超分辨率恢复与实指数和分离的统一方法
A unified method for super-resolution recovery and real exponential-sum separation
AI总结：
本文提出一种统一方法，解决多变量超分辨率问题和盲源分离实值指数和问题，适用于荧光显微镜、天文观测及磁共振成像等应用。
摘要：
本文受衍射传播光波的启发，提出一个简单的数学模型，用于多变量超分辨率问题和实值指数和的盲源分离问题。该模型促进了本文中两个问题的统一理论和统一解决方案的发展。超分辨率问题的研究旨在应用于荧光显微镜和天文观测，而第二个问题的动机是当前需要从磁共振波谱学中提取多变量指数特征，以帮助神经科医生和放射科医生，并为核化学中的同位素分离提供数学工具。本文介绍的统一方法可通过处理有限数量的数据实现，这些数据在非预先指定的位置采样，计算方案仅包括矩阵-向量乘法、峰值寻找和聚类。
英文摘要：
In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums. This model facilitates the development of a unified theory and a unified solution of both problems in this paper. Our consideration of the super-resolution problem is aimed at applications to fluorescence microscopy and observational astronomy, and the motivation for our consideration of the second problem is the current need of extracting multivariate exponential features in magnetic resonance spectroscopy (MRS) for the neurologist and radiologist as well as for providing a mathematical tool for isotope separation in Nuclear Chemistry. The unified method introduced in this paper can be easily realized by processing only finitely many data, sampled at locations that are not necessarily prescribed in advance, with computational scheme consisting only of matrix - vector multiplication, peak finding, and clustering.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
