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

Variational and learning models for image and time series inverse problems

Inverse problems are at the core of many challenging applications. Variational and learning models provide estimated solutions of inverse problems as the outcome of specific reconstruction maps. In the variational approach, the result of the reconstruction map is the solution of a regularized minimization problem encoding information on the acquisition process and prior knowledge on the solution. In the learning approach, the reconstruction map is a parametric function whose parameters are identified by solving a minimization problem depending on a large set of data. In this thesis, we go beyond this apparent dichotomy between variational and learning models and we show they can be harmoniously merged in unified hybrid frameworks preserving their main advantages. We develop several highly efficient methods based on both these model-driven and data-driven strategies, for which we provide a detailed convergence analysis. The arising algorithms are applied to solve inverse problems involving images and time series. For each task, we show the proposed schemes improve the performances of many other existing methods in terms of both computational burden and quality of the solution. In the first part, we focus on gradient-based regularized variational models which are shown to be effective for segmentation purposes and thermal and medical image enhancement. We consider gradient sparsity-promoting regularized models for which we develop different strategies to estimate the regularization strength. Furthermore, we introduce a novel gradient-based Plug-and-Play convergent scheme considering a deep learning based denoiser trained on the gradient domain. In the second part, we address the tasks of natural image deblurring, image and video super resolution microscopy and positioning time series prediction, through deep learning based methods. We boost the performances of supervised, such as trained convolutional and recurrent networks, and unsupervised deep learning strategies, such as Deep Image Prior, by penalizing the losses with handcrafted regularization terms

Development and application of molecular and computational tools to image copper in cells

Copper is a trace element which is essential for many biological processes. A deficiency or excess of copper(I) ions, which is its main oxidation state of copper in cellular environment, is increasingly linked to the development of neurodegenerative diseases such as Parkinson’s and Alzheimer’s disease (PD and AD). The regulatory mechanisms for copper(I) are under active investigation and lysosomes which are best known as cellular “incinerators” have been found to play an important role in the trafficking of copper inside the cell. Therefore, it is important to develop reliable experimental methods to detect, monitor and visualise this metal in cells and to develop tools that allow to improve the data quality of microscopy recordings. This would enable the detailed exploration of cellular processes related to copper trafficking through lysosomes. The research presented in this thesis aimed to develop chemical and computational tools that can help to investigate concentration changes of copper(I) in cells (particularly in lysosomes), and it presents a preliminary case study that uses the here developed microscopy image quality enhancement tools to investigate lysosomal mobility changes upon treatment of cells with different PD or AD drugs. Chapter I first reports the synthesis of a previously reported copper(I) probe (CS3). The photophysical properties of this probe and functionality on different cell lines was tested and it was found that this copper(I) sensor predominantly localized in lipid droplets and that its photostability and quantum yield were insufficient to be applied for long term investigations of cellular copper trafficking. Therefore, based on the insights of this probe a new copper(I) selective fluorescent probe (FLCS1) was designed, synthesized, and characterized which showed superior photophysical properties (photostability, quantum yield) over CS3. The probe showed selectivity for copper(I) over other physiological relevant metals and showed strong colocalization in lysosomes in SH-SY5Y cells. This probe was then used to study and monitor lysosomal copper(I) levels via fluorescence lifetime imaging microscopy (FLIM); to the best of my knowledge this is the first copper(I) probe based on emission lifetime. Chapter II explores different computational deep learning approaches for improving the quality of recorded microscopy images. In total two existing networks were tested (fNET, CARE) and four new networks were implemented, tested, and benchmarked for their capabilities of improving the signal-to-noise ratio, upscaling the image size (GMFN, SRFBN-S, Zooming SlowMo) and interpolating image sequences (DAIN, Zooming SlowMo) in z- and t-dimension of multidimensional simulated and real-world datasets. The best performing networks of each category were then tested in combination by sequentially applying them on a low signal-to-noise ratio, low resolution, and low frame-rate image sequence. This image enhancement workstream for investigating lysosomal mobility was established. Additionally, the new frame interpolation networks were implemented in user-friendly Google Colab notebooks and were made publicly available to the scientific community on the ZeroCostDL4Mic platform. Chapter III provides a preliminary case study where the newly developed fluorescent copper(I) probe in combination with the computational enhancement algorithms was used to investigate the effects of five potential Parkinson’s disease drugs (rapamycin, digoxin, curcumin, trehalose, bafilomycin A1) on the mobility of lysosomes in live cells.Open Acces

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity