COMPRESSIVE SENSING WITH APPLICATIONS TO HYPERSPECTRAL IMAGE PROCESSING

Author/Creator ORCID

Date

2019-01-01

Department

Computer Science and Electrical Engineering

Program

Engineering, Electrical

Citation of Original Publication

Rights

Distribution Rights granted to UMBC by the author.
Access limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan thorugh a local library, pending author/copyright holder's permission.
This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.

Abstract

Compressive sensing (CS) is a recent method of sampling sparse, finite, discrete or continuous signals below the Shannon-Nyquist rate with minimal loss of information. To make this possible, CS requires the signals to be sparse in some unspecified basis and the acquiring sensor to sample globally and incoherently. Since hyperspectral images (HSI) consist of hundreds of contiguous spectral bands, a single HSI is several hundreds of megabytes in size which requires expensive sensors to acquire, a high bandwidth to transmit, and are costly to store and process. However, due to the high spectral correlations, HSI has a low information rate and are reduced in size considerably using data reduction algorithms. This implies the images can be sparsely represented in some unspecified basis making HSI ideal for CS. The goal of the work presented in this dissertations is to reduce the data size of HSI using simulated CS acquisition, or data directly obtained from a compressive sensor, and then process the data in the reduced sensed form. By extending the fundamental CS concepts of the Restricted Isometry Property (RIP) and Restricted Conformal Property (RCP) to two new properties, Restricted Entropy Property (REP) and Restricted Spectrum Property (RSP) it is shown that fundamental HSI discrimination metrics in the sensed data space can be maintained. In addition to REP and RSP, this dissertations also shows that three concepts, sample correlation/covariance matrix, orthogonal subspace projection (OSP) and subspace volume, commonly used to design HSI algorithms, are also preserved via CS. By taking advantage of these CS-derived concepts, two specific hyperspectral imaging application, hyperspectral target detection/anomaly detection and band selection can operate in the compressively sensed sample domain (CSSD) which is a significantly reduced data space. The derivations of the analytical forms and the experimental results of these two applications show that the accuracy of results obtained from using data in the CSSD suffers minimal loss when the compressive sensing sampling rates (CSSR) are adequate. In addition, a new approach to estimating the CSSR is developed in this dissertations.