Efficient Approximation of Jacobian Matrices Involving a Non-Uniform Fast Fourier Transform (NUFFT)
Efficient Approximation of Jacobian Matrices Involving a Non-Uniform Fast Fourier Transform (NUFFT)
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DOI：
10.1109/tci.2023.3240081
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发表时间：
2023-01-01
影响因子：
5.4
通讯作者：
Fessler，Jeffrey A.
中科院分区：
文献类型：
--
作者：
Wang，Guanhua;Fessler，Jeffrey A.
使用优化方法学习傅里叶域采样策略（特别是磁共振成像，MRI）的兴趣越来越大。对于非笛卡尔采样，系统模型通常涉及非均匀快速傅里叶变换（NUFFT）操作。常用的NUFFT算法包含频域插值，这对于采样模式是不可微的，使梯度方法的使用复杂化。本文描述了一种高效、准确的计算涉及nufft的近似梯度的方法。多个数值实验验证了该方法的精度和效率的提高。作为计算成像的一个应用，NUFFT雅可比矩阵通过数据驱动的随机优化来优化非笛卡尔MRI采样轨迹。具体来说，我们学习了各种基于模型的图像重建（MBIR）算法的采样模式。由于内存限制，标准的自区分方法无法实现图像大小的采样优化。协同采集和重建设计显著提高了图像质量。事实上，我们表明，基于模型的图像重建方法，通过适当优化成像参数，几乎可以达到基于cnn的方法的效果。
There is growing interest in learning Fourier domain sampling strategies (particularly for magnetic resonance imaging, MRI) using optimization approaches. For non-Cartesian sampling, the system models typically involve non-uniform fast Fourier transform (NUFFT) operations. Commonly used NUFFT algorithms contain frequency domain interpolation, which is not differentiable with respect to the sampling pattern, complicating the use of gradient methods. This paper describes an efficient and accurate approach for computing approximate gradients involving NUFFTs. Multiple numerical experiments validate the improved accuracy and efficiency of the proposed approximation. As an application to computational imaging, the NUFFT Jacobians were used to optimize non-Cartesian MRI sampling trajectories via data-driven stochastic optimization. Specifically, the sampling patterns were learned with respect to various model-based image reconstruction (MBIR) algorithms. The proposed approach enables sampling optimization for image sizes that are infeasible with standard auto-differentiation methods due to memory limits. The synergistic acquisition and reconstruction design leads to remarkably improved image quality. In fact, we show that model-based image reconstruction methods with suitably optimized imaging parameters can perform nearly as well as CNN-based methods.