Following on the heels of the previous post, and the post previous to that, I am now comparing recovery performance of the recommended version (by Maleki and Donoho) of two stage thresholding (TST) — which is essentially subspace pursuit without the oracle — and cyclic MP. Click on the image below to see the results.
For Normal, Laplacian, and uniform distributed sparse vectors, CMP clearly dominates recovery. TST excels for Bernoulli, and bimodal Gaussian and uniform, but not for bimodal Rayleigh. The sharp drop of TST, I assume, becomes even sharper as the dimensionality of the problem increases. Do we want a long tail, or a short one?