Structural sparsity in multiple measurements

讲座题目Title：Structural sparsity in multiple measurements

讲座时间 Datetime: 2024.6.13  10:00—12:00

地点 Venue: 海琴2号楼A457

报告人 Speaker: Florian Bossmann 副教授

单位 Affiliation: 哈尔滨工业大学

主持人Host：Davide Bianchi 副教授

报告摘要 Abstract:

Structured sparsity models are of interest in many applications where multiple

measurements are taken. One assumes that the desired solution is not only sparse, but the non-zero elements form a structure or pattern. However, many of the common models, such as row sparsity or block-sparsity, are far too restrictive for applications.

We propose a novel sparsity model for distributed compressed sensing where the sparsity patterns are encoded in a matrix C. The sparsity of a solution is then measured via a corresponding norm  ·  _C,0 and the reconstruction problem formulates as

By adapting C, our model allows more general types of structured sparsity arising in a variety of applications such as dynamic MRI or PET, wireless com- munication, seismic exploration, and non-destructive testing.

To reconstruct structured data from observed measurements, we derive a non-convex but well-conditioned LASSO-type functional. We design a pro- jected gradient descent algorithm by exploiting the convex-concave geometry of the functional.

报告人简介：

Prof. Florian Bossmann

He is currently working as an Associate Professor at Harbin Institute of Technology (Department of Mathematics). His research interests are signal and image processing, greedy methods and fast algorithms, inverse and NP-hard problems, and applications.