  Fast and effective image compression for multi-dimensional images has become
increasingly important for efficient storage and transfer of massive amounts of
high-resolution images and videos. Desirable properties in compression methods
include (1) high reconstruction quality at a wide range of compression rates
while preserving key local details, (2) computational scalability, (3)
applicability to a variety of different image/video types and of different
dimensions, (4) progressive transmission, and (5) ease of tuning. We present
such a method for multi-dimensional image compression called Compression via
Adaptive Recursive Partitioning (CARP). CARP uses an optimal permutation of the
image pixels inferred from a Bayesian probabilistic model on recursive
partitions of the image to reduce its effective dimensionality, achieving a
parsimonious representation that preserves information. CARP uses a multi-layer
Bayesian hierarchical model to achieve in-situ compression along with
self-tuning and regularization, with just one single parameter to be specified
by the user to achieve the desired compression rate. Extensive numerical
experiments using a variety of datasets including 2D still images, real-life
YouTube videos, and surveillance videos show that CARP dominates the
state-of-the-art image/video compression approaches---including JPEG, JPEG2000,
BPG, MPEG4, HEVC and a neural network-based method---for all of these different
image types and on nearly all of the individual images and videos over some
methods.
