Templates for Convex Cone Problems with Applications to Sparse Signal Recovery

This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fi elds. The approach works as follows: first, determine a conic formulation of the problem; second, determine its dual; third, apply smoothing; and fourth, solve using an optimal first-order method. A … Read more

Compressed Sensing with Quantized Measurements

We consider the problem of estimating a sparse signal from a set of quantized, Gaussian noise corrupted measurements, where each measurement corresponds to an interval of values. We give two methods for (approximately) solving this problem, each based on minimizing a differentiable convex function plus an l1 regularization term. Using a first order method developed … 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