Towards geometry-aware and learning-based solutions for inverse problems
Zehni, Mona
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Permalink
https://hdl.handle.net/2142/117659
Description
Title
Towards geometry-aware and learning-based solutions for inverse problems
Author(s)
Zehni, Mona
Issue Date
2022-11-28
Director of Research (if dissertation) or Advisor (if thesis)
Zhao, Zhizhen
Do, Minh N
Doctoral Committee Chair(s)
Zhao, Zhizhen
Committee Member(s)
Bresler, Yoram
Liang, Zhi-Pei
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Inverse problems
Geometry aware
Machine learning
Abstract
In this dissertation, we develop geometry-aware and learning-based solutions for various inverse problems. First, we study multi-segment reconstruction (MSR). We introduce MSR-SWD, a distribution matching approach that recovers a signal such that the distribution of its synthesized measurements matches that of the given observations, in a sliced Wasserstein distance sense. Our numerical results reveal the robustness of MSR-SWD against several benchmarks, especially when the segment lengths are short.
Second, we turn to the 2D unknown view tomography (2D UVT) problem. We introduce a geometric-invariant based solution for 2D UVT of point-source images. In addition, we propose an adversarial learning based method to recover a generic image and the viewing angle distribution by matching the empirical distribution of the tomographic observations with the generated data, using the notion of Gumbel-Softmax reparameterization. Our theoretical analysis and numerical experiments showcase the potential of our method to accurately recover the image and the viewing angle distribution.
Third, we direct our attention to 3D ab-initio reconstruction and refinement in cryo-electron microscopy (cryo-EM). We start by introducing an ab-initio moment-based approach for the 3D UVT task for 3D point-source models. We also introduce CryoSWD, a 3D cryo-EM ab-initio solution. CryoSWD, inspired by CryoGAN, recovers a 3D map such that the distribution of its synthesized measurements matches the observations, in a sliced Wasserstein sense. Next, we investigate the problem of 3D refinement in cryo-EM. We propose a new approach that refines the projection angles on the continuum, jointly with the 3D map. Finally, we describe DeepSharpen, our deep-learning based solution for cryo-EM map sharpening. Numerical results demonstrate the feasibility and performance of our solutions compared to several baselines.
Finally, we focus on 3D human pose estimation from video data. More specifically, we study a pose lifter architecture with kinematic pose representation. We show the advantages of the kinematic representation in semi-supervised settings with scarce labeled data and improved generalization on challenging camera view videos. We also discuss an application -- namely digital neurological examination (DNE). We demonstrate the effectiveness of DNE in capturing digital biomarkers from the extracted 2D/3D pose given recordings of subjects performing neurological examinations.
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