  The ratio of L1 and L2 norms (L1/L2), serving as a sparse promoting function,
receives considerable attentions recently due to its effectiveness for sparse
signal recovery. In this paper, we propose an L1/L2 based penalty model for
recovering sparse signals from noiseless or noisy observations. It is proven
that stationary points of the proposed problem tend to those of the
elliptically constrained L1/L2 minimization problem as the smoothing parameter
goes to zero. Moreover, inspired by the parametric approach for the fractional
programming, we design a parameterized proximal-gradient algorithm (PPGA) as
well as its line search counterpart (PPGA_L) for solving the proposed model.
The closed-form solution of the involved proximity operator is derived, which
enable the efficiency of the proposed algorithms. We establish the global
convergence of the entire sequences generated by PPGA and PPGA_L with monotone
objective values by taking advantage of the fact that the objective of the
proposed model is a KL function. Numerical experiments show the efficiency of
the proposed algorithms over the state-of-the-art methods in both noiseless and
noisy sparse signal recovery problems.
