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首页> 外文期刊>IEEE Transactions on Medical Imaging >Recovery of Damped Exponentials Using Structured Low Rank Matrix Completion
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Recovery of Damped Exponentials Using Structured Low Rank Matrix Completion

机译：使用结构化低秩矩阵补余恢复阻尼指数

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摘要

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of exponentials. We exploit the exponential behavior of the signal at every pixel, along with the spatial smoothness of the exponential parameters to derive an annihilation relation in the Fourier domain. This relation translates to a low-rank property on a structured matrix constructed from the Fourier samples. We enforce the low-rank property of the structured matrix as a regularization prior to recover the images. Since the direct use of current low rank matrix recovery schemes to this problem is associated with high computational complexity and memory demand, we adopt an iterative re-weighted least squares algorithm, which facilitates the exploitation of the convolutional structure of the matrix. Novel approximations involving 2-D fast Fourier transforms are introduced to drastically reduce the memory demand and computational complexity, which facilitates the extension of structured low-rank methods to large scale 3-D problems. We demonstrate our algorithm in the MR parameter mapping setting and show improvement over the state-of-the-art methods.
机译：我们引入了一种结构化的低秩矩阵完成算法，以从欠采样测量中恢复一系列图像，其中沿每个像素的参数维的信号由指数的线性组合来描述。我们利用信号在每个像素处的指数行为以及指数参数的空间平滑度来推导傅立叶域中的an灭关系。这种关系转换为由傅立叶样本构造的结构化矩阵的低秩属性。在恢复图像之前，我们将结构化矩阵的低秩属性强制为正则化。由于直接将当前的低秩矩阵恢复方案用于此问题会导致较高的计算复杂性和内存需求，因此我们采用了迭代的重新加权最小二乘算法，这有利于矩阵的卷积结构的利用。引入了涉及2-D快速傅里叶变换的新型近似方法，以大大降低内存需求和计算复杂度，从而有助于将结构化的低秩方法扩展到大规模3-D问题。我们在MR参数映射设置中演示了我们的算法，并显示了对最新方法的改进。

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