Sparse FIR filters have lower implementation complexity than full filters, while keeping a good performance level. This paper describes a new method for designing 1D and 2D sparse filters in the minimax sense using a mixture of reweighted l1 minimization and greedy iterations. The combination proves to be quite efficient; after the reweighted l1 minimization stage introduces zero coefficients in bulk, a small number of greedy iterations serve to eliminate a few extra coefficients. Experimental results and a comparison with the latest methods show that the proposed method performs very well both in the running speed and in the quality of the solutions obtained.
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