Recovering spectral images from compressive measurements using designed coded apertures and Matrix Completion Theory

Tatiana Gelvez, Hoover Rueda, Henry Arguello


Compressive spectral imaging (CSI) captures spectral information at various spatial locations of a spectral image with few compressed projections. Traditionally, the original scene is recovered by assuming sparsity in some known representation basis. In contrast, the matrix completion techniques (MC) rely on a low-rank structure that avoids using any known representation basis. The coded aperture snapshot spectral imager (CASSI) is a CSI optical architecture that modulates light by using a coded aperture with a pattern that determines the quality of reconstruction. The objective of this paper is to design optimal coded aperture patterns when MC is used to recover a spectral scene from CASSI measurements. The patterns are attained by maximizing the distance between the translucent elements, which become more precise measurements given the MC constraints. Simulations from different databases show an average improvement of 1 to 9 dBs when the designed patterns are used compared to the conventional random and complementary patterns. The proposed approach solves an integer optimization problem with a complexity that is commonly NP-hard but can be reduced with proper relaxation. Finally, an effective alternative method using coded aperture patterns for MC to solve the inverse compressive spectral imaging problem is presented.


Matrix Completion, Spectral Imaging, Optimization problems, Compressive Sensing, Coded apertures.

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