In this study, we propose a modeling-based compression approach for dense/lenslet light field images captured by Plenoptic 2.0 with square microlenses. This method employs the 5-D Epanechnikov Kernel (5-D EK) and its associated theories. Owing to the limitations of modeling larger image block using the Epanechnikov Mixture Regression (EMR), a 5-D Epanechnikov Mixture-of-Experts using Gaussian Initialization (5-D EMoE-GI) is proposed. This approach outperforms 5-D Gaussian Mixture Regression (5-D GMR). The modeling aspect of our coding framework utilizes the entire EI and the 5D Adaptive Model Selection (5-D AMLS) algorithm. The experimental results demonstrate that the decoded rendered images produced by our method are perceptually superior, outperforming High Efficiency Video Coding (HEVC) and JPEG 2000 at a bit depth below 0.06bpp.

With the emergence of light field imaging in recent years, the compression of its elementary image array (EIA) has become a significant problem. Our coding framework includes modeling and reconstruction. For the modeling, the covariance-matrix form of the 4D Epanechnikov kernel (4D EK) and its correlated statistics were deduced to obtain the 4-D Epanechnikov mixture models (4-D EMMs). A 4D Epanechnikov mixture regression (4D EMR) was proposed based on this 4D EK, and a 4D adaptive model selection (4D AMLS) algorithm was designed to realize the optimal modeling for a pseudo video sequence (PVS) of the extracted key-EIA. A linear function based reconstruction (LFBR) was proposed based on the correlation between adjacent elementary images (EIs). The decoded images realized a clear outline reconstruction and superior coding efficiency compared to high-efficiency video coding (HEVC) and JPEG 2000 below approximately 0.05 bpp. This work realized an unprecedented theoretical application by (1) proposing the 4D Epanechnikov kernel theory, (2) exploiting the 4D Epanechnikov mixture regression and its application in the modeling of the pseudo video sequence of light field images, (3) using 4D adaptive model selection for the optimal number of models, and (4) employing a linear function-based reconstruction according to the content similarity.

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.

In this paper, we propose an optimal modeling framework for image compression using EMM (Epanechnikov Mixture Model). Epanechnikov Kernel and its correlated statistics are basement of our Epanechnikov Mixture Regression (EMR). In our scheme, the stochastic processes of the pixel values are modelled as an EMM with K experts in three-dimensional space and then we use EMR to search for the optimal solution, whose parameters are determined through EM (Expectation-Maximization) algorithm. In the process of regression, the conditional density is the regression kernel function. Experimental results show that the proposed scheme is effective especially for the image with complex texture without consuming extra bits compared to Gaussian Mixture Regression (GMR).