Abstract

The signal reconstruction process from discrete samples is inherently band-limited due to the limited amount of spectral content in the discrete set of measurements. In the case of 1D sampling using ideal measurements, the maximum bandwidth of regular and irregular sampling is well known using Nyquist and GrÃ¶chenig sampling theorems and lemmas, respectively. However, determining the appropriate reconstruction bandwidth becomes difficult when considering 2D sampling geometries, samples with variable apertures, or signal to noise ratio limitations. Instead of determining the maximum bandwidth a priori, this thesis introduces the use of a bandlimited inverse to simultaneously reconstruct a signal and determine its effective bandwidth. Throughout this work, several existing inverse methods are modified to be bandlimited using spatial and frequency constraints. The benefit of spatial localization is demonstrated using the Backus Gilbert local inverse method. The benefit of frequency constraints are demonstrated using a frequency-constrained QR decomposition and other frequency-constrained iterative methods. A bandlimited conjugate gradient descent algorithm is derived to illustrate the practicality of bandlimited inverse constraints. Comparisons between these various bandlimited reconstruction methods further demonstrate that a bandlimited inverse is well-suited for variable aperture reconstruction.

Degree

PhD

College and Department

Ira A. Fulton College of Engineering; Electrical and Computer Engineering

Rights

https://lib.byu.edu/about/copyright/