Browsing by Subject "Inverse Problems"

Now showing 1 - 5 of 5
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    BAYESIAN SEQUENTIAL OPTIMAL EXPERIMENTAL DESIGN FOR INVERSE PROBLEMS USING DEEP REINFORCEMENT LEARNING
    (2022-04) Anderson, Loren
    We perform a comprehensive study on Bayesian sequential optimal experimental design techniquesapplied to inverse problems. We transform the Bayesian sequential optimal experimental design problem into a reinforcement learning problem to gauge the power of recent deep reinforcement learning algorithms compared to other baseline algorithms. Using KL-divergence as a measure of information gain, we construct objectives to maximize information gain for batch design, greedy design, black-box Bayesian optimization, multi-armed bandit optimization, dynamic programming, approximate dynamic programming, and reinforcement learning. This work showcases novel comparisons between the aforementioned methods and a new application of off-the-shelf reinforcement learning algorithms to Bayesian sequential optimal experimental design for inverse problems in differential equation models.
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    Bridging Mri Reconstruction Across Eras: From Novel Optimization Of Traditional Methods To Efficient Deep Learning Strategies
    (2024-03) Gu, Hongyi
    Magnetic Resonance Imaging (MRI) has been extensively used as a non-invasive modality for imaging the human body. Despite substantial advances over the past decades, scan duration remains as a principal issue for MRI scanning, requiring novel techniques to accelerate data acquisition. Such techniques are poised to improve clinical patient throughput, reduce motion artifacts, enhance subject comfort, and allow higher resolution imaging in many applications. Several methods have been proposed to accelerate MRI scans. In parallel imaging (PI), k-space data was acquired at a sub-Nyquist rate with with multiple receiver coils, and the redundancy among these coils were used for image reconstruction. Following the clinical impact and success of PI methods, compressed sensing (CS) techniques were developed to reconstruct images by using compressibility of images in a pre-specified linear transform domain. Transform learning (TL) was another line of work that learned the linear transforms from data, while enforcing sparsity as in CS. Recently, deep learning (DL) has shown great promise for MRI reconstruction, especially at high acceleration rates where other traditional methods would fail. Specially, physics-guided DL (PG-DL) unrolls a traditional optimization algorithm for solving regularized least squares for a fixed number of iterations, and uses neural networks to implicitly perform regularization. These unrolled networks are trained end-to-end with large databases, using well-designed loss functions and advanced optimizers, usually using a reference fully-sampled image for supervised learning. Several approaches have noted the difficulty or impossibility of acquiring fully-sampled data in various MRI applications. Among these, self-supervised learning with data undersmapling (SSDU) was developed to allow training without fully-sampled data, and multi-mask SSDU was subsequently proposed for better reconstruction quality at high acceleration rates. Although PG-DL generally shows strong ability for excellent reconstruction performance, there are concerns for generalizabilty, interpretability and stability issues. In this thesis, we aimed to bridge the gap between traditional and DL methods, while also extending the utility of DL methods for non-Cartesian imaging. We first revisited l1-wavelet CS reconstruction for accelerated MRI by using modern data science tools similar to those used in DL for optimized performance. We showed that our proposed optimization approach improved traditional CS, and further performance boost was observed by incorporating wavelet subband processing and reweighted l1 minimization. The final version reached a performance similar to state-of-the-art PG-DL, while preserving better interpretability by solving a convex optimization problem in inference time. Second, we combined ideas from CS, TL and DL to enable the learning of deep linear convolutional transforms in a format similar to PG-DL. Our proposed method performed better than CS and TL, and gave similar performance as state-of-the-art PG-DL. It used a linear representation of image as regularization at inference time, and enabled convex sparse image reconstruction that may have better robustness, stability and generalizability properties. Third, we adapted a self-supervised PG-DL technique to non-Cartesian trajectories and showed its potential for reconstructing 10-fold accelerated spiral fMRI multi-echo acquisitions. Our proposed approach gave substantial improvements in reconstructed image quality over conventional methods. Furthermore, the blood oxygenation level dependent (BOLD) signal analysis of our proposed method provided meaningful sensitivities, with similar activation patterns and extent to the expected baselines.
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    Experimental validation of the Topological Sensitivity approach to elastic-wave imaging
    (2015-08) Tokmashev, Roman
    The focus of this dissertation is on: i) non-invasive imaging of discrete damage in solids by way of the Topological Sensitivity (TS) approach to elastic-wave tomography, ii) experimental verification of the TS imaging technique using non-contact vibration measurements obtained by 3D Scanning Laser Doppler Vibrometer, and iii) upgrade of the Finite Element (FE) elastodynamic computational platform to treat long range wave propagation toward enhancing the imaging performance of TS under the conditions of limited testing aperture.
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    A level set method for an inverse problem arising in photolithography
    (2009-08) Tuzel, Vasfiye Hande
    Photolithography is a key process used in the semiconductor industry during the fabrication of integrated circuits. It is the process in which a given circuit layout pattern is transferred onto a substrate by employing a mask. The role of the mask is to block out the ultraviolet light exposure on certain areas on the substrate, hence allowing the emergence of specific patterns after chemical post-processing. Designing the perfect mask that takes into account all optical effects, especially at nanometer resolutions, is a challenging task. In this thesis, we formulate this as an inverse problem, i.e. finding the mask that produces the desired pattern. In order to do this, we first introduce the forward problem of calculating the light intensity at the substrate, given the initial mask. We then formulate a variational problem, which minimizes the mismatch between the desired mask and the one predicted by the model. The variational problem is solved using a level-set approach. Our results show that we can successfully produce masks that match the desired patterns with an error less than 2%. We believe our algorithm can enable further automation of the mask design process, and help manufacturers design better layouts at nanometer scales.
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    Robustness in Deep Learning: Single Image Denoising using Untrained Networks
    (2021-05) Singh, Esha
    Deep Learning has become one of the cornerstones of today’s AI advancement and research. Deep Learning models are used for achieving state-of-the-art results on a wide variety of tasks, including image restoration problems, specifically image denoising. Despite recent advances in applications of deep neural networks and the presence of a substantial amount of existing research work in the domain of image denoising, this task is still an open challenge. In this thesis work, we aim to summarize the study of image denoising research and its trend over the years, the fallacies, and the brilliance. We first visit the fundamental concepts of image restoration problems, their definition, and some common misconceptions. After that, we attempt to trace back where the study of image denoising began, attempt to categorize the work done till now into three main families with the main focus on the neural network family of methods, and discuss some popular ideas. Consequently, we also trace related concepts of over-parameterization, regularisation, low-rank minimization and discuss recent untrained networks approach for single image denoising, which is fundamental towards understanding why the current state-of-art methods are still not able to provide a generalized approach for stabilized image recovery from multiple perturbations.