Kernel-based Nonlinear Learning for Fast Magnetic Resonance Imaging with Sub-Nyquist Sampling

 描述（由申请人提供）：对快速图像采集速度的追求一直是MRI界的一个长期话题。为了减少最大空间和时间分辨率的采集时间，现代MRI协议通常执行低于奈奎斯特速率的减少的采集。然后，通过利用关于MRI系统的一些先验信息（例如，并行成像）和/或MR信号（例如，压缩传感）。由于这种先验信息是患者和系统特定的，所以最近的技术使用通过经验校准过程获得的训练数据来获得先验信息。所有现有方法都假设先验模型是线性的。由于训练数据中固有的非线性关系不能 在这种简单的模型中，重建由于先验信息的不准确而退化。从训练数据中进行非线性学习在机器学习中被证明是更强大的，因为它更一般，并且包括线性模型作为特殊情况。然而，学习非线性模型通常更具挑战性，并且由于自由度增加，将模型纳入重建中更具挑战性。最近，我们在MR重建中引入了一个新的概念“核”，以及时解决上述挑战。我们的并行成像和稀疏约束重建的初步结果表明，基于核的算法提高了重建质量与线性先验模型的原始算法。建立在我们强大的初步结果，这个应用程序的目标是开发一个创新的基于内核的框架，从欠采样数据的MR图像重建。该框架不需要非线性映射的明确知识（如在初步工作中），这样可以探索更广泛的非线性函数家族用于不同的临床应用。预计拟议的工作将垂直推进MR图像重建领域。具体而言，成功完成拟议的项目将导致一个通用框架，导致许多新的算法（包括本项目中开发的两个），从减少采集重建。因此，几乎所有当前的临床MRI都可以受益于新框架将促进的提高的分辨率、图像质量和/或减少的采集时间或可能实现的新应用。

 DESCRIPTION (provided by applicant): The quest for fast image acquisition speed has always been a perennial topic in the MRI community. To reduce the acquisition time for maximal spatial and temporal resolution, modern MRI protocols usually perform reduced acquisitions below the Nyquist rate. The reduced data is then used to reconstruct the image through advanced reconstruction techniques that leverage some prior information about the MRI system (e.g., parallel imaging) and/or MR signal (e.g., compressed sensing). Since such prior information is patient and system specific, recent techniques obtain the prior information using training data obtained through an empirical calibration procedure. All existing methods assume the prior models are linear. Since the intrinsic nonlinear relationship in the training data cannot be characterized in such simple models, the reconstruction is degraded by the inaccuracy of the prior information. Nonlinear learning from the training data have proven to be more powerful in machine learning because it is more general and includes the linear model as a special case. However, it is usually more challenging to learn the nonlinear models and even more challenging to incorporate the model in reconstruction due to the increased degree of freedom. We recently have introduced a novel concept of "kernel" in MR reconstruction to address the above challenges timely. Our preliminary results on parallel imaging and sparsity-constrained reconstruction demonstrate that the kernel-based algorithms improve the reconstruction quality over the original algorithms with linear prior models. Built upon our strong preliminary results, the objective of this application is to develop an innovative kernel-based framework for MR image reconstruction from undersampled data. This framework does not require explicit knowledge of nonlinear mapping (as in preliminary work) such that a broader family of nonlinear functions can be explored for different clinical applications. The proposed work is expected to advance the field of MR image reconstruction vertically. Specifically, the successful completion of the proposed project will result in a general framework leading to many new algorithms (including two developed in this project) for reconstruction from reduced acquisition. Therefore, virtually all of current clinical MRI could benefit from the improved resolution, image quality, and/or reduced acquisition times that the new framework will facilitate or the novel applications i may enable.