Temporal Colored Coded Aperture Design in Compressive Spectral Video Sensing

Compressive spectral video sensing (CSVS) systems obtain spatial, spectral, and temporal information of a dynamic scene through the encoding of the incoming light rays by using a temporal-static coded aperture (CA). CSVS systems use CAs with binary entries spatially distributed at random. The random spatial encoding of the binary CAs entails a poor quality in the reconstructed images even though the CSVS sensing matrix is incoherent with the sparse representation basis. In addition, since some pixels are totally blocked, information such as object motion is missed over time. This paper substitutes the temporal-static binary coded apertures by a richer spatio-spectro-temporal encoding based on selectable color filters, named temporal colored coded apertures (T-CCA). The spatial, spectral, and time distributions of the T-CCAs are optimized by better satisfying the restricted isometry property (RIP) of the CSVS system. The RIP-optimized T-CCAs lead to spatio-spectral-time structures that tend to sense more uniformly the spatial, spectral, and temporal dimensions. An algorithm for optimally designing the T-CCAs is developed. In addition, a regularization term based on the scene motion is included in the inverse problem leading to a better quality of the reconstructed images. Computational experiments using four different spectral videos show an improvement of up to 6 dB in terms of peak signal-to-noise ratio of the reconstructed images by using the proposed inverse problem and the T-CCA patterns compared with the binary CAs and random and image-optimized CCA patterns.