Iterative reweighted l1 design of sparse FIR filters

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.

► Sparse FIR filters have lower implementation complexity than full filters.
► We optimize sparse 1D and 2D linear phase filters.
► We start with reweighted l1l1 minimization, which eliminates coefficients in bulk.
► Further greedy iterations eliminate coefficients one by one.
► The overall process gives better results or is faster than previous methods.