  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.
