An Accelerated Smoothing Gradient Method for Nonconvex Nonsmooth Minimization in Image Processing

In this paper, we propose a fast and provably convergent smoothing gradient descent type algorithm with extrapolation for solving a general class of nonsmooth and nonconvex inverse problems arising from image processing. Our algorithm has a localizer selective policy to switch between gradient descent scheme with or without extrapolation to possibly speed up the decreasing of the smoothed objective function and ensure the convergence. Moreover, the algorithm adaptively reduces the smoothing factor to guarantee that any accumulation point of the generated sequence is an (affine-scaled) Clarke stationary point of the original nonsmooth and nonconvex problem. Extensive numerical experiments and comparisons indicate the effectiveness of the proposed algorithm in natural image deblurring, CT and MRI reconstruction.