一、主 题：On spatial-domain approach to deconvolution of point-sources in super-resolution
二、主讲人：王建忠
三、时 间：2018年12月13日，下午：15:30-16:30（周四）
四、地 点：闻理园A4-305室
摘要: A point-source is formulated as a linear combination of Dirac functions. Stars in the sky, cancer cells, abnormal mass in medical images, can be modeled as point-sources. A main problem of super-resolution is to recover a blind point-source using data samples acquired from a convolution of the point-source and a kernel, which represents the low-resolution components of the point-source. This recovering is mentioned as the spatial-domain approach to super-resolution, distinct from the spectral one, which recovered the point-source from a finite set of spectral values of the point-source. In this talk, we mainly introduce the domain-approach to the recovery of the blind point-sources. We introduce the recent researches on the deconvolutions that adopt Gaussian kernel. Based on the orthonormal Hermite polynomial basis, Chui and Mhaskar approximate the point-source recovery using the inverse Gaussian kernel. Fernandez-Granda introduces a discrete deconvolution technique in the recovery. He also develop the sample theorem for the deconvolution. Then we focus on the study of the dual certification functions, that guarantee the uniqueness of the solution of the deconvolution.
附个人简介：Jianzhong Wang got Bachelor Degree (1967) from Peking University and Master Degree (1981) from Zhejiang University. He was a professor at Wuhan University, now is a professor at Sam Houston State University in the United States. He has published one monograph and about 90 papers. His research mainly focuses on spline wavelets, image enhancement, and dimensionality reduction. Recently, he is interested in mathematical super-resolution and hyperspectral image analysis.
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