Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

TL;DR

This paper introduces a Gaussian mixture model-based framework for image inverse problems, utilizing a MAP-EM algorithm with structured sparsity interpretation, achieving competitive results with lower computational cost.

Contribution

The paper presents a novel, efficient approach combining Gaussian mixture models and structured sparse estimation for solving various image inverse problems.

Findings

Achieves comparable or better results than state-of-the-art methods.

Reduces computational cost significantly.

Applicable to multiple inverse problems like inpainting, zooming, and deblurring.

Abstract

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.