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

Abstract

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.

Multi-layer Clustering-based Residual Sparsifying Transform for Low-dose CT Image Reconstruction

“…The formulation for training the MCST model is given as in (P0). Since (P0) is nonconvex, similar to the recent MARS work YLR21 , we apply the BCD algorithm to solve this problem, which takes an iterative updating strategy among different variables to be optimized. Algorithm 1 shows the full MCST learning pipeline.…”

“…The solving process for (11) is identical to the image update step in Ref. YLR21 For each outer iteration, we update the image T i times with parameter ρ decreasing as in (12). The formulae to compute ∇S 2 (x) and the Hessian matrix H S2 for image update are given in (13) and (14), respectively.…”

“…We investigate the PWLS-MCST algorithm with different numbers of layers (2, 3 layers) with each layer containing 5 clusters to classify input patches into various groups. We compare the proposed methods against several baseline methods including FBP FDK84 , PWLS with EP regularization CF15 , and the recent MARS YLR21 and ULTRA ZRLF18 regularizations in PWLS, respectively. The details of these methods are described as follows.…”

“…Several applications of sparsifying transform (ST) learning and various extensions have been demonstrated in the field of medical image reconstruction such as magnetic resonance image reconstruction and computed tomography (CT) image reconstruction ZRLF18,YLR21 . The conventional method for regular-dose CT image reconstruction is the analytical filtered back-projection (FBP) FDK84 .…”

“…The sparsifying transform learned in an unsupervised manner is incorporated into a prior term, which is equivalent to involving effective information extracted from the training slices into the process of image reconstruction. Moreover, using multiple sparsifying transforms increases the number of obtained features ZRLF18,YLR21 and further boosts the performance of reconstruction algorithms.…”