2016/05/16 by Mithun Das Gupta, Gupta, Mithun Das
Engineering · #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Microwave Imaging and Scattering Analysis #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1605.04657
openalex publication_date 2016/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the theory of compressed sensing (CS), the sparsity ‖x‖0 of the unknown signal x ∈ Rn is of prime importance and the focus of reconstruction algorithms has mainly been either ‖x‖0 or its convex relaxation (via ‖x‖1). However, it is typically unknown in practice and has remained a challenge when nothing about the size of the support is known. As pointed recently, ‖x‖0 might not be the best metric to minimize directly, both due to its inherent complexity as well as its noise performance. Recently a novel stable measure of sparsity s(x) := ‖x‖12/‖x‖22 has been investigated by Lopes \citeLopes2012, which is a sharp lower bound on ‖x‖0. The estimation procedure for this measure uses only a small number of linear measurements, does not rely on any sparsity assumptions, and requires very little computation. The usage of the quantity s(x) in sparse signal estimation problems has not received much importance yet. We develop the idea of incorporating s(x) into the signal estimation framework. We also provide a three step algorithm to solve problems of the form Ax=b with no additional assumptions on the original signal x.