Local low-rank matrix recovery for hyperspectral image denoising with ℓ gradient constraint.

•A novel hyperspectral image denoising method is proposed by using l0 gradient.•A global l0 gradient constraint is utilized to recover the global smoothness of the HSI.•An efficient algorithm is designed to solve the constrained nonconvex optimization problem.•It is revealed that the developed algorithm is more effective than the low rank based methods in matrix recovery.