Matching Items (2)
Description

When creating computer vision applications, it is important to have a clear image of what is represented such that further processing has the best representation of the underlying data. A common factor that impacts image quality is blur, caused either by an intrinsic property of the camera lens or by

When creating computer vision applications, it is important to have a clear image of what is represented such that further processing has the best representation of the underlying data. A common factor that impacts image quality is blur, caused either by an intrinsic property of the camera lens or by introducing motion while the camera’s shutter is capturing an image. Possible solutions for reducing the impact of blur include cameras with faster shutter speeds or higher resolutions; however, both of these solutions require utilizing more expensive equipment, which is infeasible for instances where images are already captured. This thesis discusses an iterative solution for deblurring an image using an alternating minimization technique through regularization and PSF reconstruction. The alternating minimizer is then used to deblur a sample image of a pumpkin field to demonstrate its capabilities.

ContributorsSmith, Zachary (Author) / Espanol, Malena (Thesis director) / Ozcan, Burcin (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2023-05
Description
This thesis focuses on solving separable nonlinear least squares (SNLLS) problems and explores how the so-called Variable Projection (VarPro) method can be used to solve this particular type of problem. First, there is a brief discussion on curve fitting methods and SNLLS models. Then, an overview of the VarPro algorithm

This thesis focuses on solving separable nonlinear least squares (SNLLS) problems and explores how the so-called Variable Projection (VarPro) method can be used to solve this particular type of problem. First, there is a brief discussion on curve fitting methods and SNLLS models. Then, an overview of the VarPro algorithm is discussed, along with the optimization concepts that facilitate the method's success. We examine how to derive the Jacobian for the nonlinear solvers and consider different ways to approximate it numerically. This leads into a section focusing on a variety of numerical experiments that illustrate the effectiveness of the VarPro method. The tests demonstrate how different initial guesses, noise levels, and Jacobian approximations affect the accuracy and efficiency of the computations. The thesis also briefly talks through some of the many applications of VarPro across a wide spectrum of topics, which include numerical analysis, biomedical imaging, spectroscopy, and chemistry.
ContributorsPawloski, Robert (Author) / Espanol, Malena (Thesis director) / Ozcan, Burcin (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Music, Dance and Theatre (Contributor)
Created2024-05