Separable Inverse Problems, Blind Deconvolution, and Stray Light Correction for Extreme Ultraviolet Solar Images.

The determination of the inputs to a system given noisy output data is known as an inverse problem. When the system is a linear transformation involving unknown side parameters, the problem is called separable. A quintessential separable inverse problem is blind deconvolution: given a blurry image one must determine the sharp image and point spread function (PSF) that were convolved together to form it. This thesis describes a novel optimization approach for general separable inverse problems, a new blind deconvolution method for images corrupted by camera shake, and the first stray light correction for extreme ultraviolet (EUV) solar images from the EUVI/STEREO instruments. We present a generalization of variable elimination methods for separable inverse problems beyond least squares. Existing variable elimination methods require an explicit formula for the optimal value of the linear variables, so they cannot be used in problems with Poisson likelihoods, bound constraints, or other important departures from least squares. To address this limitation, we propose a generalization of variable elimination in which standard optimization methods are modified to behave as though a variable has been eliminated. Computational experiments indicate that this approach can have significant speed and robustness advantages. A new incremental sparse approximation method is proposed for blind deconvolution of images corrupted by camera shake. Unlike current state-of-the-art variational Bayes methods, it is based on simple alternating projected gradient optimization. In experiments on a standard test set, our method is faster than the state-of-the-art and competitive in deblurring performance. Stray light PSFs are determined for the two EUVI instruments, EUVI-A and B, aboard the STEREO mission. The PSFs are modeled using semi-empirical parametric formulas, and their parameters are determined by semiblind deconvolution of EUVI images. The EUVI-B PSFs were determined from lunar transit data, exploiting the fact that the Moon is not a significant EUV source. The EUVI-A PSFs were determined by analysis of simultaneous A/B observations from December 2006, when the instruments had nearly identical lines of sight to the Sun. We provide the first estimates of systematic error in EUV deconvolved images.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99797/1/shearerp_1.pd

Machine Learning Methods for Cancer Immunology

Tumours are highly heterogeneous collections of tissues characterised by a repertoire of heavily mutated and rapidly proliferating cells. Evading immune destruction is a fundamental hallmark of cancer, and elucidating the contextual basis of tumour-infiltrating leukocytes is pivotal for improving immunotherapy initiatives. However, progress in this domain is hindered by an incomplete characterisation of the regulatory mechanisms involved in cancer immunity. Addressing this challenge, this thesis is formulated around a fundamental line of inquiry: how do we quantitatively describe the immune system with respect to tumour heterogeneity? Describing the molecular interactions between cancer cells and the immune system is a fundamental goal of cancer immunology. The first part of this thesis describes a three-stage association study to address this challenge in pancreatic ductal adenocarcinoma (PDAC). Firstly, network-based approaches are used to characterise PDAC on the basis of transcription factor regulators of an oncogenic KRAS signature. Next, gene expression tools are used to resolve the leukocyte subset mixing proportions, stromal contamination, immune checkpoint expression and immune pathway dysregulation from the data. Finally, partial correlations are used to characterise immune features in terms of KRAS master regulator activity. The results are compared across two independent cohorts for consistency. Moving beyond associations, the second part of the dissertation introduces a causal modelling approach to infer directed interactions between signaling pathway activity and immune agency. This is achieved by anchoring the analysis on somatic genomic changes. In particular, copy number profiles, transcriptomic data, image data and a protein-protein interaction network are integrated using graphical modelling approaches to infer directed relationships. Generated models are compared between independent cohorts and orthogonal datasets to evaluate consistency. Finally, proposed mechanisms are cross-referenced against literature examples to test for legitimacy. In summary, this dissertation provides methodological contributions, at the levels of associative and causal inference, for inferring the contextual basis for tumour-specific immune agency.This PhD was supported by the Cancer Research UK and Engineering and Physical Sciences Research Council Imaging Centre in Cambridge and Manchester (C197/A16465