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Linear Inverse Problem in Signal Processing with Applications in Time Series Processing and Urban Sensing.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Linear Inverse Problem in Signal Processing with Applications in Time Series Processing and Urban Sensing./
Author:	Feng, Yining Nick.
Description:	1 online resource (155 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-05, Section: B.
Contained By:	Dissertations Abstracts International85-05B.
Subject:	Electrical engineering. -
Online resource:	click for full text (PQDT)
ISBN:	9798380847230

Linear Inverse Problem in Signal Processing with Applications in Time Series Processing and Urban Sensing.
Feng, Yining Nick.

Linear Inverse Problem in Signal Processing with Applications in Time Series Processing and Urban Sensing. - 1 online resource (155 pages)

Source: Dissertations Abstracts International, Volume: 85-05, Section: B.

Thesis (Ph.D.)--New York University Tandon School of Engineering, 2023.

Includes bibliographical references

Deducing the state or structure of a system from partial, noisy measurements, known as inverse problems, is a fundamental task throughout engineering and the sciences. In signal processing, linear inverse problems, ranging from denoising, deconvolution, to super-resolution, compressive sensing, are prevalent estimation problems in many applications in neuroscience, medical imaging, and remote sensing. Despite the constantly evolving focus of the field, there are two major recurring challenges: crafting representative and interpretable signal models and developing efficient and robust algorithms for estimation. In this dissertation, we present four approaches to address these two challenges.One popular way of signal modeling is via regularizer design when formulating a regularized optimization problem. Convex regularizers are often preferred because of their maximum a posteriori interpretation, global optimality guarantee, and established fast solvers. In the first work presented, we propose a convex variational norm for better modeling sparse piece-wise constant signals in fused lasso problems. The proposed latent fused lasso norm is based on (1) promoting sparsity in first-order difference with total variation norm and (2) exploiting latent group structure in first-order difference with simple linear constraints.Despite the good properties of convex regularizers, non-convex regularizers can help to achieve better estimation performance because the corresponding estimators are closer to the minimum mean square error estimators. The design of non-convex regularizers becomes an essential task. The generalized Moreau envelope is a framework that generates non-separable non-convex regularizers without destroying the overall problem convexity, by exploiting the relative strong convexity of the data fidelity term. The second and third works focus on applying the framework to the morphological component analysis problem for the suppression of transient artifacts in medical time series and the directional total least square problem for LiDAR point cloud denoising.The fourth work presents the theoretical analysis of a type of robust estimation algorithm, the adaptive iterative soft-thresholding algorithm (ISTA) with the thresholding strategy of estimating noise level by median absolute deviation. While the adaptive ISTA has been a successful practical algorithm, few theoretical results exist. In this work, we show properties of the fixed points of the algorithm including scale equivariance, non-uniqueness, and local stability, prove the local linear convergence guarantee, and show its global convergence behavior.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798380847230Subjects--Topical Terms:

596380
Electrical engineering.
Subjects--Index Terms:

Machine learningIndex Terms--Genre/Form:

554714
Electronic books.

Linear Inverse Problem in Signal Processing with Applications in Time Series Processing and Urban Sensing.
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520 $a Deducing the state or structure of a system from partial, noisy measurements, known as inverse problems, is a fundamental task throughout engineering and the sciences. In signal processing, linear inverse problems, ranging from denoising, deconvolution, to super-resolution, compressive sensing, are prevalent estimation problems in many applications in neuroscience, medical imaging, and remote sensing. Despite the constantly evolving focus of the field, there are two major recurring challenges: crafting representative and interpretable signal models and developing efficient and robust algorithms for estimation. In this dissertation, we present four approaches to address these two challenges.One popular way of signal modeling is via regularizer design when formulating a regularized optimization problem. Convex regularizers are often preferred because of their maximum a posteriori interpretation, global optimality guarantee, and established fast solvers. In the first work presented, we propose a convex variational norm for better modeling sparse piece-wise constant signals in fused lasso problems. The proposed latent fused lasso norm is based on (1) promoting sparsity in first-order difference with total variation norm and (2) exploiting latent group structure in first-order difference with simple linear constraints.Despite the good properties of convex regularizers, non-convex regularizers can help to achieve better estimation performance because the corresponding estimators are closer to the minimum mean square error estimators. The design of non-convex regularizers becomes an essential task. The generalized Moreau envelope is a framework that generates non-separable non-convex regularizers without destroying the overall problem convexity, by exploiting the relative strong convexity of the data fidelity term. The second and third works focus on applying the framework to the morphological component analysis problem for the suppression of transient artifacts in medical time series and the directional total least square problem for LiDAR point cloud denoising.The fourth work presents the theoretical analysis of a type of robust estimation algorithm, the adaptive iterative soft-thresholding algorithm (ISTA) with the thresholding strategy of estimating noise level by median absolute deviation. While the adaptive ISTA has been a successful practical algorithm, few theoretical results exist. In this work, we show properties of the fixed points of the algorithm including scale equivariance, non-uniqueness, and local stability, prove the local linear convergence guarantee, and show its global convergence behavior.
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