  This paper introduces a nonconvex approach to the problem of recovering
sparse signals. We propose a novel model, termed the $\tau_2$-model, which
utilizes the square of $\ell_1/\ell_2$ norms for sparse recovery. This model is
an advancement over the $\ell_0$ norm, which is often computationally
intractable and less effective in handling practical scenarios. Our approach is
grounded in the concept of effective sparsity, which robustly measures the
number of effective coordinates in a signal. We demonstrate that our model is a
powerful alternative for sparse signal estimation, with the $\tau_2$-model
offering computational advantages and practical applicability. The model's
formulation and the accompanying algorithm, based on Dinkelbach's procedure
combined with a difference of convex functions strategy, are detailed. We
further explore the properties of our model, including the existence of
solutions under certain conditions, and discuss the algorithm's convergence
properties. Numerical experiments with various sensing matrices are conducted
to validate the effectiveness of our model.
