Evolution from total variation to nonlinear sparsifying transform for sparse-view CT image reconstruction

Sparse-view CT has been widely studied as an effective strategy for reducing radiation dose to patients. However, the conventional image reconstruction algorithms, such as filtered back-projection method and classical algebraic reconstruction techniques, can no longer be competent in the image reconstruction task of sparse-view CT. A new principle, called compressed sensing (CS), has been therefore developed to provide an effective solution for the ill-posed inverse problem of sparse-view CT image reconstruction. Total variation (TV) minimization, which is most extensively studied among the existing CS techniques, has been recognized as a powerful tool for dealing with this difficult problem in image reconstruction community. However, in recent years, the drawbacks of TV are being increasingly reported, which are appearance of patchy artifacts, depict of incorrect object boundaries, and loss in image textures or smooth intensity changes. These degradations appear especially in reconstructing actual CT images with complicated intensity changes. In order to address these drawbacks, a series of advanced algorithms using nonlinear sparsifying transform (NLST) have been proposed very recently. The NLST-based CS is based on a different framework from the TV, and it achieves an improvement in image quality. Since it is a relatively newly proposed idea, within the scope of our knowledge, there exist few literatures that discusses comprehensively how the image quality improvement occurs in comparison with the conventional TV method. In this study, we investigated the image quality differences between the conventional TV minimization and the NLST-based CS, as well as image quality differences among different kinds of NLST-based CS algorithms in the sparse-view CT image reconstruction. More specifically, image reconstructions of actual CT images of different body parts were carried out to demonstrate the image quality differences.