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An iterative solution to the problem of blind image deconvolution is presented whereby a previous image estimate is explicitly used in the new image estimation process. The previous image is pre-filtered using an adaptive, non-parametric stabilizing function that is updated based on a current error estimate. This function is experimentally shown to dramatically benefit the convergence rate for the a priori restoration case. Noise propagation from one iteration to the next is reduced by the use of a second, regularizing operator, resulting in a hybrid iteration technique. Further, error terms are developed that shed new light on the error propagation properties of this method and others by quantifying the extent of noise and regularization error propagation. Optimal non-parametric, frequency adaptive stabilizing and regularization functions are then derived based on this error analysis. / Thesis / Master of Engineering (ME)

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<p dir="ltr">The past two decades have seen photography shift from the hands of professionals to that of the average smartphone user. However, fitting a camera module in the palm of your hand has come with its own cost. The reduced sensor size, and hence the smaller pixels, has made the image inherently noisier due to fewer photons being captured. To compensate for fewer photons, we can increase the exposure of the camera but this may exaggerate the effect of hand shake, making the image blurrier. The presence of both noise and blur has made the post-processing algorithms necessary to produce a clean and sharp image. </p><p dir="ltr">In this thesis, we discuss various methods of deblurring images in the presence of noise. Specifically, we address the problem of photon-limited deconvolution, both with and without the underlying blur kernel being known i.e. non-blind and blind deconvolution respectively. For the problem of blind deconvolution, we discuss the flaws of the conventional approach of joint estimation of the image and blur kernel. This approach, despite its drawbacks, has been the go-to method for solving blind deconvolution for decades. We then discuss the relatively unexplored kernel-first approach to solving the problem which is numerically stable than the alternating minimization counterpart. We show how to implement this framework using deep neural networks in practice for both photon-limited and noiseless deconvolution problems. </p>

Treating cancer is difficult as the disease is complex and drug responses often depend on the patient's characteristics. Precision medicine aims to solve this by selecting individualized treatments. Since this involves the analysis of large datasets, machine learning can be used to make the drug selection process more efficient. Traditionally, such models utilize bulk gene expression data. However, this potentially masks information from small cell populations and fails to address tumor heterogeneity. Therefore, this thesis applies data deconvolution methods to bulk gene expression data and estimates the corresponding cell type-specific gene expression profiles. This "increases" the resolution of the input data for the drug response prediction. A hold-out dataset, LODOCV and LOCOCV were used for the evaluation of this approach. Furthermore, all results are compared against a baseline model, which was trained on bulk data. Overall, the accuracy of the cell type-specific model did not show an improvement compared to the bulk model. It also prioritizes information from bulk samples, which makes the additional data unnecessary. The robustness of the cell type-specific model is slightly lower than that of the bulk model. Note, that these outcomes are not necessarily due to a flaw in the underlying concept, but may be connected to poor deconvolution results as the same reference matrix was used for the deconvolution of all bulk samples regardless of the cancer type or disease.

Une image hyperspectrale est un cube de données 3D dont chaque pixel fournit des informations spectrales locales sur un grand nombre de bandes contiguës sur une scène d'intérêt. Les images observées peuvent subir une dégradation due à l'instrument de mesure, avec pour conséquence l'apparition d'un flou sur les images qui se modélise par une opération de convolution. La déconvolution d'image hyperspectrale (HID) consiste à enlever le flou pour améliorer au mieux la résolution spatiale des images. Un critère de HID du type Tikhonov avec contrainte de non-négativité est proposé dans la thèse de Simon Henrot. Cette méthode considère les termes de régularisations spatiale et spectrale dont la force est contrôlée par deux paramètres de régularisation. La première partie de cette thèse propose le critère de courbure maximale MCC et le critère de distance minimum MDC pour estimer automatiquement ces paramètres de régularisation en formulant le problème de déconvolution comme un problème d'optimisation multi-objectif. La seconde partie de cette thèse propose l'algorithme de LMS avec un bloc lisant régularisé (SBR-LMS) pour la déconvolution en ligne des images hyperspectrales fournies par les systèmes de whiskbroom et pushbroom. L'algorithme proposé prend en compte la non-causalité du noyau de convolution et inclut des termes de régularisation non quadratiques tout en maintenant une complexité linéaire compatible avec le traitement en temps réel dans les applications industrielles. La troisième partie de cette thèse propose des méthodes de séparation-déconvolution conjointes basés sur le critère de Tikhonov en contextes hors-ligne ou en-ligne. L'ajout d'une contrainte de non-négativité permet d’améliorer leurs performances / A hyperspectral image is a 3D data cube in which every pixel provides local spectral information about a scene of interest across a large number of contiguous bands. The observed images may suffer from degradation due to the measuring device, resulting in a convolution or blurring of the images. Hyperspectral image deconvolution (HID) consists in removing the blurring to improve the spatial resolution of images at best. A Tikhonov-like HID criterion with non-negativity constraint is considered here. This method considers separable spatial and spectral regularization terms whose strength are controlled by two regularization parameters. First part of this thesis proposes the maximum curvature criterion MCC and the minimum distance criterion MDC to automatically estimate these regularization parameters by formulating the deconvolution problem as a multi-objective optimization problem. The second part of this thesis proposes the sliding block regularized (SBR-LMS) algorithm for the online deconvolution of hypserspectral images as provided by whiskbroom and pushbroom scanning systems. The proposed algorithm accounts for the convolution kernel non-causality and including non-quadratic regularization terms while maintaining a linear complexity compatible with real-time processing in industrial applications. The third part of this thesis proposes joint unmixing-deconvolution methods based on the Tikhonov criterion in both offline and online contexts. The non-negativity constraint is added to improve their performances

published_or_final_version / abstract / Physics / Doctoral / Doctor of Philosophy