Browsing by Subject "inverse problem"
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Item Advancing Deep Learning For Scientific Inverse Problems(2023-09) Zhuang, ZhongArtificial intelligence (AI) has ushered in a new paradigm for addressing scientific complexities, harnessing the computational prowess of robust machines and sophisticated algorithms tailored to domain-specific constraints. Across diverse domains encompass- ing scientific and engineering landscapes such as astronomy, biomedical science, and material science, the emergence of inverse problems is inherent. These quandaries are distinguished by the overarching objective of elucidating the reconstruction of meticulously structured entities from observational data, buoyed by a foundational bedrock of prior knowledge. In a generalized sense, the inverse problem is cast as Y = F(x), subject to the constraint G(x) = 0, wherein F denotes the function orchestrating the transformation of object x to observation Y, while G embodies the constraints imposed by pre-existing knowledge. Owing to the intrinsic characteristics of F—often marked by pronounced nonlinearity—inverse problems seldom conform to well-posed paradigms. Herein lies the significance of AI tools that leverage the extraction of latent insights from voluminous empirical data, epitomizing the realm of data-driven AI tools. This innovation extends the purview of inference beyond the bounds of human-established priors and experiential wisdom. However, the scientific realm stands in contrast to the more prolific AI domains, as the availability and fidelity of data are not perpetually assured in the context of inverse problems. Consequently, a promising avenue emerges in the form of singular-instance AI tools, underpinned by the potency of formidable constructs such as deep neural networks (DNNs). Operating autonomously from expansive data repositories, these tools offer an alternative avenue to address inverse problems within the scientific continuum. Within this work, we delineate our recent endeavors directed at catalyzing break- throughs in the resolution of intricate scientific inverse problems. Central to our approach are pragmatic strategies that harmoniously blend the attributes of data-driven and singular-instance AI tools into coherent pipelines. These endeavors culminate in a iiinovel problem-solving landscape that bridges the domains of AI and science, encapsulating the essence of innovation and advancement.Item Information Extraction from Non-Line-of-Sight Objects Using Plenoptic Data from Scattered Light(2020-01) Sasaki, TakahiroWe investigate the utility of plenoptic data for extracting information from a scene where the light from unknown objects in the scene is viewable only after scattering from a diffuse surface. A primary goal of this research is to estimate the objects’ locations in the hidden scene, and to extract additional information, such as the object’s shape and brightness. In the first part, we derive a rigorous relationship between the object and the scattered light fields, which is cast in terms of a system of Fredholm integral equations of the first kind with the BRDF of the scattering surface, and the object information is reconstructed by solving these equations. Based on the Fourier transformation, we propose a simple BRDF model and analyze the reconstruction errors by introducing newly defined parameters reflecting the BRDF’s characteristic, the degree of specularity and the effective SNR. We then obtain optimal regularized solutions to the equations under a variety of conditions. Moreover, we provide a fundamental limit of retrievable information content from the scattered light. A comparison with experimental results is reported. In the second part, we investigate the use of plenoptic data for locating objects from a scattered light field by using the results obtained in the first part. The resolution limits of the transverse and longitudinal location estimates are derived from fundamental considerations on the scattering physics and measurement noise. Based on the refocusing algorithm developed in the computer vision field, we derive a simple alternative formulation of the projection slice theorem in a form directly connecting the light field and spatial frequency spectrum. Using this alternative formulation, we propose a spatial frequency filtering method that is defined on a newly introduced mixed space-frequency plane and achieves the theoretically-limited depth resolution. Moreover, we propose an improved refocusing algorithm to more accurately estimate the object’s brightness information. An experimental verification is provided.Item Robustness and Stability of Deep Learning(2021-06) Lai, Chieh-HsinThis dissertation serves as a collection of my three projects after I received the Ph.D. candidacy in 2018. The first two projects (in Chapter 2 and 3, respectively), joint works with Dongmian Zou and Gilad Lerman, are about novel algorithms for unsupervised and semi-supervised anomaly detection tasks, respectively. Our new methods allow datasets with a high ratio of corruption by outliers. The third project (in Chapter 4), a joint work with Kshitij Tayal, Raunak Manekar, Zhong Zhuang, Vipin Kumar and Ju Sun, brings out a methodology for improving the performance of end-to-end deep learning approaches for inverse problems with many-to-one forward mappings. General features of these three projects are introduced in the following. In Chapter 2, we propose a neural network for unsupervised anomaly detection with a novel robust subspace recovery layer (RSR layer). This layer seeks to extract the underlying subspace from a latent representation of the given data and removes outliers that lie away from this subspace. It is used within an autoencoder. The encoder maps the data into a latent space, from which the RSR layer extracts the subspace. The decoder then smoothly maps back the underlying subspace to a ``manifold" close to the original inliers. Inliers and outliers are distinguished according to the distances between the original and mapped positions (small for inliers and large for outliers). Extensive numerical experiments with both image and document datasets demonstrate state-of-the-art precision and recall. In Chapter 3, we propose a new method for novelty detection that can tolerate high corruption of the training points, whereas previous works assumed either no or very low corruption. Our method trains a robust variational autoencoder (VAE), which aims to generate a model for the uncorrupted training points. To gain robustness to high corruption, we incorporate the following four changes to the common VAE: 1. Extracting crucial features of the latent code by a carefully designed dimension reduction component for distributions; 2. Modeling the latent distribution as a mixture of Gaussian low-rank inliers and full-rank outliers, where the testing only uses the inlier model; 3. Applying the Wasserstein-1 metric for regularization, instead of the Kullback-Leibler (KL) divergence; and 4. Using a robust error for reconstruction. We establish both robustness to outliers and suitability to low-rank modeling of the Wasserstein metric as opposed to the KL divergence. We illustrate state-of-the-art results on standard benchmarks. In Chapter 4, we propose a methodology to resolve the irregular approximation of the inverse mapping in some inverse problems with many-to-one forward mappings; especially, we focus on 2D Fourier phase retrieval problem. In many physical systems, inputs related by intrinsic system symmetries generate the same output. So when inverting such systems, an input is mapped to multiple symmetry-related outputs. This causes fundamental difficulties for tackling these inverse problems by the emerging end-to-end deep learning approach. Taking phase retrieval as an illustrative example, we show that careful symmetry breaking on the training data can help get rid of the difficulties and significantly improve learning performance in real data experiments. We also extract and highlight the underlying mathematical principle of the proposed solution, which is directly applicable to other inverse problems.