Calibration reinforcement regularizations for optimized snapshot spectral imaging

Abstract

Optical coding is a fundamental tool in snapshot computational spectral imaging for capturing encoded scenes that are then decoded by solving an inverse problem. Optical encoding design is crucial, as it determines the invertibility properties of the system sensing matrix. To ensure a realistic design, the optical mathematical forward model must match the physical sensing. However, stochastic variations related to non-ideal characteristics of the implementation exist; therefore, these variables are not known a priori and have to be calibrated in the laboratory setup. Thus, the optical encoding design leads to suboptimal performance in practice, even if an exhaustive calibration process is carried out. This work proposes an algorithm to speed up the reconstruction process in a snapshot computational spectral imaging, in which theoretically optimized coding design is distorted by the implementation process. Specifically, two regularizers are proposed that perform the gradient algorithm iterations of the distorted calibrated system in the direction of the originally, theoretically optimized system. We illustrate the benefits of the reinforcement regularizers for several state-of-the-art recovery algorithms. For a given lower bound performance, the algorithm converges in fewer iterations due to the effect of the regularizers. Simulation results show an improvement of up to 2.5 dB of peak signal-to-noise ratio (PSNR) when fixing the number of iterations. Furthermore, the required number of iterations reduces up to 50% when the proposed regularizers are included to obtain a desired performance quality. Finally, the effectiveness of the proposed reinforcement regularizations was evaluated in a test-bed implementation, where a better spectral reconstruction was evidenced when compared with a non-regularized system’s reconstruction.