  There has been a growing interest in the use of data-driven regularizers to
solve inverse problems associated with computational imaging systems. The
convolutional sparse representation model has recently gained attention, driven
by the development of fast algorithms for solving the dictionary learning and
sparse coding problems for sufficiently large images and data sets.
Nevertheless, this model has seen very limited application to tomographic
reconstruction problems. In this paper, we present a model-based tomographic
reconstruction algorithm using a learnt convolutional dictionary as a
regularizer. The key contribution is the use of a data-dependent weighting
scheme for the l1 regularization to construct an effective denoising method
that is integrated into the inversion using the Plug-and-Play reconstruction
framework. Using simulated data sets we demonstrate that our approach can
improve performance over traditional regularizers based on a Markov random
field model and a patch-based sparse representation model for sparse and
limited-view tomographic data sets.
