Advanced Statistical Learning Methods in Image Processing

With the rapid development of modern technology, massive imaging datasets have been routinely collected in a wide range of applications, e.g., ImageNet in natural image processing and Human Connectome Project in computational neuroscience. These big and complex imaging datasets have facilitated a surge of interest in image processing at the interplay of statistics, computer vision, and medical science domains. While new approaches are constantly being developed, scalability, interpretability and uncertainty quantification are still considered as main challenges. This thesis encompasses three projects, in which we develop advanced statistical methods to address daunting challenges in three key imaging processing problems. First, in the image compression problem, we develop a scalable and model-based method called Compression through Adaptive Recursive Partitioning (CARP) to compress m-dimensional images in a unified fashion. 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. Extensive experiments show that CARP dominates the state-of-the-art image/video compression approaches including JPEG, JPEG2000, BPG, MPEG-4, HEVC and a neural network-based method for all of different image/video types and often on nearly all of the individual images. Second, in the image reconstruction problem, we establish posterior concentration rates for wavelets with adaptive recursive partitioning for multi-dimensional imaging data, which are minimax optimal up to a logarithmic factor under the supremum norm. This provides strong theoretical support for a fast reconstruction method that scales linearly to the number of pixels and provides uncertainty quantification. Third, in the brain image parcellation problem, we propose a new principal parcellation analysis for learning the relevant ROIs automatically based on white matter fiber bundles. We develop a novel framework that conducts the clustering analysis on the fibers' ending points to redefine parcellation and eventually predict human traits, which dramatically improves parsimony and prediction, compared to anatomical parcellation based connectomes. It eliminates the need to choose ROIs manually, reducing subjectivity and leading to a substantially different representation of the connectome.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

2020

Author dc:creator

• Liu, Rongjie

Advisor dc:contributor.advisor

• Li, Meng

• Image processing
• Bayesian statistics
• image compression
• image reconstruction
• human brain parcellation

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/109604

OAI identifier oai:identifier

oai:repository.rice.edu:1911/109604