D$^\text{2}$UF: Deep Coded Aperture Design and Unrolling Algorithm for Compressive Spectral Image Fusion

Compressive spectral imaging (CSI) has attracted significant attention since it employs synthetic apertures to codify spatial and spectral information, sensing only 2D projections of the 3D spectral image. However, these optical architectures suffer from a trade-off between the spatial and spectral resolution of the reconstructed image due to technology limitations. To overcome this issue, compressive spectral image fusion (CSIF) employs the projected measurements of two CSI architectures with different resolutions to estimate a high-spatial high-spectral resolution. This work presents the fusion of the compressive measurements of a low-spatial high-spectral resolution coded aperture snapshot spectral imager (CASSI) architecture and a high-spatial low-spectral resolution multispectral color filter array (MCFA) system. Unlike previous CSIF works, this paper proposes joint optimization of the sensing architectures and a reconstruction network in an end-to-end (E2E) manner. The trainable optical parameters are the coded aperture (CA) in the CASSI and the colored coded aperture in the MCFA system, employing a sigmoid activation function and regularization function to encourage binary values on the trainable variables for an implementation purpose. Additionally, an unrolling-based network inspired by the alternating direction method of multipliers (ADMM) optimization is formulated to address the reconstruction step and the acquisition systems design jointly. Finally, a spatial-spectral inspired loss function is employed at the end of each unrolling layer to increase the convergence of the unrolling network. The proposed method outperforms previous CSIF methods, and experimental results validate the method with real measurements.