LOSoft - ℓ0 Minimization via Soft Thresholding.

We propose a new algorithm for finding sparse solution of a linear system of equations using l(0) minimization. The proposed algorithm relies on approximating the non-smooth l(0) (pseudo) norm with a differentiable function. Unlike other approaches, we utilize a particular definition of l(0) norm which states that the l(0) norm of a vector can be computed as the l(1) norm of its sign vector. Then, using a smooth approximation of the sign function, the problem is converted to l(1) minimization. This problem is solved via iterative proximal algorithms. Our simulations on both synthetic and real data demonstrate the promising performance of the proposed scheme.