Analysis of View Aliasing for the Generalized Radon Transform in [math]

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-02-23 DOI:10.1137/23m1554746

Alexander Katsevich

引用次数: 0

Abstract

SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 415-440, March 2024.
Abstract. In this paper we consider the generalized Radon transform [math] in the plane. Let [math] be a piecewise smooth function, which has a jump across a smooth curve [math]. We obtain a formula, which accurately describes view aliasing artifacts away from [math] when [math] is reconstructed from the data [math] discretized in the view direction. The formula is asymptotic, it is established in the limit as the sampling rate [math]. The proposed approach does not require that [math] be band-limited. Numerical experiments with the classical Radon transform and generalized Radon transform (which integrates over circles) demonstrate the accuracy of the formula.

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数学]中广义拉顿变换的视差分析

SIAM 影像科学杂志》第 17 卷第 1 期第 415-440 页，2024 年 3 月。摘要本文考虑平面内的广义 Radon 变换 [math]。设[math]是一个片断光滑函数，它在光滑曲线[math]上有一个跳跃。我们得到了一个公式，当[math]从视图方向离散的数据[math]重建时，它能准确描述远离[math]的视图混叠伪影。该公式是渐近公式，在采样率[math]的极限范围内成立。所提出的方法并不要求 [math] 具有频带限制。经典拉顿变换和广义拉顿变换（对圆进行积分）的数值实验证明了公式的准确性。

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

SIAM Journal on Imaging Sciences COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

3.80

自引率

4.80%

发文量

审稿时长

>12 weeks

期刊介绍： SIAM Journal on Imaging Sciences (SIIMS) covers all areas of imaging sciences, broadly interpreted. It includes image formation, image processing, image analysis, image interpretation and understanding, imaging-related machine learning, and inverse problems in imaging; leading to applications to diverse areas in science, medicine, engineering, and other fields. The journal’s scope is meant to be broad enough to include areas now organized under the terms image processing, image analysis, computer graphics, computer vision, visual machine learning, and visualization. Formal approaches, at the level of mathematics and/or computations, as well as state-of-the-art practical results, are expected from manuscripts published in SIIMS. SIIMS is mathematically and computationally based, and offers a unique forum to highlight the commonality of methodology, models, and algorithms among diverse application areas of imaging sciences. SIIMS provides a broad authoritative source for fundamental results in imaging sciences, with a unique combination of mathematics and applications. SIIMS covers a broad range of areas, including but not limited to image formation, image processing, image analysis, computer graphics, computer vision, visualization, image understanding, pattern analysis, machine intelligence, remote sensing, geoscience, signal processing, medical and biomedical imaging, and seismic imaging. The fundamental mathematical theories addressing imaging problems covered by SIIMS include, but are not limited to, harmonic analysis, partial differential equations, differential geometry, numerical analysis, information theory, learning, optimization, statistics, and probability. Research papers that innovate both in the fundamentals and in the applications are especially welcome. SIIMS focuses on conceptually new ideas, methods, and fundamentals as applied to all aspects of imaging sciences.