Image denoising and deblurring: non-convex regularization, inverse diffusion and shock filter

Abstract

A large number of applications in image processing and computer vision depend on image quality. In this paper, main concerns are image denoising and deblurring simultaneously in a restoration task by three types of methodologies: non-convex regularization, inverse diffusion and shock filter. We discuss their relations in the context of image deblurring: the inverse diffusion implied by the non-convex regularization, and the superior ability of deblurring edge of the shock filter to that of the inverse diffusion, both in 1D and 2D cases. Finally, we propose a region-based adaptive anisotropic diffusion with shock filter method, which shows advantages of deblurring edges, denoising and smoothing contours in experiments, compared with some related methods. Therein an idea of "divide and rule" is introduced.

Multiplicative noise removal combining a total variation regularizer and a nonconvex regularizer

“…Theorem 1 For fixed positive parameters λ, ε(0 < ε < 1), α, and for a given function b ∈ adm 2 , the functional J(u) in the minimization problem (14) has a unique minimizer u * ∈ adm 1 ∩ L ∞ ( ).…”

“…The only challenging to implement Algorithm 1 is to minimize the functional (26), or to minimize the more general functional in the minimization problem (14). In order to construct an efficient solver, we first equivalently convert the minimization problem (14) into the form shown as follows,…”

“…In order to construct an efficient solver, we first equivalently convert the minimization problem (14) into the form shown as follows,…”

“…Note that if the above ADMM iteration process is used to solve the discrete version of the model (14), the corresponding sequence {u n } must converge. This conclusion can be similarly proved as the work in [3].…”

“…Furthermore, the TV regularizer, to a certain degree, is used to preserve the details of the restored images. However, a large number of applications indicate that some nonconvex regularizers [8,14,17,23] show better performance than convex ones Downloaded by [University of Tennessee, Knoxville] at 19:54 04 January 2015 Table 1. Quantitative evaluation (SNR (db), PSNR (db), and the running time (s)) for different denoising models: the proposed model, our previous model in [17], and the SO model.…”