SIAM Undergraduate Research Online
Volume 16
In This Volume
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Learning the Truncation Index of the Kronecker Product SVD for Image Restoration
Published electronically December 27, 2023DOI: 10.1137/23S1576281
Authors
Salina Bermudez (Corresponding author – Arizona State University)
Project Advisors
Rosemary Renaut (Arizona State University)
Abstract
The image processing task of the recovery of an image from a noisy or compromised image is an ill-posed inverse problem. To solve this problem, it is necessary to incorporate prior information about the smoothness, or the structure, of the solution, by incorporating regularization. Here, we consider linear blur operators with an efficiently-found singular value decomposition. Then, regularization is obtained by employing a truncated singular value expansion for image recovery. In this study, we focus on images for which the image blur operator is separable and can be represented by a Kronecker product such that the associated singular value decomposition is expressible in terms of the singular value decompositions of the separable components. The truncation index k can then be identified without forming the full Kronecker product of the two terms. This report investigates the problem of learning an optimal k using two methods. For one method to learn k we assume the knowledge of the true images, yielding a supervised learning algorithm based on the average relative error. The second method uses the method of generalized cross validation and does not require knowledge of the true images. The approach is implemented and demonstrated to be successful for Gaussian, Poisson and salt and pepper noise types across noise levels with signal to noise ratios as low as 10. This research contributes to the field by offering insights into the use of the supervised and unsupervised estimators for the truncation index, and demonstrates that the unsupervised algorithm is not only robust and computationally efficient, but is also comparable to the supervised method.
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Particle Deposition Driven by Evaporation in Membrane Pores and Droplets
Published electronically December 8, 2023 -
Malaria Early Warning Application for Individual Risk Assessment
Published electronically November 7, 2023 -
Understanding a Measure for Synchrony: Spike Time Tiling Coefficient Method
Published electronically October 31, 2023 -
In Pursuit of Higher Power Through Integrated Multivariate Regression
Published electronically October 19, 2023 -
Maximizing Harvest Yields in a Three-Species System
Published electronically October 6, 2023 -
Long-time L2 Stability for an IMEX Discretization of the 1D Fujita Equation
Published electronically September 13, 2023 -
Implementation of the Boneh-Franklin IBE Scheme
Published electronically September 1, 2023 -
Comparison of Vector Voting Rules and Their Relation to Simple Majority Voting
Published electronically August 23, 2023 -
Ride Like the Wind Without Getting Winded: The Growth of E-Bike Use
Published electronically August 15, 2023 -
Iterative Methods at Lower Precision
Published electronically August 1, 2023 -
A Comparative Study of Penalized Regression and Machine Learning Algorithms in High Dimensional Scenarios
Published electronically July 17, 2023 -
Linear Stability Analysis of Solitons Governed by the 2D Complex Cubic-Quintic Ginzburg-Landau Equation
Published electronically July 7, 2023 -
Adapting Zeroth Order Algorithms for Comparison-Based Optimization
Published electronically June 26, 2023 -
Modelling the Evolutionary Dynamics of an Infectious Disease with an Initial Asymptomatic Infection Stage with Recovery
Published electronically June 16, 2023 -
Predicting Molecular Phenotypes with Single Cell RNA Sequencing Data: An Assessment of Unsupervised Machine Learning Models
Published electronically May 26, 2023 -
Opinion Dynamics with Slowly Evolving Zealot Populations
Published electronically May 4, 2023 -
A Quasi-Optimal Spectral Solver for the Heat and Poisson Equations in a Closed Cylinder
Published electronically April 26, 2023 -
Quantifying Uncertainty in Ensemble Deep Learning
Published electronically April 17, 2023 -
Multi-scale Hybridized Topic Modeling: A Pipeline for Analyzing Unstructured Text Datasets via Topic Modeling
Published electronically March 27, 2023 -
Numerical Analysis of Crowding Effects in Competing Species
Published electronically March 10, 2023 -
Food Deserts and k-Means Clustering
Published electronically March 9, 2023 -
Symmetry and Free Boundary Points in a Class of Linear Ordinary Differential Equations
Published electronically January 10, 2023
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