Nonlocal Patches based Gaussian Mixture Model for Image Inpainting

TL;DR

This paper introduces a nonlocal variational method based on Gaussian Mixture Models for simultaneous image inpainting and denoising, effectively handling large missing regions and noise.

Contribution

It develops a novel regularization framework using GMM and MAP estimation, with an EM algorithm for efficient optimization, advancing inpainting techniques under noisy conditions.

Findings

Effective inpainting of large missing regions

Simultaneous denoising and inpainting achieved

Numerical results demonstrate high-quality reconstructions

Abstract

We consider the inpainting problem for noisy images. It is very challenge to suppress noise when image inpainting is processed. An image patches based nonlocal variational method is proposed to simultaneously inpainting and denoising in this paper. Our approach is developed on an assumption that the small image patches should be obeyed a distribution which can be described by a high dimension Gaussian Mixture Model. By a maximum a posteriori (MAP) estimation, we formulate a new regularization term according to the log-likelihood function of the mixture model. To optimize this regularization term efficiently, we adopt the idea of the Expectation Maximum (EM) algorithm. In which, the expectation step can give an adaptive weighting function which can be regarded as a nonlocal connections among pixels. Using this fact, we built a framework for non-local image inpainting under noise. Moreover, we mathematically prove the existence of minimizer for the proposed inpainting model. By using a spitting algorithm, the proposed model are able to realize image inpainting and denoising simultaneously. Numerical results show that the proposed method can produce impressive reconstructed results when the inpainting region is rather large.