Structured and Low-Rank Decompositions for Large-Scale Imaging Datasets
R.A.R. Moens (TU Delft - Team Raf Van de Plas)
R. Van de Plas – Promotor (TU Delft - Team Raf Van de Plas)
B. De Schutter – Promotor (TU Delft - Delft Center for Systems and Control)
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Abstract
A common strategy to address new scientific challenges consists of abstracting the underlying problem, recasting it to an existing problem formulation and applying an established methodology. In this dissertation, we offer a variation on this familiar academic theme. The setting we will focus on is primarily found within image-acquiring instruments, characterized by producing vast quantities of data, from several hundreds up to more than half a million images per experiment. The challenges that we address throughout this work will mainly consist of (a) reducing dimensionality and (b) denoising, which have a direct and significant impact on the analysis and thus interpretation of these extensive image sets.
We investigate computational methods for two specific imaging instruments: (1) a time-of-flight imaging mass spectrometer, employed in biochemical research to visualize molecular distributions across very small organic tissues, and (2) a mid-infrared imager, utilized in astronomical research to study very large protostars, temperate exoplanets, and objects within our solar system. Despite their considerable promise in acquiring detailed molecular maps and critical astronomical insights, respectively, the practical analysis and interpretation of their image sets face substantial obstacles, namely their dimensionality and the effect of noise. Addressing these challenges may involve drawing on existing computational and storage capacity and harnessing any available prior information or problem-specific structure. Fortunately, analytical solutions to the obstacles across imaging instruments often bear a resemblance to each other, as we distil them to abstract mathematical models and eventually formulate those problems as optimization problems.
The computational methods we are interested in are so-called low-rankmethods, they can simultaneously provide insight in data structure (analysis), as well as reduce the dimensionality of the data and denoise it....