HomeNewsListCongratulations on receiving ChinaSIP'15 Best Presentation of Journal Paper

Congratulations on receiving ChinaSIP'15 Best Presentation of Journal Paper

Congratulations to Laming Chen and Yuantao Gu! The ChinaSIP'15 Committee selected their presentation titled "The Convergence Guarantees of a Non-Convex Approach for Sparse Recovery" as Best Presentation of Journal Paper.

The Third IEEE China Summit and International Conference on Signal and Information Processing (ChinaSIP 2015) is held in Chengdu, China from 12th to 15th July 2015. Sponsored by the IEEE Signal Processing Society (SPS), ChinaSIP is an annual summit and international conference held in China for domestic and international scientists, researchers, and practitioners to network and discuss the latest progress in theoretical, technological, and educational aspects of signal and information processing.

 

Title:

The Convergence Guarantees of a Non-Convex Approach for Sparse Recovery 

Abstract:

In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now those corresponding non-convex algorithms lack convergence guarantees from the initial solution to the global optimum. This paper aims to provide performance guarantees of a non-convex approach for sparse recovery. Specifically, the concept of weak convexity is incorporated into a class of sparsity-inducing penalties to characterize the non-convexity. Borrowing the idea of the projected subgradient method, an algorithm is proposed to solve the non-convex optimization problem. In addition, a uniform approximate projection is adopted in the projection step to make this algorithm computationally tractable for large scale problems. The convergence analysis is provided in the noisy scenario. It is shown that if the non-convexity of the penalty is below a threshold (which is in inverse proportion to the distance between the initial solution and the sparse signal), the recovered solution has recovery error linear in both the step size and the noise term. Numerical simulations are implemented to test the performance of the proposed approach and verify the theoretical analysis.