On the Atoms of Robustness

On the Atoms of Robustness: Robust Matrix Decomposition for Spectral Imaging

Moens, Roger (TU Delft Aerospace Engineering; TU Delft Mechanical, Maritime and Materials Engineering)

van de Plas, R. (mentor)
Brandl, B.R. (mentor)

Delft University of Technology

Aerospace Engineering

2021-04-30

Modern imaging modalities across many application domains increasingly acquire a large number of very high-dimensional measurements, commonly collecting hundreds to millions of variables per spatial resolution element. That high-dimensional nature can severely challenge traditional (often Euclidean distance based) approaches to noise and dimensionality reduction. Furthermore, statistical analysis of such data is often hampered by the curse of dimensionality, concomitant with large numbers of pixels and channels, by the growing abundance of low signal-to-noise ratio (SNR) measurements, and by the detrimental effects of noise accumulation. It is therefore necessary to find efficient means of reducing high-dimensional (and large data size) measurement sets to a lower-dimensional representation while incurring minimal information loss. Addressing this challenge is essential (a) to enable processing of the massively multivariate measurement sets acquired by several promising imaging technologies today (commonly hundreds of gigabytes to terabytes per experiment), (b) to avoid that computational analysis becomes a bottleneck for the development of new instrumental capabilities, with hardware setups theoretically capable of yielding terabyte to petabyte imaging but currently considered impractical, and (c) to enable archiving massively multivariate measurement sets, often required to be stored for several years and containing information suitable for additional science projects. This thesis focuses on this challenge specifically. First, it explores structured and regularized matrix decomposition methods based on the l₁-norm, e.g. building on principal component pursuit (PCP), to address this challenge. Second, it delivers custom implementations of these methods. Third, it develops and implements an application-driven framework for automatic setting of hyperparameters. Finally, it applies and compares these methods using several spectral imaging case studies spanning both very small scales, in molecular imaging of organic tissue, as well as very large scales, in the spectroscopic imaging of Outer space.

big data
spectral imaging
imaging mass spectrometry
integral field spectroscopy
matrix decomposition
linear algebra
sparsity
molecular imaging
astronomical imaging

http://resolver.tudelft.nl/uuid:78817107-d34a-4d6f-9ea1-d7298436d63c

2026-04-30

Master of Science in Systems and Control Master of Science in Aerospace Engineering

Student theses

master thesis

© 2021 Roger Moens