Authors: Rongjie Liu, Meng Li, Li Ma Description: 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, and (4) 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 self-tuning and regularization to avoid overfitting-- resulting in 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 ImageNet, 3D medical image, and real-life YouTube and surveillance videos show that CARP dominates the state-of-the-art compression approaches-- including JPEG, JPEG2000, MPEG4, and a neural network-based method--for all of these different image types and often on nearly all of the individual images.