Convolutional Basis Pursuit Denoising of Spectral Images Using a Tri-Dimensional Sparse Representation

Spectral images (SI) can be represented as 3D arrays of spatial information across a multitude of wavelengths, plus some noise intrinsic to the capturing process. This must be removed to improve SI's processing and analysis. Basis pursuit allows to remove the noise by finding a noise-free sparse representation of the original image. State-of-the-art analysis basis, like the one proposed by Arce et. al., allow to sparsely represent SIs. In the other hand, synthesis dictionaries, like Wohlberg's CBPDN allow to represent independently each spectral band, missing the spectral correlation. This work proposes to sparsely represent an SI using a synthesis dictionary, composed by a collection of 3D convolutional filters, within a basis pursuit scheme for noise removal. The simulation results show that the proposed synthesis dictionaries can outperform the analysis basis at recovering spectral images at different levels of noise, using both full-frequencies and high-frequencies SIs.