Evaluation of classical and sparsity-based methods for parametric recovery problems

Date

2020

Author

Başkaya, Hasan Can

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

25
views

11
downloads

Cite This

Parametric reconstruction problems arise in many areas such as array processing, wireless communication, source separation, and spectroscopy. In a parametric recovery problem, the unknown model parameters in each superimposed signal are estimated from noisy observations. Classical methods perform the recovery over directly on the continuous-valued parameter space by solving a nonlinear inverse problem. Recently sparsity-based methods have also been applied to parametric recovery problems. These methods discretize the parameter space to form a dictionary whose atoms correspond to candidate parameter values, represent the data as a linear combination of small number of dictionary atoms, and then solve the resulting linear inverse problem. These sparsity-based methods can be classified into three categories, namely, on-grid, off-grid and gridless sparse methods. On-grid methods require that the true parameter values lie on a set of fixed grid points. Off-grid methods also use a grid, but the recovered parameter values are allowed to be out of the grid points. On the other hand, gridless methods do not require a grid and they work directly in the continuous-valued parameter space. In this thesis, we first review the classical and sparsity-based methods developed for parametric recovery problems with single or multiple measurement vectors. We then analyze and evaluate these methods in the direction-of- arrival and parameterized source separation problems.

Subject Keywords

Inverse problems (Differential equations), Keywords: parametric recovery, inverse problem, sparsity, block-sparsity, joint sparsity, single measurement vector, multiple measurement vector, direction-of-arrival, parameterized source separation.

URI

http://etd.lib.metu.edu.tr/upload/12625326/index.pdf
https://hdl.handle.net/11511/45278

Collections

Graduate School of Natural and Applied Sciences, Thesis