A Scale Invariant Approach for Sparse Signal Recovery

• Activity Number: 580 - Statistical and Computational Challenges in Nonparametric Learning
• Type: Topic Contributed
• Date/Time: Thursday, August 6, 2020 : 3:00 PM to 4:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yifei Lou*
• Companies: University of Texas At Dallas
• Keywords: Compressed sensing; Lasso; scale invariant; null space property

Abstract

I will talk about the ratio of the L1 and L2 norms, denoted as L1/L2, to promote sparsity. Due to the non-convexity and non-linearity, there has been little attention to this scale-invariant model. Compared to popular models in the literature such as the Lp model for 0< p< 1 and the transformed L1 (TL1), this ratio model is parameter-free. Theoretically, we present a strong null space property (sNSP) and prove that any sparse vector is a local minimizer of the L1/L2 model provided with this sNSP condition. The experimental results demonstrate the proposed approaches are comparable to the state-of-the-art methods in sparse recovery and work particularly well when the ground-truth signal has a high dynamic range. In addition, a variant of the L1/L2 model to apply to the gradient is also discussed with a proof-of-concept example of the MRI reconstruction.