A class of Landweber-type iterative methods based on the Radon transform for incomplete view tomography.

IF 1.4 3区 医学 Q3 INSTRUMENTS & INSTRUMENTATION
Journal of X-Ray Science and Technology Pub Date : 2025-01-01 Epub Date: 2025-01-10 DOI:10.1177/08953996241301697
Duo Liu, Gangrong Qu
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引用次数: 0

Abstract

Background: We study the reconstruction problem for incomplete view tomography, including sparse view tomography and limited angle tomography, by the Landweber iteration and its accelerated version. Traditional implementations of these Landweber-type iterative methods necessitate multiple large-scale matrix-vector multiplications, which in turn require substantial time and storage resources.

Objective: This paper aims to develop and test a novel and efficient discretization approach for a class of Landweber-type methods that minimizes storage requirements by incorporating the specific structure of the incomplete view Radon transform.

Methods: We prove that the normal operator of incomplete view Radon transform in these methods is a compact convolution operator, and derive the explicit representation of its convolution kernel. Discretized by the pixel basis, these Landweber-type iterative methods can be implemented quickly and accurately by introducing a discretized convolution operation between two small-scale matrices with minimal storage requirements.

Results: For the simulated complete and limited angle data, the reconstruction results using various Landweber-type methods with our proposed discretization scheme achieve a 1-5dB improvement in PSNR and require one-third of computation time compared to the traditional approach. For the simulated sparse view data, our discretization scheme yields a valid image with the highest PSNR.

Conclusions: The Landweber-type iterative methods, when combined with our proposed discretization approach based on the Radon transform, are effective for addressing the incomplete view tomography problem.

一类基于Radon变换的landweber型不完全视图层析成像迭代方法。
背景:利用Landweber迭代及其加速算法,研究了稀疏层析成像和有限角度层析成像的不完全层析成像重建问题。这些landweber型迭代方法的传统实现需要多次大规模的矩阵向量乘法,这反过来又需要大量的时间和存储资源。目的:本文旨在开发和测试一种新颖有效的离散化方法,用于一类Landweber-type方法,该方法通过结合不完整视图Radon变换的特定结构来最小化存储需求。方法:证明了这些方法中的不完全视图Radon变换的正规算子是紧卷积算子,并推导出其卷积核的显式表示。这些landweber型迭代方法被像素基离散化,通过在两个小尺度矩阵之间引入离散卷积运算,以最小的存储需求快速准确地实现。结果:对于模拟的完整和有限角度数据,采用不同的landweber型方法和本文提出的离散化方案的重建结果比传统方法的PSNR提高了1-5dB,计算时间减少了1 / 3。对于模拟稀疏视图数据,我们的离散化方案产生了具有最高PSNR的有效图像。结论:landweber型迭代方法与基于Radon变换的离散化方法相结合,可以有效地解决不完全视图层析成像问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
4.90
自引率
23.30%
发文量
150
审稿时长
3 months
期刊介绍: Research areas within the scope of the journal include: Interaction of x-rays with matter: x-ray phenomena, biological effects of radiation, radiation safety and optical constants X-ray sources: x-rays from synchrotrons, x-ray lasers, plasmas, and other sources, conventional or unconventional Optical elements: grazing incidence optics, multilayer mirrors, zone plates, gratings, other diffraction optics Optical instruments: interferometers, spectrometers, microscopes, telescopes, microprobes
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