^{1}

Radiation dose reduction without losing CT image quality has been an increasing concern. Reducing the number of X-ray projections to reconstruct CT images, which is also called sparse-projection reconstruction, can potentially avoid excessive dose delivered to patients in CT examination. To overcome the disadvantages of total variation (TV) minimization method, in this work we introduce a novel adaptive TpV regularization into sparse-projection image reconstruction and use FISTA technique to accelerate iterative convergence. The numerical experiments demonstrate that the proposed method suppresses noise and artifacts more efficiently, and preserves structure information better than other existing reconstruction methods.

X-ray computed tomography (CT), as an important medical imaging protocol, has been widely used in clinical applications. However, the involved X-ray radiation dose delivered to patients may potentially increase the probability of causing cancer [

Radiation dose in CT examination can be reduced by decreasing the number of projections. However, conventional filtered back-projection (FBP) reconstruction algorithm suffers from systematic geometric distortion and streak artifacts when the measured projection data is not sufficient [

In this study, to deal with the trade-off between smoothing nonedge part and preserving edge part of the image, we propose a CT reconstruction algorithm using adaptive TpV regularization wherein each pixel in reconstructed image corresponds to one

CT reconstruction problem can be converted to a constrained optimization problem

To solve

The ART-TV method is implemented by performing ART algorithm as the first step and TV minimization using gradient descent method as the second step. One can see [

For traditional TpV algorithm, the quantity

When

To overcome this limitation, in this work we propose an adaptive TpV (ATpV) regularization defined by

In summary, the benefit of the proposed ATpV is that the parameter

According to aforementioned methods, in this paper we propose CT image iterative reconstruction using ATpV regularization. The reconstruction is implemented by solving the following constrained minimization problem:

The algorithm implementation can follow ART-TV in [

Besides, we apply fast iterative shrinkage/thresholding algorithm (FISTA) [

In summary, the main steps of ART-ATpV-FISTA are as follows.

Initialization:

ART reconstruction:

Positivity constraint:

ATpV minimization:

calculate

minimize

FISTA acceleration:

Return to (B) until the stopping criterion is satisfied.

In our experimental implementation, the initial to-be-reconstructed image was set to be uniform with pixel values of 0. The relaxation parameter ^{−5}.

In this section, we study the ART, ART-TV, ART-TpV (^{2}. The detector whose length is 61.44 cm is modeled as a straight-line array of 512 detector bins. All the tests are performed by MATLAB on a PC with Intel (R) Core (TM) 2 Quad CPU 2.50 GHz and 3.25 GB RAM.

Shepp-Logan phantom.

Fan beam CT geometry configuration.

The generation of projection data is using Siddon’s ray-driven algorithm [

The reconstruction results are shown in Figure

The images reconstructed by different reconstruction algorithms from the noise-free and noisy data. ((a)–(e)) Reconstructed images from noise-free data: (a) image reconstructed by ART, (b) image reconstructed by ART-TV, (c) image reconstructed by ART-TpV, (d) image reconstructed by ART-ATpV, and (e) image reconstructed by ART-ATpV-FISTA; ((f)–(j)) reconstructed images from noisy data: (f) image reconstructed by ART, (g) image reconstructed by ART-TV, (h) image reconstructed by ART-TpV, (i) image reconstructed by ART-ATpV, and (j) image reconstructed by ART-ATpV-FISTA.

Figure

The comparison between reconstructed images using three different reconstruction algorithms and original Shepp-Logan phantom. (a) The horizontal profiles in reconstructed images using ART-TV, ART-TpV, and ART-ATpV methods from noise-free data and original Shepp-Logan phantom and (b) the horizontal profiles in reconstructed images using ART-TV, ART-TpV, and ART-ATpV methods from noisy data and original Shepp-Logan image.

To assess the accuracy of the reconstructed image, the mean absolute error (MAE) is used and defined by

As shown in Figure

The MAE curves of reconstructed images with different reconstruction algorithms at 20 projection angles and different iteration numbers, and the iteration numbers range from 1 to 200. (a) The MAE curves of reconstructed images from noise-free projection data and (b) the curves of reconstructed images from noisy projection data.

To challenge our ART-ATpV/ART-ATpV-FISTA method further, we use a complicated low-contrast FORBILD phantom to reconstruct image and compare it to other methods. The corresponding images are in Figure

The images reconstructed by different reconstruction algorithms from noisy data: (a) image reconstructed by ART, (b) image reconstructed by ART-TV, (c) image reconstructed by ART-TpV, (d) image reconstructed by ART-ATpV, and (e) image reconstructed by ART-ATpV-FISTA.

In this section, we use a real CT image (head phantom) obtained from a commercial medical CT scanner to test the effectiveness of our ART-ATpV and ART-ATpV-FISTA algorithms and compare them with other algorithms. 40 projections are simulated in this case, with the aforementioned geometrical parameters unchanged. For all iterative methods except ART-ATpV-FISTA, the number of iterations is 50. For ART-ATpV-FISTA, the number of iterations is 20.

As shown in Figure

The reconstructed images by different algorithms from real head phantom projection data. (a) The original image, (b) the reconstructed image using ART, (c) the reconstructed image using ART-TV, (d) the reconstructed image using ART-TpV, (e) the reconstructed image using ART-ATpV, and (f) the reconstructed image using ART-ATpV-FISTA.

In this paper, we present ART-ATpV-FISTA method for X-ray CT reconstruction from few-view or sparse projections. The main contribution of this work is to minimize adaptive TpV norm of reconstructed image instead of traditional TpV norm and TV norm. FISTA technique is employed to speed up iterative convergence rate.

The advantage of adaptive TpV is that if a pixel’s gradient magnitude is large, this pixel is on the edge and corresponds to a small

The performance of the propose method is compared to ART, ART-TV, and ART-TpV methods on Shepp-Logan phantom, low-contrast FORBILD phantom, and a real head phantom. Both qualitative and quantitative comparisons are performed to show the proposed method provides more superior results than other existing methods. Since the main goal of this work is to demonstrate the effectiveness of the proposed ATpV-based regularization, the parameters were empirically set through extensive experiments by visual inspection and quantitative measures in this study.

Although the presented ART-ATpV-FISTA algorithm in this paper is used in fan beam CT geometry, it is also easily extended to cone beam CT (CBCT) geometry due to its iterative-correction property. Furthermore, the ART-ATpV-FISTA algorithm may also be useful for other tomographic imaging modalities. In the further research, we will apply the developed algorithm in CBCT system and study the few-view CBCT reconstruction, which will reduce radiation dose as much as possible.

Similar to FBP, serious streaking artifacts in the reconstructed CT images using FDK type algorithms [

In conclusion, the proposed algorithm using adaptive TpV regularization in this work can reconstruct high-quality images from few-view projections and will have great potential clinical applications.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by Guangdong strategic emerging industry core technology research (Grant no. 2011A081402003) and Guangzhou municipal special major science and technology programs (Grant no. 2011Y1-00019).

_{1/2}regularization