There has been a growing interest in using 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 an iteration dependent weighting scheme to construct an effective de- noising method that is integrated into the inversion using the Plug-and-Play reconstruction framework. Using simulated data sets we demonstrate how 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.