  Signal models based on sparse representation have received considerable
attention in recent years. Compared to synthesis dictionary learning,
sparsifying transform learning involves highly efficient sparse coding and
operator update steps. In this work, we propose a Multi-layer Residual
Sparsifying Transform (MRST) learning model wherein the transform domain
residuals are jointly sparsified over layers. In particular, the transforms for
the deeper layers exploit the more intricate properties of the residual maps.
We investigate the application of the learned MRST model for low-dose CT
reconstruction using Penalized Weighted Least Squares (PWLS) optimization.
Experimental results on Mayo Clinic data show that the MRST model outperforms
conventional methods such as FBP and PWLS methods based on edge-preserving (EP)
regularizer and single-layer transform (ST) model, especially for maintaining
some subtle details.
