Convolutional sparse coding framework for compressive spectral imaging

Spectral images (SI) can be represented as 3D-arrays of spatial information across multiple wavelengths. Compressive Spectral Imaging (CSI) reduces sensing costs by sensing compressed versions of the scene, recovering a suitable version of the original SI solving a sparsity-inducing inverse problem. On the other hand, Convolutional Sparse Coding (CSC) has been successfully proved for representing gray-scale images, however it misses any correlation between images. This work considers the spatial-spectral correlation within SIs introducing an extension of the CSC signal model describing the SI as the sum of convolutions of 3D sparse coefficient maps with their respective 3D dictionary filters. Furthermore, we use the proposed CSC framework for recovering SIs from CSI measurements. The simulations results, using two different CSI acquisition architectures, show that the proposed CSC framework yields better representations of the SIs than those obtained under the traditional sparse signal representation approach, improving the quality of the recovered Sls. (C) 2019 Elsevier Inc. All rights reserved.