CARP: Compression Through Adaptive Recursive Partitioning for Multi-Dimensional Images

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.