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首页> 外文会议>IEEE International Conference on Image Processing >Generalized Fast Iteratively Reweighted Soft-Thresholding Algorithm for Sparse Coding Under Tight Frames in the Complex-Domain
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Generalized Fast Iteratively Reweighted Soft-Thresholding Algorithm for Sparse Coding Under Tight Frames in the Complex-Domain

机译：复杂域下紧框架下稀疏编码的广义快速迭代加权软阈值算法

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摘要

We present a new method for fast magnetic resonance image (MRI) reconstruction in the complex-domain under tight frames. We propose a generalized problem formulation that allows for different weight-update strategies for iteratively reweighted ℓ1-minimization under tight frames. Further, we impose sufficient conditions on the function of the weights that leads to the reweighting strategy, which follows the interpretation originally given by Candès et al, but is more efficient than theirs. Since the objective function in complex-domain compressive sensing MRI (CS-MRI) reconstruction problem is nonholomorphic, we resort to Wirtinger calculus for deriving the update strategies. We develop an algorithm called generalized iteratively reweighted soft-thresholding algorithm (GIRSTA) and its fast variant, namely, generalized fast iteratively reweighted soft-thresholding algorithm (GFIRSTA). We provide convergence guarantees for GIRSTA and empirical convergence results for GFIRSTA. Our experiments show a remarkable performance of the proposed algorithms for complex-domain CS-MRI reconstruction considering both random sampling and radial sampling strategies. GFIRSTA outperforms state-of-the-art techniques in terms of peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM).
机译：我们提出了一种新方法，用于在紧框架下在复杂域中进行快速磁共振图像（MRI）重建。我们提出了一个通用的问题表述，它允许采用不同的权重更新策略来迭代地加权ℓ 1 -在紧绷的框架下最小化。此外，我们对权重的功能施加了足够的条件，从而导致了重新加权策略，该条件遵循了Candès等人最初给出的解释，但是比它们的效率更高。由于复杂域压缩感知MRI（CS-MRI）重建问题中的目标函数是非全同性的，因此我们求助于Wirtinger演算来得出更新策略。我们开发了一种称为广义迭代重加权软阈值算法（GIRSTA）及其快速变体，即广义快速迭代重加权软阈值算法（GFIRSTA）。我们为GIRSTA提供收敛保证，并为GFIRSTA提供经验收敛结果。我们的实验表明，考虑到随机采样和径向采样策略，针对复杂域CS-MRI重建提出的算法具有显着的性能。在峰值信噪比（PSNR）和结构相似性指标度量（SSIM）方面，GFIRSTA优于最新技术。

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