An interactive method based on multi-objective optimization for limited-angle CT reconstruction

Objective. Limited-angle x-ray computed tomography (CT) is a typical ill-posed inverse problem, leading to artifacts in the reconstructed image due to the incomplete projection data. Most iteration CT reconstruction methods involve optimization for a single object. This paper explores a multi-objective optimization model and an interactive method based on multi-objective optimization to suppress the artifacts of limited-angle CT.Approach. The model includes two objective functions on the dual domain within the data consistency constraint. In the interactive method, the structural similarity index measure (SSIM) is regarded as the value function of the decision maker (DM) firstly. Secondly, the DM arranges the objective functions of the multi-objective optimization model to be optimized according to their absolute importance. Finally, the SSIM and the simulated annealing (SA) method help the DM choose the desirable reconstruction image by improving the SSIM value during the iteration process.Main results. Simulation and real data experiments demonstrate that the artifacts can be suppressed by the proposed method, and the results were superior to those reconstructed by the other three reconstruction methods in preserving the edge structure of the image.Significance. The proposed interactive method based on multi-objective optimization shows some potential advantages over classical single object optimization methods.

Multiobjective optimization guided by image quality index for limited-angle CT image reconstruction

BACKGROUND

Due to the incomplete projection data collected by limited-angle computed tomography (CT), severe artifacts are present in the reconstructed image. Classical regularization methods such as total variation (TV) minimization, ℓ0 minimization, are unable to suppress artifacts at the edges perfectly. Most existing regularization methods are single-objective optimization approaches, stemming from scalarization methods for multiobjective optimization problems (MOP).

OBJECTIVE

To further suppress the artifacts and effectively preserve the edge structures of the reconstructed image.

METHOD

This study presents a multiobjective optimization model incorporates both data fidelity term and ℓ0-norm of the image gradient as objective functions. It employs an iterative approach different from traditional scalarization methods, using the maximization of structural similarity (SSIM) values to guide optimization rather than minimizing the objective function.The iterative method involves two steps, firstly, simultaneous algebraic reconstruction technique (SART) optimizes the data fidelity term using SSIM and the Simulated Annealing (SA) algorithm for guidance. The degradation solution is accepted in the form of probability, and guided image filtering (GIF) is introduced to further preserve the image edge when the degradation solution is rejected. Secondly, the result from the first step is integrated into the second objective function as a constraint, we use ℓ0 minimization to optimize ℓ0-norm of the image gradient, and the SSIM, SA algorithm and GIF are introduced to guide optimization process by improving SSIM value like the first step.

RESULTS

With visual inspection, the peak signal-to-noise ratio (PSNR), root mean square error (RMSE), and SSIM values indicate that our approach outperforms other traditional methods.

CONCLUSIONS

The experiments demonstrate the effectiveness of our method and its superiority over other classical methods in artifact suppression and edge detail restoration.

Definition of the Region of Interest for the Assessment of Alveolar Bone Repair Using Micro-computed Tomography

The objective of this study was to evaluate the influence of the extraction socket (distal or lingual root) and the type of region of interest (ROI) definition (manual or predefined) on the assessment of alveolar repair following tooth extraction using micro-computed tomography (micro-CT). The software package used for scanning, reconstruction, reorientation, and analysis of images (NRecon®, DataViewer®, CT-Analyzer®) was acquired through Bruker <  https://www.bruker.com  > . The sample comprised the micro-CT volumes of seven Wistar rat mandibles, in which the right first molar was extracted. The reconstructed images were analyzed using the extraction sockets, i.e., the distal and intermediate lingual root and the method of ROI definition: manual (MA), central round (CR), and peripheral round (PR). The bone volume fraction (BV/TV) values obtained were analyzed by two-way ANOVA with Tukey's post hoc test (α = 5%). The distal extraction socket resulted in significantly lower BV/TV values than the intermediate lingual socket for MA (P = 0.001), CR (P < 0.001), and PR (P < 0.001). Regarding the ROI, when evaluating the distal extraction socket, the BV/TV was significantly higher (P < 0.001) for MA than for CR and PR, with a lower BV/TV for CR. However, no significant difference was observed for MA (P = 0.855), CR (P = 0.769), or PR (P = 0.453) in the intermediate lingual extraction socket. The bone neoformation outcome (BV/TV) for alveolar bone repair after tooth extraction is significantly influenced by the ROI and the extraction socket. Using the predefined method with a standardized ROI in the central region of the distal extraction socket resulted in the assessment of bone volume, demonstrating the most critical region of the bone neoformation process.

Exterior computed tomography image reconstruction based on anisotropic relative total variation in polar coordinates

In computed tomography (CT) image reconstruction problems, exterior CT is an important application in industrial non-destructive testing (NDT). Different from the limited-angle problem that misses part of the rotation angle, the rotation angle of the exterior problem is complete, but for each rotation angle, the projection data through the central region of the object cannot be collected, so that the exterior CT problem is ill-posed inverse problem. The results of traditional reconstruction methods like filtered back-projection (FBP) and simultaneous algebra reconstruction technique (SART) have artifacts along the radial direction edges for exterior CT reconstruction. In this study, we propose and test an anisotropic relative total variation in polar coordinates (P-ARTV) model for addressing the exterior CT problem. Since relative total variation (RTV) can effectively distinguish edges from noises, and P-ARTV with different weights in radial and tangential directions can effectively enhance radial edges, a two-step iteration algorithm was developed to solve the P-ARTV model in this study. The fidelity term and the regularization term are solved in Cartesian and polar coordinate systems, respectively. Numerical experiments show that our new model yields better performance than the existing state-of-the-art algorithms.

A neural network with encoded visible edge prior for limited-angle computed tomography reconstruction

PURPOSE

Limited-angle computed tomography is a challenging but important task in certain medical and industrial applications for nondestructive testing. The limited-angle reconstruction problem is highly ill-posed and conventional reconstruction algorithms would introduce heavy artifacts. Various models and methods have been proposed to improve the quality of reconstructions by introducing different priors regarding to the projection data or ideal images. However, the assumed priors might not be practically applicable to all limited-angle reconstruction problems. Convolutional neural network (CNN) exhibits great promise in the modeling of data coupling and has recently become an important technique in medical imaging applications. Although existing CNN methods have demonstrated promising results, their robustness is still a concern. In this paper, in light of the theory of visible and invisible boundaries, we propose an alternating edge-preserving diffusion and smoothing neural network (AEDSNN) for limited-angle reconstruction that builds the visible boundaries as priors into its structure. The proposed method generalizes the alternating edge-preserving diffusion and smoothing (AEDS) method for limited-angle reconstruction developed in the literature by replacing its regularization terms by CNNs, by which the piecewise constant assumption assumed by AEDS is effectively relaxed.

METHODS

The AEDSNN is derived by unrolling the AEDS algorithm. AEDSNN consists of several blocks, and each block corresponds to one iteration of the AEDS algorithm. In each iteration of the AEDS algorithm, three subproblems are sequentially solved. So, each block of AEDSNN possesses three main layers: data matching layer, x -direction regularization layer for visible edges diffusion, and y -direction regularization layer for artifacts suppressing. The data matching layer is implemented by conventional ordered-subset simultaneous algebraic reconstruction technique (OS-SART) reconstruction algorithm, while the two regularization layers are modeled by CNNs for more intelligent and better encoding of priors regarding to the reconstructed images. To further strength the visible edge prior, the attention mechanism and the pooling layers are incorporated into AEDSNN to facilitate the procedure of edge-preserving diffusion from visible edges.

RESULTS

We have evaluated the performance of AEDSNN by comparing it with popular algorithms for limited-angle reconstruction. Experiments on the medical dataset show that the proposed AEDSNN effectively breaks through the piecewise constant assumption usually assumed by conventional reconstruction algorithms, and works much better for piecewise smooth images with nonsharp edges. Experiments on the printed circuit board (PCB) dataset show that AEDSNN can better encode and utilize the visible edge prior, and its reconstructions are consistently better compared to the competing algorithms.

CONCLUSIONS

A deep-learning approach for limited-angle reconstruction is proposed in this paper, which significantly outperforms existing methods. The superiority of AEDSNN consists of three aspects. First, by the virtue of CNN, AEDSNN is free of parameter-tuning. This is a great facility compared to conventional reconstruction methods; Second, AEDSNN is quite fast. Conventional reconstruction methods usually need hundreds even thousands of iterations, while AEDSNN just needs three to five iterations (i.e., blocks); Third, the learned regularizer by AEDSNN enjoys a broader application capacity, which could work well with piecewise smooth images and surpass the piecewise constant assumption frequently assumed for computed tomography images.

Deep learning based image reconstruction algorithm for limited-angle translational computed tomography

As a low-end computed tomography (CT) system, translational CT (TCT) is in urgent demand in developing countries. Under some circumstances, in order to reduce the scan time, decrease the X-ray radiation or scan long objects, furthermore, to avoid the inconsistency of the detector for the large angle scanning, we use the limited-angle TCT scanning mode to scan an object within a limited angular range. However, this scanning mode introduces some additional noise and limited-angle artifacts that seriously degrade the imaging quality and affect the diagnosis accuracy. To reconstruct a high-quality image for the limited-angle TCT scanning mode, we develop a limited-angle TCT image reconstruction algorithm based on a U-net convolutional neural network (CNN). First, we use the SART method to the limited-angle TCT projection data, then we import the image reconstructed by SART method to a well-trained CNN which can suppress the artifacts and preserve the structures to obtain a better reconstructed image. Some simulation experiments are implemented to demonstrate the performance of the developed algorithm for the limited-angle TCT scanning mode. Compared with some state-of-the-art methods, the developed algorithm can effectively suppress the noise and the limited-angle artifacts while preserving the image structures.

l0 regularization based on a prior image incorporated non-local means for limited-angle X-ray CT reconstruction

PURPOSES

Restricted by the scanning environment in some CT imaging modalities, the acquired projection data are usually incomplete, which may lead to a limited-angle reconstruction problem. Thus, image quality usually suffers from the slope artifacts. The objective of this study is to first investigate the distorted domains of the reconstructed images which encounter the slope artifacts and then present a new iterative reconstruction method to address the limited-angle X-ray CT reconstruction problem.

METHODS

The presented framework of new method exploits the structural similarity between the prior image and the reconstructed image aiming to compensate the distorted edges. Specifically, the new method utilizes l0 regularization and wavelet tight framelets to suppress the slope artifacts and pursue the sparsity. New method includes following 4 steps to (1) address the data fidelity using SART; (2) compensate for the slope artifacts due to the missed projection data using the prior image and modified nonlocal means (PNLM); (3) utilize l0 regularization to suppress the slope artifacts and pursue the sparsity of wavelet coefficients of the transformed image by using iterative hard thresholding (l0W); and (4) apply an inverse wavelet transform to reconstruct image. In summary, this method is referred to as "l0W-PNLM".

RESULTS

Numerical implementations showed that the presented l0W-PNLM was superior to suppress the slope artifacts while preserving the edges of some features as compared to the commercial and other popular investigative algorithms. When the image to be reconstructed is inconsistent with the prior image, the new method can avoid or minimize the distorted edges in the reconstructed images. Quantitative assessments also showed that applying the new method obtained the highest image quality comparing to the existing algorithms.

CONCLUSIONS

This study demonstrated that the presented l0W-PNLM yielded higher image quality due to a number of unique characteristics, which include that (1) it utilizes the structural similarity between the reconstructed image and prior image to modify the distorted edges by slope artifacts; (2) it adopts wavelet tight frames to obtain the first and high derivative in several directions and levels; and (3) it takes advantage of l0 regularization to promote the sparsity of wavelet coefficients, which is effective for the inhibition of the slope artifacts. Therefore, the new method can address the limited-angle CT reconstruction problem effectively and have practical significance.