去除掩码--通过球面傅里叶分析法从掩码场重构球面上的实值场

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-09-05 DOI:10.1137/23m1603157

Jan Hamann, Quoc T. Le Gia, Ian H. Sloan, Robert S. Womersley

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引用次数: 0

摘要

SIAM 影像科学期刊》第 17 卷第 3 期第 1820-1843 页，2024 年 9 月。摘要.本文分析了一种重建球面上标量场的频谱方法，该方法仅给定场的掩膜版本信息以及（光滑）掩膜的精确信息。理论是针对一般掩模提出的，后来又专门针对轴对称掩模的情况。针对由宇宙微波背景引起的轴向掩蔽，给出了数值实验结果，假设底层场是具有中等程度人工角功率谱的高斯随机场的实现（[math]）。在没有噪声的情况下，甚至在有中等噪声的情况下，恢复效果都非常令人满意。

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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Removing the Mask—Reconstructing a Real-Valued Field on the Sphere from a Masked Field by Spherical Fourier Analysis

SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1820-1843, September 2024.
Abstract.The paper analyzes a spectral approach to reconstructing a scalar field on the sphere, given only information about a masked version of the field, together with precise information about the (smooth) mask. The theory is developed for a general mask and later specialized to the case of an axially symmetric mask. Numerical experiments are given for the case of an axial mask motivated by the cosmic microwave background, assuming that the underlying field is a realization of a Gaussian random field with an artificial angular power spectrum of moderate degree ([math]). The recovery is highly satisfactory in the absence of noise and even in the presence of moderate noise.

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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.