为盲反问题训练自适应重构网络

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-06-21 DOI:10.1137/23m1545628

Alban Gossard, Pierre Weiss

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引用次数: 0

摘要

SIAM 影像科学杂志》，第 17 卷第 2 期，第 1314-1346 页，2024 年 6 月。摘要：神经网络能以前所未有的性能解决许多难以解决的逆问题。在实际应用中，物理信息方法已经逐渐取代了精心设计的手工重建算法。然而，这些网络存在一个主要缺陷：当在给定的前向算子上进行训练时，它们不能很好地泛化到不同的算子上。本文的目的有两个。首先，我们通过各种应用表明，用一系列前向算子训练网络可以解决适应性问题，而不会明显影响重构质量。其次，我们说明这种训练程序可以解决具有挑战性的盲反问题。我们的实验包括磁共振成像中出现的部分傅立叶采样问题、灵敏度估计和非共振效应、倾斜几何的计算机断层扫描以及使用菲涅尔衍射核的图像去模糊。

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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Training Adaptive Reconstruction Networks for Blind Inverse Problems

SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1314-1346, June 2024.
Abstract.Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these networks suffer from a major defect: when trained on a given forward operator, they do not generalize well to a different one. The aim of this paper is twofold. First, we show through various applications that training the network with a family of forward operators allows solving the adaptivity problem without compromising the reconstruction quality significantly. Second, we illustrate that this training procedure allows tackling challenging blind inverse problems. Our experiments include partial Fourier sampling problems arising in magnetic resonance imaging with sensitivity estimation and off-resonance effects, computerized tomography with a tilted geometry, and image deblurring with Fresnel diffraction kernels.

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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.