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