In the field of signal processing, there have been a number of techniques introduced to process and reconstruct sparse signals. This problem, known as the "Sparse Reconstruction Problem", involves determining the signal that has the smallest number of non-zero components, generally referred to as the support of the signal. This problem, in general, is NP-hard, and thus, finding an exact solution is computationally intractable, but by taking certain simplifying assumptions, the reconstruction problem can be phrased as an l1 minimization. A set of optimization techniques referred to as "Alternating Direction Methods" provide simple and efficient means to solve these l1-problems. The implementation of these techniques is the topic of this talk.