Salazar, Edgar Eduardo2022-10-182022-10-182022https://udspace.udel.edu/handle/19716/31495Inverse problems have become a topic of broad interest in science and engineering, given that only incomplete data might be available as a consequence of hardware limitations that can be intentionally or unintentionally created. Spectral image acquisition has been positively favored from inverse problems, such that conventional sensing methods present limitations linked to the time required to fully acquire a hyperspectral scene. By implementing an optical device that accounts for pseudo-random compressed sampling, also known as coded aperture, inverse problems algorithms may be run and a fully hyperspectral scene is reconstructed from a few 2-dimensional projections. ☐ The Coded Aperture Snapshot Spectral Imager (CASSI), represents the first attempt to experimentally validate the recovery of spectral information from incomplete data. Although results in terms of spatial and spectral quality are remarkable, CASSI possesses limitations which inherently affect the reconstructed datacubes. One of them is the fact that a spectrally dispersed image must arrive at the detector in order to estimate the spectral information. The Spatial Spectral Compressive Spectral Imager (SSCSI) was proposed as an alternative to overcome, from the hardware point of view, the many drawbacks of CASSI. Nevertheless, when first proposed, the resolution limits of the SSCSI were unknown, nor was a discrete sensing model well understood. This dissertation deeply analyses the physics and mathematics of the coding and information capturing process in SSCSI. A strong theoretical analysis of the continuous model is developed, and the proposed hypothesis is validated through a test-bed implementation. ☐ As it was done for CASSI and other compressive spectral imagers (CSI), the optimization of the implemented coding patterns was further explored, based on the developed sensing model. The Restricted Isometry Property, a sensing matrix metric widely utilized in Compressive Sampling, was adapted to the SSCSI framework. Results show that the optimal codes must exhibit a certain structure that can be explained using the blue-green noise patterns. This work then further explores coded aperture imagers in the X-rays regime, where we focus on Compton backscatter X-ray sensing, a commonly used technique to identify low atomic number and organic materials. Unlike traditional X-ray backscatter imaging devices, the proposed work avoids pencil-beam X-rays illumination. Instead, we adopt cone-beam coded illumination to capture the information parallel-wise. The proposed architecture, coined Compressive X-rays Compton Backscattering Imager, is analyzed in detail, and a discrete measurements model is proposed and tested in simulations using Geant4 Application for Tomographic Emission (GATE), under realistic conditions for several types of targets.Coded aperturesCompressive sensingCompton backscatteringHyperspectral imagingInverse problemsOptimizationThesis1348103509https://doi.org/10.58088/2crq-3r142022-08-10en