  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 4-D Epanechnikov kernel (4-D EK) and its
correlated statistics were deduced to obtain the 4-D Epanechnikov mixture
models (4-D EMMs). A 4-D Epanechnikov mixture regression (4-D EMR) was proposed
based on this 4-D EK, and a 4-D adaptive model selection (4-D 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 4-D Epanechnikov kernel theory, (2) exploiting
the 4-D Epanechnikov mixture regression and its application in the modeling of
the pseudo video sequence of light field images, (3) using 4-D adaptive model
selection for the optimal number of models, and (4) employing a linear
function-based reconstruction according to the content similarity.
