Numerical Implementation of Generalized V-Line Transforms on 2D Vector Fields and their Inversions

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-03-07 DOI:10.1137/23m1573112

Gaik Ambartsoumian, Mohammad J. Latifi Jebelli, Rohit K. Mishra

引用次数: 0

Abstract

SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 595-631, March 2024.
Abstract.The paper discusses numerical implementations of various inversion schemes for generalized V-line transforms on vector fields introduced in [G. Ambartsoumian, M. J. Latifi, and R. K. Mishra, Inverse Problems, 36 (2020), 104002]. It demonstrates the possibility of efficient recovery of an unknown vector field from five different types of data sets, with and without noise. We examine the performance of the proposed algorithms in a variety of setups, and illustrate our results with numerical simulations on different phantoms.

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二维矢量场的广义 V 型线变换及其反演的数值实现

SIAM 影像科学杂志》第 17 卷第 1 期第 595-631 页，2024 年 3 月。摘要：本文讨论了[G. Ambartsoumian, M. J. Latifi, and R. K. Mishra, Inverse Problems, 36 (2020), 104002]中介绍的矢量场广义 V 线变换的各种反演方案的数值实现。它展示了从有噪声和无噪声的五种不同类型数据集中高效恢复未知向量场的可能性。我们检验了所提算法在各种设置下的性能，并通过在不同模型上的数值模拟说明了我们的结果。

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.