Blind image deblurring based on multi-resolution ringing removal.

•Latent sharp image and the blur PSF are estimated jointly via a multi-functional optimization problem addressed by a first-order primal-dual solver.•This approach generates a multi-resolution pyramid of the input blurred image.•We introduce a PSF initiation method that benefits from the salient structure obtained via an l0 gradient smoothing of blurred image.•A first-order primal-dual solution to the l0 gradient smoothing problem is introduced in this paper.