2019/10/19 by Yuan Tian, Tian, Yuan
Computer Science · Engineering · Medicine · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Microwave Imaging and Scattering Analysis #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #Ultrasound Imaging and Elastography #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1910.08771
openalex publication_date 2019/10/19 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We investigate the problem of reconstructing n-by-n structured matrix signal\nX via convex programming, where each column xj is a vector of s-sparsity and\nall columns have the same l1-norm. The regularizer in use is matrix norm\n|||X|||1=maxj|xj|1.The contribution in this paper has two parts. The first part\nis about conditions for stability and robustness in signal reconstruction via\nsolving the convex programming from noise-free or noisy measurements.We\nestablish uniform sufficient conditions which are very close to necessary\nconditions and non-uniform conditions are also discussed. Similar as the\ntraditional compressive sensing theory for reconstructing vector signals, a\nrelated RIP condition is established. In addition, stronger conditions are\ninvestigated to guarantee the reconstructed signal's support stability, sign\nstability and approximation-error robustness. The second part is to establish\nupper and lower bounds on number of measurements for robust reconstruction in\nnoise. We take the convex geometric approach in random measurement setting and\none of the critical ingredients in this approach is to estimate the related\nwidths bounds in case of Gaussian and non-Gaussian distributions. These bounds\nare explicitly controlled by signal's structural parameters r and s which\ndetermine matrix signal's column-wise sparsity and l1-column-flatness\nrespectively.\n