Evaluation of Continuous Approximation Functions for the L0-Norm for Compressed Sensing

Carlos A. Sing-Long^1,2, Cristian A. Tejos^1,2, Pablo Irarrazaval^1,2

Compressed Sensing allows reconstructing signals from some of its Fourier coefficients, if they are sparse in some representation. It is usually implemented as an l₁-minimization, although it was recently shown that the reconstruction process can be accelerated and the undersampling rate increased by using continuous approximations of the l₀-norm. We evaluated the performance of four different approximation functions in terms of reconstruction error, number of iterations to convergence and size of the reconstructed signals support. We observed that their convergence properties differed significantly, and we recommend a rational function with discontinuous derivative at the origin.