Comparison of the L1-magic and the gradient algorithm for sparse signals reconstruction

Reconstruction of the sparse signals, performed by two algorithms which belongs to the class of convex optimization algorithms, is considered in this paper. Widely used algorithm implemented by the l₁-magic code packet is used as the first algorithm. Its realization is based on the primal dual interior point algorithm for convex optimization. The second considered algorithm also belongs to the convex optimization group of algorithms. It is a recently proposed adaptive step gradient-based algorithm. The reconstruction of missing data is based on the direct adaptation of the signal values by minimizing the concentration/sparsity measure of the signal in the transformation domain, where the signal is sparse. Comparison of these two algorithms is done here.