Convex Optimization Algorithms for Sparse Signal Reconstruction

Compressive sensing is a very important field of research in signal processing as it is based on the idea that a signal, sparse in a certain transform domain, can be completely recovered based on a small set of available measurements. Many algorithms, dealing with sparse signal recovery have been proposed through the years. This paper focuses on convex optimization algorithms and explores their performance in two different transform domains - discrete Fourier and discrete cosine transforms. The observed algorithms are the adaptive gradient based algorithm, primal-dual interior point method and the log barrier algorithm, all which are used to solve different formulations of the l1-minimization problem.