High Accuracy Compressive Chromo-Tomography Reconstruction via Convolutional Sparse Coding

Over the last decade various compressive snapshot hyperspectral imaging methods have been proposed. The limited reconstruction quality from severely compressed measurements, however, has been a practical barrier to real applications. This paper proposes a compressive chromo-tomography framework that incorporates the convolutional sparse coding (CSC) prior into the classical total variation and L₁ regularization functionals. Such a combination allows excellent high-frequency recovery capabilities of CSC, while effectively suppressing ghost artifacts in tomographic reconstructions. Since nondifferentiable regularizers are employed, we propose a preconditioned alternating direction method of multipliers (ADMM) for flexible and efficient solutions, both for the reconstruction task and for hyperspectral convolutional dictionary learning. We demonstrate in our numerical experiments that just 25 learned 3D CSC filters can fulfill a rather effective hyperspectral imagery representation and that the proposed method is capable of high accuracy reconstructions.