[7]

Anderssen, Golub, Richardson's nonstationary matrix iterative procedure, STAN-CS-72-304, (1972)

[8]

Wozniakowski, Numerical stability of the Chebyshev method for the solution of large linear systems, Numer. Math., 28, pp. 191-209, (1977)

[9]

Reid, On the method of conjugate gradients for the solution of large spare systems of linear equations, Large Spare Sets of Linear Equations, pp. 231-254, (1971)

[10]

Lakshminarayanan, Lent, Methods of least squares and SIRT in reconstruction, J. Theor. Biol., 76, pp. 267-295, (1979)

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