A comparison between quadratic and sign adaptive iterative algorithms for spikey deconvolution

The authors introduce two algorithms in quadratic and sign gradient-type versions for spikey deconvolution based on a double (detection-estimation) formulation of the problem. Both algorithms are based on the application of a selection operator to detect the nonzero values of a solution provided by a standard approach. In the first algorithm, a gradient-type iterative reduction of the error is used. The second algorithm minimizes the signal to be obtained. Their performances using l₁ and l₂ norms in the minimization are compared in terms of resolution, robustness, speed of convergence, and computational load