Fidelity

Initial value problem

Algorithm

Statistics

Applied mathematics

Regularization (linguistics)

Image processing

Total variation denoising

Astrophysics

Telecommunications

Image restoration

Computer science

Mathematical optimization

Variation (astronomy)

Physics

Mathematics

Image (mathematics)

Mathematical analysis

Minification

Artificial intelligence

Cauchy distribution

Noise reduction

Noise (video)

Computers & Mathematics with Applications

In this paper, we propose a novel model to restore an image corrupted by blur and Cauchy noise. The model is composed of a data fidelity term and two regularization terms including total variation and high-order total variation. Total variation provides well-preserved edge features, but suffers from staircase effects in smooth regions, whereas high-order total variation can alleviate staircase effects. Moreover, we introduce a strategy for adaptively selecting regularization parameters. We develop an efficient alternating minimization algorithm for solving the proposed model. Numerical examples suggest that the proposed method has the advantages of better preserving edges and reducing staircase effects.

Total variation and high-order total variation adaptive model for restoring blurred images with Cauchy noise