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 $\ell _{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.

中文翻译：

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基于全变分和小波帧正则化的稀疏视图CT图像重建

由于其在降低辐射剂量方面的巨大潜力，计算机断层扫描 (CT) 中遇到的图像重建的稀疏视图问题是一个重要的研究问题。在这些研究中，全变差（TV）方法在稀疏视图CT重建中尤其有效，因为它具有良好的保留锐利边缘和抑制噪声的能力。然而，基于电视的方法通常会在重建图像的平滑区域产生不希望的阶梯伪影，因为重建问题通常是不适定的，并且电视正则化有利于分段常数函数。此外，在适当的小波紧框架下，图像可以通过稀疏系数精确逼近，具有良好的稀疏估计分段平滑函数的能力，并且可以通过稀疏先验信息提高重构图像的质量。针对稀疏视图CT重建问题，提出了一种结合TV与小波帧的最小化混合重建模型，即利用低频小波帧系数的TV范数和$\ell_{0} $ - 高频小波框架系数的范数，以消除阶梯效应，同时保持锐利边缘，同时在平滑区域提供足够的正则化。此外，考虑到两个正则化项产生的参数较多，采用交替乘法器方向法（ADMM）算法分别迭代最小化求解最小化问题。最后，