Limited-angle computed tomography (CT) has great impact in some clinical applications. Existing iterative reconstruction algorithms could not reconstruct high-quality images, leading to severe artifacts nearby edges. Optimal selection of initial image would influence the iterative reconstruction performance but has not been studied deeply yet. In this work, we proposed to generate optimized initial image followed by total variation (TV) based iterative reconstruction considering the feature of image symmetry. The simulated data and real data reconstruction results indicate that the proposed method effectively removes the artifacts nearby edges.

Computed tomography (CT) has been applied extensively in clinical diagnosis. Under some CT applications, limited-angle scan mode has deserved wide interest [

CT image reconstruction algorithms can be classified into analytical reconstructions and iterative reconstructions. Filtered back projection (FBP) reconstruction [

Utilizing the prior information plays a vital role in reconstructing high-quality images for limited-angle CT. However, the existing iterative methods do include priors inside the main iteration body, while initialization was overlooked [

In some specific applications, outer contours of some reconstructed objects are roughly axis-symmetrical, for example, head imaging and industry component imaging. The symmetry axis is often located in the central row (or column) of an image, if the scanned object is placed properly. Additionally, the structures surrounding object’s outer contour are also roughly axis-symmetrical. Based on the observation, we propose an iterative image reconstruction algorithm with optimized initial image for limited-angle CT. Using the property of object’s outer contour axis-symmetry, the local artifacts in image reconstructed by FBP can be removed. Then, the artifacts-removed image is regarded as initial image for iterative reconstruction (POCS-TV is applied in this paper). Results from different initial images (zero image, FBP image, and our optimized image) for POCS-TV are compared. The efficacy of the proposed method was assessed by simulations on the Shepp-Logan phantom and realistic head phantoms. We addressed limited-angle artifacts in POCS-TV, already evidenced in the cited paper [

The rest of the paper is organized as follows. In the next section, the contour symmetry and mirroring filling method is described, and the POCS-TV method is summarized. In the third section, experimental results are presented and discussed. Section

The imaging geometry for fan-beam limited-angle CT is illustrated as in Figure

Fan-beam limited-angle CT geometry configuration.

In such an imaging geometry, the image reconstructed by traditional methods (such as FBP) contains severe artifacts and most of them are located in the second and forth quadrants. The results can be seen in the experiments from Section

From many medical CT images, we have observed that some of objects’ outer contours are roughly axis-symmetrical and the symmetry axes are parallel with columns (or rows) of images, if the objects are suitably positioned. Additionally, the information surrounding object’s outer contour is also roughly axis-symmetrical. Although the reconstructed image under the scanning modality described in Figure

Illustration of calculating the symmetry axis and mirroring filling operation: (a) FBP image model with artifacts, (b) calculating the symmetry axis, and (c) mirror filling operation to remove artifacts.

The method of calculating the symmetry axis of outer contour in an image can be described as follows. First, the image of object is reconstructed by FBP in which the projection data with zero values is used to set the pixels out of the object to be zero. The above process facilitates the positioning of object’s contour. Then, we search for the pixels row by row until the contour is detected. The left contour point and right contour point are noted as

The method of canceling artifacts is described as follows. Suppose an image with

The symmetry is employed to produce an image with a smart reduction of artifacts. The image serves as initialization for iterative reconstruction. Classical POCS-TV method is applied to perform iterative reconstruction in this paper. Implementation of the POCS-TV algorithm [

Define initial image as

ART reconstruction is as follows:

Positivity constraint is as follows:

TV minimization using gradient steep algorithm is as follows:

Return to Step

To assess the effectiveness of our proposed method, Shepp-Logan phantom and real head phantom are used for limited-angle CT reconstruction. Both qualitative and quantitative studies on the results are conducted.

In this section, we conduct numerical studies to evaluate the performance of POCS-TV with different initial images (zero image, FBP image, and our optimized initialization). The size of Shepp-Logan phantom image is 256 × 256. The distance between X-ray source and rotating axis is 40 cm and the distance between detector and rotating axis is 40 cm. The detector is a line array consisting of 512 elements. The initial position of X-ray source is located in

Shepp-Logan phantom and initial images: (a) phantom, (b) reconstructed image using FBP method, (c) reconstructed image using both FBP method and air correction, and (d) reconstructed image using the proposed algorithm.

The images reconstructed by POCS-TV choosing zero image, FBP image (Figure

Reconstruction results by different initial images: (a) result from POCS-TV with initial zero image, (b) result from POCS-TV with initial FBP image, and (c) result from POCS-TV with proposed initial image.

In addition to visual inspection of the results, the mean square error (MSE) and signal to noise ratio (SNR) measures are used. The definitions of SNR and MSE are listed as follows:

Figure

MSE and SNR curves from different initial image: (a) MSE curves and (b) SNR curves.

Practically, the outer contour of an object is not accurately axis-symmetrical. To verify the effectiveness of our proposed method, we modify Shepp-Logan phantom to be asymmetrical. Two experiments in this case are studied.

The modified Shepp-Logan is shown in Figure

Modified Shepp-Logan phantom and initially reconstructed images: (a) modified phantom, (b) reconstructed image by FBP, and (c) reconstructed image using the proposed algorithm.

Reconstruction results by different initial images: (a) result from POCS-TV with initial zero image, (b) result from POCS-TV with initial FBP image, and (c) result from POCS-TV with proposed initial image.

Another modified Shepp-Logan is shown in Figure

Modified Shepp-Logan phantom and initially reconstructed images: (a) modified phantom, (b) reconstructed image by FBP, and (c) reconstructed image using the proposed algorithm.

Reconstruction results by different initial images: (a) result from POCS-TV with initial zero image, (b) result from POCS-TV with initial FBP image, and (c) result from POCS-TV with proposed initial image.

From the reconstructions for modified Shepp-Logan phantom, we can see that, although the scanned object is not strictly axis-symmetrical, our proposed algorithm is able to show more advantages for limited-angle CT.

To evaluate the performance of proposed algorithm for X-ray CT, reconstruction using real CT projection data is tested. Single circle scan and fan-beam imaging geometry are used to obtain the projections in our developed laboratory CT scanner. The distance between X-ray source and rotation axis is 106.61 cm and the distance between detector and rotation axis is 52.36 cm. The initial position of X-ray source is located in

Different initial images and iterative reconstruction results of real head phantom: (a) reference image, (b) initial image by FBP, (c) initial image by proposed algorithm, (d) result from POCS-TV with initial zero image, (e) result from POCS-TV with initial FBP image, and (f) result from POCS-TV with proposed initial image.

In this work, we propose an initialization procedure for limited-angle CT iterative image reconstruction when an object’s outer contour is roughly axis-symmetrical. The proposed method makes full use of the image symmetry to eliminate the deformation artifacts and supply POCS-TV with good initial image. For numerical experiments, compared with zero image and FBP image as initial images for POCS-TV, results by our method are better with 92% (0.0002 < 0.0024) gains in terms of MSE measure and with 46% (22.99 dB > 12.42 dB) gains in terms of SNR measure. The results of the real head phantom also validate the superiority of the proposed method.

The POCS-TV algorithm was implemented effectively using the widely utilized OSL iteration scheme. However, global convergence is an open issue as many existing OSL algorithms. POCS-TV is lack of strict global convergence proof. As presented in reconstructed images and the cost figures, poorly initialized POCS-TV gets locked into a local minimum (MSE) and a local maximum (SNR), and the outcome could not be improved apparently by further iterations. Meanwhile, well initialized POCS-TV performs effectively in practice although the global convergence cannot be guaranteed. In this paper, we studied the results based on visualization of reconstructed images, maximum of SNR, and minimum of MSE. Obviously, more theoretical insight of POCS-TV convergence issue is necessary in the future.

The position of artifacts varies due to the different arch explored by the focal spot. It is true that our proposed method would be useless if the sampled arch is centered on the object axis of symmetry. However, satisfactory images reconstructed by POCS-TV with poor initialization (zero image and FBP image) cannot be generated in this case. Thus, instead of letting the sampled arch centered on the object axis of symmetry, one can decide the side of the body to be explored and reconstruct initial image with less artifacts using the prior information of object symmetry.

3D FDK algorithm, as an extension to 2D FBP algorithm, has been widely used in CBCT reconstruction. In the limited-angle scanning case, the artifacts of 3D reconstruction using FDK are as almost the same as those of 2D FBP. Our proposed initialization can be promisingly applied to 3D reconstruction where FDK algorithm combined with object symmetry property is used and then POCS-TV in 3D case is performed.

In this work, for the modified Shepp-Logan phantom, we tested the case of a small asymmetry to show that our method can produce satisfactory results. On top of this, another test for real head phantom was done when the symmetry axis of object does not exactly match the scanner axis (namely, the

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