'Truncated £1 for Compressed Sensing,' by Lu Zhong

Abstract

In compressed sensing, to accurately reconstruct a sparse signal from a limited mea­surements via £1 minimization, an appropriate measurement matrix is necessary. In this proposal, we introduce the truncated £1 minimization to reconstruct sparse signals in real­ world data. The proposed solution is robust when measurements matrices do not satisfy the restricted isometry property and thus £1 minimization would normally fail. To solve the proposed non-convex optimization problem, we apply the Augmented Lagrangian JVIethod and Alternating Direction Method of Multipliers and show that a local optimal solution is guaranteed. Furthermore, a conjecture on transforming the non-convex optimization prob­lem into a convex one is proposed as well. We propose to apply these ideas to real world data sets from MNIST and computerized tomography. 

Adviser: Randy Paffenroth