无分离的多元超分辨率

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-04-27 DOI:10.1093/imaiai/iaad024
Bakytzhan Kurmanbek, Elina Robeva
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引用次数: 0

摘要

摘要本文研究了高维超分辨率成像问题。在这里,我们得到了一些点光源的图像,它们的位置和强度都是未知的。图像被像素化,并由成像装置产生的已知点扩散函数模糊。我们通过非负测度对未知点源及其强度进行编码,并提出了一个凸优化程序来寻找未知点源及其强度。假设装置的点扩散函数是可分解的,我们证明了最优解是无噪声情况下的真测度,并且它很好地近似于有噪声情况下的广义Wasserstein距离的真测度。我们的主要假设是,点扩展函数的分量在无噪声情况下形成一个Tchebychev系统($T$-system),在有噪声情况下形成一个$T^{*}$-系统,高斯点扩展函数满足温和的条件。我们的工作是对工作的所有维度的推广[14],其中在二维中进行了相同的分析。我们还将[27]中的结果推广到点扩散函数分解时的高维情况。
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Multivariate super-resolution without separation
Abstract In this paper, we study the high-dimensional super-resolution imaging problem. Here, we are given an image of a number of point sources of light whose locations and intensities are unknown. The image is pixelized and is blurred by a known point-spread function arising from the imaging device. We encode the unknown point sources and their intensities via a non-negative measure and we propose a convex optimization program to find it. Assuming the device’s point-spread function is componentwise decomposable, we show that the optimal solution is the true measure in the noiseless case, and it approximates the true measure well in the noisy case with respect to the generalized Wasserstein distance. Our main assumption is that the components of the point-spread function form a Tchebychev system ($T$-system) in the noiseless case and a $T^{*}$-system in the noisy case, mild conditions that are satisfied by Gaussian point-spread functions. Our work is a generalization to all dimensions of the work [14] where the same analysis is carried out in two dimensions. We also extend results in [27] to the high-dimensional case when the point-spread function decomposes.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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