Non‐convex nonlocal adaptive tight frame image deblurring

Abstract

The challenge of the image restoration is to recover more detailed information from the degraded images. Based on the observations that wavelet frames have efficient representation ability to image details and the nonconvex regularization in the model may admit unbiased solutions, in this paper, in order to recover more details, a wavelet frames nonconvex ℓ p ( 0 < p < 1 $\ell _p(0<p<1$ ) regularization image restoration model is established that combing with a nonlocal adaptive mean doubly augmented Lagrangian (MDAL) method and context model. Specifically, a nonlocal adaptive MDAL method is proposed to solve the established nonconvex model. Furthermore, in order to mitigate the trade-off between the regularization error and the noise magnification error, spatially adaptive wavelet thresholding methods based on the context model and nonlocal mean filter are introduced in the algorithm. The convergence analysis of this nonlocal adaptive nonconvex algorithm is also obtained using the KL inequality. Numerical experiments demonstrate that the proposed method has a competent deblurring and denoising ability, also is efficient and is comparable to state-of-the-art methods.