Representative of L1/2 Regularization among Lq (0 < q ≤ 1) Regularizations: an Experimental Study Based on Phase Diagram

Recently, regularization methods have attracted increasing 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 regularizations 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 significant difference. Accordingly, we conclude that the L1/2 regularization can be taken as a representative of Lq (0 < q < 1) regularizations.