Rapid developments in photon-counting and energy-discriminating detectors
have the potential to provide an additional spectral dimension to conventional
x-ray grayscale imaging. Reconstructed spectroscopic tomographic data can
be used to distinguish individual materials by characteristic absorption peaks.
The acquired energy-binned data, however, suffer from low signal-to-noise
ratio, acquisition artifacts, and frequently angular undersampled conditions.
New regularized iterative reconstruction methods have the potential to produce
higher quality images and since energy channels are mutually correlated it
can be advantageous to exploit this additional knowledge. In this paper, we
propose a novel method which jointly reconstructs all energy channels while
imposing a strong structural correlation. The core of the proposed algorithm
is to employ a variational framework of parallel level sets to encourage joint
smoothing directions. In particular, the method selects reference channels from which to propagate structure in an adaptive and stochastic way while
preferring channels with a high data signal-to-noise ratio. The method
is compared with current state-of-the-art multi-channel reconstruction
techniques including channel-wise total variation and correlative total nuclear
variation regularization. Realistic simulation experiments demonstrate the
performance improvements achievable by using correlative regularization
methods.