Optical coding in compressive spectral imaging systems and the multi-resolution reconstruction problem

Abstract

Traditional spectral imaging approaches require scanning the scene to construct a 3-dimensional data cube. These methods experience low sensing speed and the resulting amount of data makes its management very challenging. In contrast, compressive spectral imaging (CSI) systems capture the spatial and spectral information of the scene at once, in a 2-dimensional set of coded projections. Compressed sensing (CS) reconstruction algorithms are then used to reconstruct the underlying spectral 3D data cube from an underdetermined system of linear equations. In general, CSI projections consist on integrating encoded and dispersed versions of the input source. Thus, different optical configurations yield different sampling strategies and reconstruction performance. More specifically, image reconstruction quality depends on the employed coding of the input scene. ☐ This dissertation aims at exploring different optical coding strategies in CSI systems. A first strategy considers CSI architectures with coded apertures as the coding element. The structure of the coded apertures is crucial inasmuch as they determine the entries of the sensing matrix. Given that conventional coded aperture patterns are selected at random, leading to suboptimal reconstruction solutions, the proposed strategy exploits the restricted isometry property of the sensing matrix and its incoherence with respect to the sparse representation basis to optimize the coded aperture ensemble. ☐ On the other hand, a different coding strategy is introduced motivated by the complicated optical paths of state-of-the-art CSI systems that compromise their portability. In this case, we propose a new compact CSI architecture that exploits the benefits of colored mosaic FPA detectors and the compression capabilities of CSI sensing techniques. The optical and the mathematical models of the explored encoding strategies are presented along with testbed implementations of the systems. Simulations and experimental data evaluate the accuracy of the proposed strategies. ☐ In addition to the optical coding strategies, this dissertation studies the multiresolution (MR) reconstruction problem in compressive spectral imaging. To date, the common CSI reconstruction framework has focused on obtaining an approximation of the underlying spatial and spectral information of a scene from a set of coded projections, where the resolution of the reconstruction is as high as the measurements allow. Even though CSI enables fast multiplexed sensing, the complexity of the inverse problem depends on the spatial and spectral resolution of the data to be recovered. Motivated by such cases where a fast preview reconstruction is often desirable, we propose a multi-resolution reconstruction scheme for CSI that enables the sequential recovery of multiple versions of the same data cube at different spatial resolutions. Simulations are developed to analyze the performance of the proposed MR reconstruction model.