an Experimental Study Based on Phase Diagram

Recently, regularization methods have attracted in- creasing attention. Lq (0 < q < 1) regularizations were proposed after L1 regularization for better solution of sparsity problems. A natural question is which is the best choice among Lq regu- larizations with all q in (0;1)? By taking phase diagram studies with a set of experiments implemented on signal recovery and error correction problems, we show the following: 1) As the value of q decreases, the Lq regularization generates sparser solution. 2) When 1=2 • q < 1, the L1=2 regularization always yields the best sparse solution and when 0 < q • 1=2, the performance of the regularizatons takes no signiflcant difierence. Accordingly, we conclude that the L1=2 regularization can be taken as a rep- resentative of Lq (0 < q < 1) regularizations.