局部区域的迭代求逆

赵双任

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Iterative inverse in local-regions

首发时间：2006-06-29

Zhao Shuangren ¹

1、DoubleTask Toronto Canada

Abstract：A new iterative algorithm is introduced for a kind of inverse problem. An example of this kind of inverse problem is CT image reconstruction. The solution of non-iteration algorithm differs from the original object. The difference between the solution and original object is the error which is comprised of artifacts and noise. Compared to non-iteration algorithm, the refinement iterative inverse (RII) algorithm can reduce the artifacts but it increases the noise in the same time. Hence in general the quality of reconstructed image is not much improved. In other hand, the new iterative algorithm can reduce artifacts similar to the RII algorithm; however it does not increase the noise. Hence the image quality is improved a lot. The idea of the new iterative algorithm came from an iterative reconstruction and re-projection algorithm used in image reconstruction with limited field of view~(LFOV). This algorithm led to the iterative reconstruction in sub-regions (IRSR) in case the field of view(FOV) is unlimited. The sub-regions are square boxes. In this case there were cracks (or grid) between sub-regions. In order to eliminate the cracks, margins between sub-regions were introduced. Taking the sub-regions as small as only one pixel and keeping the margins led to the new iterative algorithm in this paper. It is referred as iterative inverse in local-regions (IILR). The error transfer function, artifact transfer function and filtering function are compared between the IILR algorithm and the RII algorithm. A simple example shows that the error obtained from the IILR algorithm is smaller than that obtained from non-iteration algorithm in the whole region, but the error obtained from the RII algorithm is smaller than non-iteration algorithm only at the vicinity of the image edges. It is proved that the RII algorithm is a special example of the IILR algorithm when the margin is taken as zero.

keywords： image reconstruction, inverse problem, back-projection

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局部区域的迭代求逆

赵双任 ¹

1、DoubleTask 多伦多加拿大

摘要：本文对一类求逆问题介绍了一个新的迭代算法。这类问题的一个例子是CT图像处理。非迭代算法的解同原来物体是不一样的。解与原物体的差值被定意为误差，误差由伪影和噪音两项构成。与非迭代算法比较，精致化的迭代算法(RII)可减少伪影，但同时引起噪音增加。因此，图像重建的质量并没有多大改进。另一方面，新的迭代算法与精致化的迭代算法一样可以减少伪影，但是它并不增加噪音。因此，图像的质量有很大改进。新算法的思想来自迭代的图像重建和重投影算法。这种图像重建和重投影算法用于视野受限的图像重建情况。这个算法导致了用于视野不受限的情况的分块迭代算法。分块形状为方形。在这种情况下在分块的边界处有裂纹或格子。为了消除这些裂纹或格子，在分块之间需要加边。如果把块分得小到只有一个像素，就导致了本片论文的新迭代算法。我们称该算法被为局部区域的迭代算法(IILR)。本文比较了IILR算法和RII算法的误差，伪影和滤波的传递函数。一个简单的例子表明IILR算法误差在整个区域内比非迭代算法小，但RII算法的误差仅在图像棱角突变处的临域比非迭代算法小。已经证明，RII算法是IILR算法的一个特殊的例子，在这个特例中加边值被取为零。

关键词：图像重建求逆问题反向投影误差伪影滤波截断线性方程局部求逆

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Zhao Shuangren . Iterative inverse in local-regions[EB/OL]. Beijing:Sciencepaper Online[2006-06-29]. https://www.paper.edu.cn/releasepaper/content/200606-499.

No.7375321381151561****

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论文编号	200606-499
论文题目	局部区域的迭代求逆
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