Abstract
Compressed sensing (CS) is attracting growing concerns in sparse-view computed tomography (CT) image
reconstruction. The most standard approach of CS is total variation (TV) minimization. However, images reconstructed
by TV usually suffer from distortions, especially in reconstruction of practical CT images, in forms of patchy artifacts,
improper serrate edges and loss of image textures. Most existing CS approaches including TV achieve image quality
improvement by applying linear transforms to object image, but linear transforms usually fail to take discontinuities into
account, such as edges and image textures, which is considered to be the key reason for image distortions. Actually,
discussions on nonlinear filter based image processing has a long history, leading us to clarify that the nonlinear filters
yield better results compared to linear filters in image processing task such as denoising. Median root prior was first
utilized by Alenius as nonlinear transform in CT image reconstruction, with significant gains obtained. Subsequently,
Zhang developed the application of nonlocal means-based CS. A fact is gradually becoming clear that the nonlinear
transform based CS has superiority in improving image quality compared with the linear transform based CS. However,
it has not been clearly concluded in any previous paper within the scope of our knowledge. In this work, we investigated
the image quality differences between the conventional TV minimization and nonlinear sparsifying transform based CS,
as well as image quality differences among different nonlinear sparisying transform based CSs in sparse-view CT image
reconstruction. Additionally, we accelerated the implementation of nonlinear sparsifying transform based CS algorithm.
