TILT：限角断层摄影中的拓扑界面恢复

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-08-19 DOI:10.1137/23m1611567

Elli Karvonen, Matti Lassas, Pekka Pankka, Samuli Siltanen

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引用次数: 0

摘要

SIAM 影像科学杂志》，第 17 卷第 3 期，第 1761-1794 页，2024 年 9 月。摘要.针对有限角度层析成像的严重求解困难的逆问题，介绍了一种新的重建方法。众所周知，根据现有的测量方法，角度指定了未知目标波前集的一个子集，而一些定向奇异点在数据中仍然不可见。有限角度断层成像的拓扑界面恢复（或称 TILT）基于在通用覆盖图下提升波前集的可见部分。在所提供的空间中，可以使用双树复合小波、专用度量和持久同源性正确连接被提升波前集的适当部分。其结果不仅是建议的不可见边界，而且是目标中所有界面的计算表示。

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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TILT: Topological Interface Recovery in Limited-Angle Tomography

SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1761-1794, September 2024.
Abstract.A novel reconstruction method is introduced for the severely ill-posed inverse problem of limited-angle tomography. It is well known that, depending on the available measurement, angles specify a subset of the wavefront set of the unknown target, while some oriented singularities remain invisible in the data. Topological Interface recovery for Limited-angle Tomography, or TILT, is based on lifting the visible part of the wavefront set under a universal covering map. In the space provided, it is possible to connect the appropriate pieces of the lifted wavefront set correctly using dual-tree complex wavelets, a dedicated metric, and persistent homology. The result is not only a suggested invisible boundary but also a computational representation for all interfaces in the target.

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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.

TILT： 限角断层摄影中的拓扑界面恢复

摘要

TILT：限角断层摄影中的拓扑界面恢复