X-ray phase CT has a potential to give the higher contrast in soft tissue observations. To shorten the measure- ment time, sparse-view CT data acquisition has been attracting the attention. This paper applies two major compressed sensing (CS) approaches to image reconstruction in the x-ray sparse-view phase tomography. The first CS approach is the standard Total Variation (TV) regularization. The major drawbacks of TV regularization are a patchy artifact and loss in smooth intensity changes due to the piecewise constant nature of image model. The second CS method is a relatively new approach of CS which uses a nonlinear smoothing filter to design the regularization term. The nonlinear filter based CS is expected to reduce the major artifact in the TV regular- ization. The both cost functions can be minimized by the very fast iterative reconstruction method. However, in the past research activities, it is not clearly demonstrated how much image quality diﬀerence occurs between the TV regularization and the nonlinear filter based CS in x-ray phase CT applications. We clarify the issue by applying the two CS applications to the case of x-ray phase tomography. We provide results with numerically simulated data, which demonstrates that the nonlinear filter based CS outperforms the TV regularization in terms of textures and smooth intensity changes.
Sparse-view CT image reconstruction is becoming a potential strategy for radiation dose reduction of CT scans.
Compressed sensing (CS) has been utilized to address this problem. Total Variation (TV) minimization, a method which
can reduce streak artifacts and preserve object boundaries well, is treated as the most standard approach of CS. However,
TV minimization cannot be solved by using classical differentiable optimization techniques such as the gradient method,
because the expression of TV (TV norm) is non-differentiable. In early stages, approximated solving methods were
proposed by changing TV norm to be differentiable in the way of adding a small constant in TV norm to enable the usage
of gradient methods. But this reduces the power of TV in preserving accuracy object boundaries. Subsequently,
approaches which can optimize TV norm exactly were proposed based on the convex optimization theory, such as
generalizations of the iterative soft-thresholding (GIST) algorithm and Chambolle-Pock algorithm. However, these
methods are simultaneous-iterative-type algorithms. It means that their convergence is rather slower compared with
row-action-type algorithms. The proposed method, called sparsity-constrained total variation (SCTV), is developed by
using the alternating direction method of multipliers (ADMM). On the method we succeeded in solving the main
optimization problem by iteratively splitting the problem into processes of row-action-type algebraic reconstruction
technique (ART) procedure and TV minimization procedure which can be processed using Chambolle’s projection
algorithm. Experimental results show that the convergence speed of the proposed method is much faster than the
conventional simultaneous iterative methods.
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.