Image Restoration: A General Wavelet Frame Based Model and Its Asymptotic Analysis

02/17/2016
by   Bin Dong, et al.
0

Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a generic wavelet frame based image restoration model, called the "general model", which includes most of the existing wavelet frame based models as special cases. Moreover, the general model also includes examples that are new to the literature. Motivated by our earlier studies [1-3], We provide an asymptotic analysis of the general model as image resolution goes to infinity, which establishes a connection between the general model in discrete setting and a new variatonal model in continuum setting. The variational model also includes some of the existing variational models as special cases, such as the total generalized variational model proposed by [4]. In the end, we introduce an algorithm solving the general model and present one numerical simulation as an example.

READ FULL TEXT
research
01/25/2017

An Edge Driven Wavelet Frame Model for Image Restoration

Wavelet frame systems are known to be effective in capturing singulariti...
research
05/13/2011

ℓ_0 Minimization for Wavelet Frame Based Image Restoration

The theory of (tight) wavelet frames has been extensively studied in the...
research
03/26/2016

Support Driven Wavelet Frame-based Image Deblurring

The wavelet frame systems have been playing an active role in image rest...
research
10/10/2015

Wavelet Frame Based Image Restoration Using Sparsity, Nonlocal and Support Prior of Frame Coefficients

The wavelet frame systems have been widely investigated and applied for ...
research
08/25/2017

A wavelet frame coefficient total variational model for image restoration

In this paper, we propose a Rudin-Osher-Fatemi(ROF)-like model for image...
research
06/16/2016

CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration

In this paper, we propose a new framework to remove parts of the systema...
research
06/01/2023

Wavelet Image Restoration Using Multifractal Priors

Bayesian image restoration has had a long history of successful applicat...

Please sign up or login with your details

Forgot password? Click here to reset