勷勤数学•专家报告

题      目：Randomized Orthogonal Matching Pursuit Algorithm with Adaptive Partial Selection for Sparse Signal Recovery

报  告  人：温金明 教授  (邀请人：李颖花)

                                      吉林大学

时      间： 11月20日  08：30-09:30

地     点：数科院东楼401

报告人简介:

        温金明，吉林大学教授、博士生导师、国家青年人才、广东省青年珠江学者；现任中国数学会理事、广东省计算数学学会常务理事、广东省运筹学会常务理事、IEEE Trans. Audio Speech Lang. Process.、Alex. Eng. J.、《人工智能科学与工程》等期刊编辑。温教授的研究方向是整数信号和稀疏信号重构的算法设计与理论分析，近年来以第一作者/通讯作者和合作者在IEEE Trans. Inf. Theory、IEEE Trans. Signal Process.、IEEE/ACM Trans. Audio Speech Lang. Process.、ACM Trans. Asian Low-Resour. Lang. Inf. Process、SIAM J. Imaging Sci.、Inverse Probl.、Appl. Comput. Harmon. Anal.等期刊发表60余篇学术论文，以第一发明人授权中国发明专利15件。2020年至今连续6年入选全球前2%顶尖科学家。

摘      要：

        The orthogonal matching pursuit (OMP) algorithm, known for its exceptional ability to reconstruct sparse signals, is a widely employed algorithm in compressed sensing. Numerous studies have provided theoretical analyses supporting its capability for achieving exact recovery. However, when applied to large-scale sparse signal recovery, the OMP algorithm incurs substantial computational overhead, leading to prolonged running time. To address this challenge, in this talk, we will introduce a Randomized OMP with Adaptive Partial Selection (AROMP) algorithm to mitigate computational overhead and reduce runtime. The novelty of the AROMP algorithm lies in its utilization of a randomized index selection method rather than a greedy approach to select the index in each iteration. Subsequently, we will theoretically characterize the gap between AROMP and OMP for exactly recovering an s-sparse signal and show that the gap decreases as the number of comparisons K increases, sparsity s decreases, or signal dimension n decreases. We will also show some experimental results to illustrate the efficiency and effectiveness of our proposed method on sparse signal recovery, face recognition tasks, and image reconstruction tasks.

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