  In this paper, we study the L1/L2 minimization on the gradient for imaging
applications. Several recent works have demonstrated that L1/L2 is better than
the L1 norm when approximating the L0 norm to promote sparsity. Consequently,
we postulate that applying L1/L2 on the gradient is better than the classic
total variation (the L1 norm on the gradient) to enforce the sparsity of the
image gradient. To verify our hypothesis, we consider a constrained formulation
to reveal empirical evidence on the superiority of L1/L2 over L1 when
recovering piecewise constant signals from low-frequency measurements.
Numerically, we design a specific splitting scheme, under which we can prove
the subsequential convergence for the alternating direction method of
multipliers (ADMM). Experimentally, we demonstrate visible improvements of
L1/L2 over L1 and other nonconvex regularizations for image recovery from
low-frequency measurements and two medical applications of MRI and CT
reconstruction. All the numerical results show the efficiency of our proposed
approach.
