2023/11/07 by Silpa Babu, Babu, Silpa, Namrata Vaswani +1
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Electrical engineering #Image and Video Processing (eess.IV) #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2311.03824
openalex publication_date 2023/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper focuses studies the following low rank + sparse (LR+S) column-wise compressive sensing problem. We aim to recover an n × q matrix, \X^* =[ \x1^*, \x2^*, ⋯ , \xq^*] from m independent linear projections of each of its q columns, given by \yk :=\Ak\xk^*, k ∈ [q]. Here, \yk is an m-length vector with m < n. We assume that the matrix \X^* can be decomposed as \X^*=Ł^*+§^*, where Ł^* is a low rank matrix of rank r << min(n,q) and §^* is a sparse matrix. Each column of § contains ρ non-zero entries. The matrices \Ak are known and mutually independent for different k. To address this recovery problem, we propose a novel fast GD-based solution called AltGDmin-LR+S, which is memory and communication efficient. We numerically evaluate its performance by conducting a detailed simulation-based study.