  In this paper, we propose a general scale invariant approach for sparse
signal recovery via the minimization of the $q$-ratio sparsity. When $1 < q
\leq \infty$, both the theoretical analysis based on $q$-ratio constrained
minimal singular values (CMSV) and the practical algorithms via nonlinear
fractional programming are presented. Numerical experiments are conducted to
demonstrate the advantageous performance of the proposed approaches over the
state-of-the-art sparse recovery methods.
