Stephane Chretien just let me know that he and Alexis Flesch (a Ph.D. student working for Jean-Yves Dauxois ) has produced a Python implementation of the Alternating L_1 method. The implementation uses cvxopt, a Python Package for Convex Optimization. The graphs shows a perfect recovery with the alternating L_1 algorithm and the same non-recovery for the L_1 algorithm.
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