Three-dimensional Epanechnikov mixture regression in image coding

TL;DR

This paper introduces a novel 3-D Epanechnikov Mixture Regression framework for image coding, outperforming traditional methods like JPEG in efficiency and image clarity by leveraging advanced kernel models and adaptive algorithms.

Contribution

It develops a new 3-D Epanechnikov kernel model, improves the EM algorithm with MSE optimization, and applies these to image coding with adaptive model selection.

Findings

Recovered images have clearer outlines.

Achieves superior coding efficiency below 0.25bpp.

Outperforms JPEG in image quality and compression.

Abstract

Kernel methods have been studied extensively in recent years. We propose a three-dimensional (3-D) Epanechnikov Mixture Regression (EMR) based on our Epanechnikov Kernel (EK) and realize a complete framework for image coding. In our research, we deduce the covariance-matrix form of 3-D Epanechnikov kernels and their correlated statistics to obtain the Epanechnikov mixture models. To apply our theories to image coding, we propose the 3-D EMR which can better model an image in smaller blocks compared with the conventional Gaussian Mixture Regression (GMR). The regressions are all based on our improved Expectation-Maximization (EM) algorithm with mean square error optimization. Finally, we design an Adaptive Mode Selection (AMS) algorithm to realize the best model pattern combination for coding. Our recovered image has clear outlines and superior coding efficiency compared to JPEG below 0.25bpp. Our work realizes an unprecedented theory application by: (1) enriching the theory of Epanechnikov kernel,(2) improving the EM algorithm using MSE optimization, (3) exploiting the EMR and its application in image coding, and (4) AMS optimal modeling combined with Gaussian and Epanechnikov kernel.