Regularization with Multilevel Non-stationary Tight Framelets for Image Restoration

TL;DR

This paper introduces a novel image restoration model utilizing multilevel non-stationary tight framelets to effectively capture first- and second-order image information, improving restoration quality.

Contribution

It proposes a new variational regularization model with a multilevel non-stationary tight framelet system for enhanced image restoration.

Findings

The model effectively captures image first- and second-order information.

Numerical experiments demonstrate the model's efficiency and effectiveness.

Outperforms other higher-order models in image restoration tasks.

Abstract

Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular for natural images, are the first-order (i.e. variance in luminance) and second-order (i.e. contrast and texture) information. In this paper, we propose a model for image restoration, using a multilevel non-stationary tight framelet system that can capture the image's first-order and second-order information. We develop an algorithm to solve the proposed model and the numerical experiments show that the model is effective and efficient as compared to other higher-order models.