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.
Multiphase abdominal CT is an imaging protocol in which the patient is scanned at different phases before and after the injection of a contrast agent. Reconstructed images with different concentrations of contrast material provide useful information for effective detection of abnormalities. However, several scanning during a short period of time eventually increase the patient radiation dose to a remarkable value up to a risky level. Reducing the patient dose by modulating the x-ray tube current or acquiring the projection data through a small number of views are known to degrade the image quality and reduce the possibility to be useful for diagnosis purpose. In this work, we propose a novel multiphase abdominal CT imaging protocol with patient dose reduction and high image quality. The image reconstruction cost function consists of two terms, namely the data fidelity term and penalty term to enforce the anatomical similarity in successive contrast phase reconstruction. The prior information, named phase-induced swap prior (PISP) is computed using total variation minimization of image acquired from different contrast phases. The new method is evaluated through a simulation study using digital abdominal phantom and real data and results are promising.
This paper focuses on fan-beam image reconstruction from free-form X-ray source trajectory in computed tomography
(CT). As in major standard image reconstruction methods, the weighting function of the redundant projection data should
be carefully considered. The data redundancy reduction principle aims to compute the projection data only one time
during image reconstruction. Usually, an X-ray line that passes through the object point intersects with the radiation
source trajectory more than once time. For the symmetric closed circular trajectory, because each X-ray line passing
through an object point would intersect with the source trajectory twice, the weighting function of 0.5 is used to handle
this problem. However, normally there is no known symmetry property for the free-form X-ray source trajectory. In
order to estimate the weighting function we have to calculate the number N of intersection between each X-ray line and
every object points, then the weighting function is set to be 1/N such that the summation of weighting operator
corresponding to a single X-ray line is the unity. However, the calculation of N is difficult and computationally
expensive. In this paper we proposed a new scheme for a robust control of the redundant projection data for both closed
and open trajectories. Instead of calculation of N, we assign each intersection point a plus or minus sign according to the
proposed weighting function. As a result of summation of successive signs, they cancel out each other and finally equal
to the unity. Numerical study was performed to evaluate the proposed weighting scheme using standard Shepp-Logan
phantom with butterfly trajectory.
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