Search

In this paper, we present an arc based fan-beam computed tomography (CT) reconstruction algorithm by applying Katsevich's helical CT image reconstruction formula to 2D fan-beam CT scanning data. Specifically, we propose a new weighting function to deal with the redundant data. Our weighting function ϖ (x _ , λ) is an average of two characteristic functions, where each characteristic function indicates whether the projection data of the scanning angle contributes to the intensity of the pixel x _. In fact, for every pixel x _ , our method uses the projection data of two scanning angle intervals to reconstruct its intensity, where one interval contains the starting angle and another contains the end angle. Each interval corresponds to a characteristic function. By extending the fan-beam algorithm to the circle cone-beam geometry, we also obtain a new circle cone-beam CT reconstruction algorithm. To verify the effectiveness of our method, the simulated experiments are performed for 2D fan-beam geometry with straight line detectors and 3D circle cone-beam geometry with flat-plan detectors, where the simulated sinograms are generated by the open-source software "ASTRA toolbox." We compare our method with the other existing algorithms. Our experimental results show that our new method yields the lowest root-mean-square-error (RMSE) and the highest structural-similarity (SSIM) for both reconstructed 2D and 3D fan-beam CT images. [ABSTRACT FROM AUTHOR]

Total variation based regularization and wavelet frame based regularization are two different methods for image restoration. Moreover, nonconvex regularization has advantages over convex regularization for preserving edges in images. In this paper, a variational model consisting of two nonconvex regularizers based respectively on total variation and wavelet frame is proposed for multiplicative noise removal. The proposed model combines the advantages of the nonconvex regularization and the hybrid regularization. So it can more effectively preserve edges and details in images than any single regularization can. The alternating minimization method is proposed to solve the novel model. Although the corresponding minimization problem is nonconvex, the convexity of all subproblems is guaranteed under some mild conditions. Therefore, we study the convergence property of the algorithm. Numerical experiments have proved that the proposed model with the corresponding algorithm outperforms some state-of-the-art models in terms of the peak signal-to-noise ratio and the relative error of the restored images. [ABSTRACT FROM AUTHOR]

It is well known that an image is the pixel-wise multiplication of two components (illumination and reflectance) that are described as intrinsic images. To enhance the visual quality of a degraded image with uneven illumination and low local contrast, it is an effective way to extract the illumination or reflectance from the image and correct the unevenness of illumination. In this paper, we propose a variational model to estimate the illumination and reflectance from the degraded image for the uneven illumination correction. The proposed model is solved by the alternating minimization scheme and the augmented Lagrange method. We give some theoretic analysis of our model and convergence analysis of the algorithm. Experimental results show that the proposed model can achieve excellent performance in the correction of the uneven illumination. [ABSTRACT FROM AUTHOR]

In this paper, we propose a variational model for the limited-angle computed tomography (CT) image reconstruction and convert it into an end-to-end deep network. We first use the penalty method to solve the model and divide it into three iterative subproblems, where the first subproblem completes the sinograms, the second refines the CT images, and the last merges the outputs of the first two subproblems. In each iteration, we use the convolutional neural networks (CNNs) to approximate the solutions of the first two subproblems and, thus, obtain an end-to-end deep network for the limited-angle CT image reconstruction. Our network tackles both the sinograms and the CT images, and can simultaneously suppress the artifacts caused by the incomplete data and recover fine structural information in the CT images. Experimental results show that our method outperforms the related methods for the limited-angle CT image reconstruction. • A variational model utilizing the prior information both in the frequency and spatial domains is proposed. • A new end-to-end deep network is proposed by using CNNs to approximate the solution of the proposed model. • A subnetwork in the Fourier transform domain is developed to complete the limited-angle sinograms. • Experiments show that our method outperforms the related methods for limited-angel CT reconstructions. [ABSTRACT FROM AUTHOR]