The sparse-view problem of image reconstruction encountered in computed tomography (CT) is an important research issue due to its considerable potential in decreasing radiation dose and improving detection efficiency. Among the current sparse-view CT reconstruction algorithms, iterative reconstruction algorithms that consider total variation (TV) regularization exhibit good performance. However, the gradient difference direction is singular or fixed in conventional TV algorithms, leading to undesired artefacts when minimizing TV in sparseview CT. To effectively address this issue, based on TV minimization, the gradient difference directional information is introduced as additional prior information in the regularization term, and a new gradient-based directional total variation minimization algorithm is proposed, which adaptively chooses mutative gradient directions to calculate the directional difference operators, and calculates the sum of the direction difference operators. In addition, to solve the fault tolerance and computational load, considering redundant blocks of reconstructed image, we can estimate the gradient directional information of each subblock via the gradient approximation method. For simplicity, the proposed algorithm is termed the BDTV algorithm. To demonstrate the superiority of the proposed algorithm, the simulation data and actual CT data from different algorithms are compared, and the results indicate that the proposed algorithm is effective at preserving details that are lost in the TV minimization, artefact reduction and noise suppression in sparse-view CT.

The sparse view problem of image reconstruction encountered in computed tomography (CT) is an important research issue due to its considerable potential in lowering radiation dose. Among the researches, the total variation (TV) method is especially effective in sparse view CT reconstruction for its good ability to preserve sharp edges and suppress noise. However, TV-based methods often produce undesired staircase artifacts in smooth regions of the reconstructed images since the reconstructed problem is usually ill-posed and TV regularization favors piecewise constant functions. Moreover, the image can be accurately approximated by sparse coefficients under a proper wavelet tight frame, which has good capability of sparsely estimating the piecewise smooth functions and the quality of reconstructed image can be improved by the sparse prior information. To deal with sparse view CT reconstruction problem, a minimization hybrid reconstruction model that incorporates TV with the wavelet frame has been proposed, which is to use the TV-norm of the low-frequency wavelet frame coefficients and the 0-norm of the high-frequency wavelet frame coefficients to eliminate staircase effect while maintaining sharp edges, simultaneously provide enough regularization in smooth regions. In addition, considering that the two regularization terms produce more parameters, an alternating direction method of multipliers (ADMM) algorithm has been applied to solve the minimization problem by iteratively minimization separately. Finally, compared with several iterative reconstruction methods, the experimental results demonstrate the competitiveness of the proposed method in terms of preserving edges, suppressing staircase artifacts and denoising. INDEX TERMS Computed tomography (CT), sparse view problem, iterative image reconstruction, total variation, wavelet frame.

The linear reconstruction of narrow-energy-width projections can suppress hardening artifacts in conventional computed tomography (CT). We develop a spectral CT blind separation algorithm for obtaining narrow-energy-width projections under a blind scenario where the incident spectra are unknown. The algorithm relies on an X-ray multispectral forward model. Based on the Poisson statistical properties of measurements, a constrained optimization problem is established and solved by a block coordinate descent algorithm that alternates between nonnegative matrix factorization and Gauss-Newton algorithm. Experiments indicate that the decomposed projections conform to the characteristics of narrow-energy-width projections. The new algorithm improves the accuracy of obtaining narrow-energy-width projections.

No abstract