Volume 35 (2017) Issue 1 Pages 63-73
In our previous paper (J Dong, H Kudo: Proposal of compressed sensing using nonlinear sparsifying transform for CT image reconstruction. Medical Imaging Technology. Vol. 34 pp235-244, 2016), we showed that nonlinear sparsifying transform provides a new framework of compressed sensing (CS) for sparse-view CT image reconstruction. Furthermore, it was experimentally demonstrated to have superiority in improving image quality compared to total variation (TV) minimization, which is the most standard approach in CS. The image quality improvement appears in removing patchy artifacts, preserving accurate object boundaries, and preserving image textures. The TV uses the gradient transform which considers only correlations between adjacent pixels, while the nonlinear sparsifying transform can consider evaluating intensity variations among a specified relatively large search window. This property can be considered to be the key reason for achieving image quality improvement by the nonlinear sparsifying transform. However, the iterative algorithm developed in our previous paper, which can be viewed as a special case of standard iterative-thresholding (IT) algorithm, suffers from a drawback that it converges very slowly leading to a long computation time. The main reason of slow convergence is that the IT algorithm belongs to a class of simultaneous iterative algorithms, in which all projection data are used simultaneously (in parallel) for each image update. However, as is well-known in past research activities of CT image reconstruction, it is expected that the convergence can be significantly accelerated by introducing a class of row-action or block-iterative algorithm. Based on this observation, in this paper, we propose an accelerated algorithm of the CS using nonlinear sparsifying transform. By using proximal splitting framework, we succeeded in performing image update with a row-action-type program. The row-action-type update showed an encouraging acceleration such that both the iteration number and the computation time were reduced significantly compared to our previous simultaneous iterative algorithm. We investigated the efficiency of proposed accelerated algorithm using a numerical phantom and a practical CT image.