Variable Projection Method for Semi-Blind Deconvolution with Mixed Gaussian Kernels
Description
The variable projection method has been developed as a powerful tool for solvingseparable nonlinear least squares problems. It has proven effective in cases where
the underlying model consists of a linear combination of nonlinear functions, such as
exponential functions. In this thesis, a modified version of the variable projection
method to address a challenging semi-blind deconvolution problem involving mixed
Gaussian kernels is employed. The aim is to recover the original signal accurately
while estimating the mixed Gaussian kernel utilized during the convolution process.
The numerical results obtained through the implementation of the proposed algo-
rithm are presented. These results highlight the method’s ability to approximate the
true signal successfully. However, accurately estimating the mixed Gaussian kernel
remains a challenging task. The implementation details, specifically focusing on con-
structing a simplified Jacobian for the Gauss-Newton method, are explored. This
contribution enhances the understanding and practicality of the approach.
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2023
Agent
- Author (aut): Dworaczyk, Jordan Taylor
- Thesis advisor (ths): Espanol, Malena
- Committee member: Welfert, Bruno
- Committee member: Platte, Rodrigo
- Publisher (pbl): Arizona State University