A random algorithm for designing the system matrix in compressive spectral imaging by homogenizing its structure

Compressive spectral imaging systems (CSI) use a focal plane array (FPA) to measure two-dimensional (2D) coded projections of a three-dimensional (3D) spatio-spectral scene. A reconstruction algorithm based on compressive sensing theory exploits the projections to retrieve the underlying 3D scene. Compressive sensing relies on two principles: sparsity and incoherence. Higher incoherence drives to better reconstructed images quality. The Colored Coded Aperture Spectral Imager (C-CASSI) is a CSI system where the coded projections are produced by optical elements named coded apertures. The C-CASSI system can be modeled as a linear transformation. The transformation matrix represents the physical effects of the coded aperture and the prism on the scene. The transformation matrix is also called the system representative matrix. The colored coded apertures modulate spatially and spectrally the light from the scene. The reconstruction image quality is highly dependent on the colored coded apertures design. An algorithm that randomly designs the coded apertures maintains the incoherence between the sensing matrix and the representation base. However, a coded aperture designed completely random, may cause the voxel information be sensed more than once, or not be sensed. This paper presents a random algorithm for colored coded apertures design by homogenizing defined parameters of the C-CASSI system representative matrix. Homogenization parameters guarantee that a voxel information would be sensed at least once. The homogenization is achieved leveling the selected parameters of the matrix, like the average of unblocking elements per column and the average of unblocking elements per row. Simulations show improvement up to 3.10 dB in the PSNR reconstructed images by using the colored coded apertures designs compared with traditional random coded apertures.