Multilayer residual sparsifying transform (MARS) model for low-dose CT image reconstruction

Purpose Signal models based on sparse representations have received considerable attention in recent years. On the other hand, deep models consisting of a cascade of functional layers, commonly known as deep neural networks, have been highly successful for the task of object classification and have been recently introduced to image reconstruction. In this work, we develop a new image reconstruction approach based on a novel multilayer model learned in an unsupervised manner by combining both sparse representations and deep models. The proposed framework extends the classical sparsifying transform model for images to a Multilayer residual sparsifying transform (MARS) model, wherein the transform domain data are jointly sparsified over layers. We investigate the application of MARS models learned from limited regular-dose images for low-dose CT reconstruction using penalized weighted least squares (PWLS) optimization. Methods We propose new formulations for multilayer transform learning and image reconstruction. We derive an efficient block coordinate descent algorithm to learn the transforms across layers, in an unsupervised manner from limited regular-dose images. The learned model is then incorporated into the low-dose image reconstruction phase. Results Low-dose CT experimental results with both the XCAT phantom and Mayo Clinic data show that the MARS model outperforms conventional methods such as filtered back-projection and PWLS methods based on the edge-preserving (EP) regularizer in terms of two numerical metrics (RMSE and SSIM) and noise suppression. Compared with the single-layer learned transform (ST) model, the MARS model performs better in maintaining some subtle details. Conclusions This work presents a novel data-driven regularization framework for CT image reconstruction that exploits learned multilayer or cascaded residual sparsifying transforms. The image model is learned in an unsupervised manner from limited images. Our experimental results demonstrate the promising performance of the proposed multilayer scheme over single-layer learned sparsifying transforms. Learned MARS models also offer better image quality than typical nonadaptive PWLS methods.