利用热噪声诱导电流成像

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-05-21 DOI:10.1137/23m1571630

Trent DeGiovanni, Fernando Guevara Vasquez, China Mauck

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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 984-1006 页，2024 年 6 月。摘要.我们利用热噪声感应电流对人体电导率的实部和虚部进行成像。在几个电极上测量的热噪声电流的协方差被证明与一个确定性问题有关。我们利用选择性加热人体时获得的协方差来恢复已知边界条件和已知频率下人体的实际功率密度。由此产生的逆问题与声电断层扫描有关，但其中的传导性是复杂的，而且只测量实际功率。我们通过确定其线性化椭圆的位置来研究该问题的局部可解性。文中还包括说明该逆问题的数值实验。

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Imaging with Thermal Noise Induced Currents

SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 984-1006, June 2024.
Abstract.We use thermal noise induced currents to image the real and imaginary parts of the conductivity of a body. Covariances of the thermal noise currents measured at a few electrodes are shown to be related to a deterministic problem. We use the covariances obtained while selectively heating the body to recover the real power density in the body under known boundary conditions and at a known frequency. The resulting inverse problem is related to acousto-electric tomography, but where the conductivity is complex and only the real power is measured. We study the local solvability of this problem by determining where its linearization is elliptic. Numerical experiments illustrating this inverse problem are included.

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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.