A First-Order Smoothed Penalty Method for Compressed Sensing

We propose a first-order smoothed penalty algorithm (SPA) to solve the sparse recovery problem min{||x||_1 : Ax=b}. SPA is efficient as long as the matrix-vector product Ax and A^Ty can be computed efficiently; in particular, A need not be an orthogonal projection matrix. SPA converges to the target signal by solving a sequence of penalized … Read more

NESTA: A Fast and Accurate First-order Method for Sparse Recovery

Accurate signal recovery or image reconstruction from indirect and possibly under- sampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel fi rst-order methods in convex optimization, most notably Nesterov’s smoothing technique, this paper … Read more