In Compressive Sensing Magnetic Resonance Imaging (CS-MRI), one can reconstruct a MR image with good quality from only a small number of measurements. This can significantly reduce MR scanning time. According to structured sparsity theory, the measurements can be further reduced to O(K + log n) for tree-sparse data instead of O(K + K log n) for standard K-sparse data with length n. However, few of existing algorithms have utilized this for CS-MRI, while most of them model the problem with total variation and wavelet sparse regularization. On the other side, some algorithms have been proposed for tree sparse regularization, but few of them have validated the benefit of wavelet tree structure in CS-MRI. In this paper, we propose a fast convex optimization algorithm to improve CS-MRI. Wavelet sparsity, gradient sparsity and tree sparsity are all considered in our model for real MR images. The original complex problem is decomposed into three simpler subproblems then each of the subproblems can be efficiently solved with an iterative scheme. Numerous experiments have been conducted and show that the proposed algorithm outperforms the state-of-the-art CS-MRI algorithms, and gain better reconstructions results on real MR images than general tree based solvers or algorithms.
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机译:在压缩感测磁共振成像(CS-MRI)中,仅需少量测量就可以重建高质量的MR图像。这样可以大大减少MR扫描时间。根据结构稀疏性理论,对于树稀疏数据,可以将测量结果进一步减少为O(K + log n),而对于长度为n的标准K稀疏数据,可以将测量结果减少为O(K + K log n)。然而,很少有现有算法将其用于CS-MRI,而大多数算法则通过总变化和小波稀疏正则化来对问题进行建模。另一方面,已经提出了一些用于树稀疏正则化的算法,但是很少有人验证了小波树结构在CS-MRI中的好处。在本文中,我们提出了一种快速凸优化算法来改进CS-MRI。在我们的真实MR图像模型中,均考虑了小波稀疏度,梯度稀疏度和树稀疏度。将原始的复杂问题分解为三个更简单的子问题,然后可以使用迭代方案有效地解决每个子问题。已经进行了许多实验,结果表明,与基于树的一般求解器或算法相比,所提出的算法优于最新的CS-MRI算法,并且在真实MR图像上获得了更好的重建结果。
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