A New TV-Stokes Model for Image Deblurring and Denoising with Fast Algorithms

The famous TV-Stokes models, which improve the restored images comfortable, have been very successful in image denoising. In this paper, we propose a new TV-Stokes model for image deblurring with a good geometry explanation. In the tangential field smoothing, the data fidelity term is chosen to measure the distance between the solution and the orthogonal projection of the tangential field of the observation image onto the range of the conjugate of the blurry operator, while the total variation of the solution is chosen as the regularization term. In the image reconstruction, we compute the smoothing part of the image from the smoothed tangential field for the first step, and use an anisotropic TV model to obtain the “texture” part of the deblurred image. The solvability properties for the minimization problems in two steps are established, and fast algorithms are presented. Numerical experiments demonstrate that the new deblurring model can capture the details of images hidden in the blurry and noisy image, and the fast algorithms are efficient and robust.