TRD3 - Image Reconstruction

项目摘要/摘要 从原始测量数据重建图像是磁共振成像中一个非常重要的逆问题。这个 这种重建的基本公式涉及在笛卡尔格网上均匀采样的k空间 而不是奈奎斯特速率，该速率被傅立叶变换以生成所需的图像。然而，这笔收购- 重建策略通常很难在实际研究和临床环境中执行，因为它导致 扫描时间，需要在空间和时间分辨率上进行权衡。这一观察结果导致了 在过去几十年中发展了多种重建战略，包括部分傅立叶成像， 并行成像、非笛卡尔采集和压缩传感，其中重建超出了 简单的傅立叶变换，通常涉及对MR系统和图像进行仔细的数学建模。这个 上述发展旨在满足对更快的成像、更高的分辨率和 在临床和研究环境中都具有健壮性。然而，由于现有方法达到了 在存在系统和生理限制的情况下实现的分辨率和加速，新 对于各种获取策略，需要采用重建策略来改善图像质量。 在此TRD中，我们寻求开发新的图像重建技术，以实现快速高分辨率 采集，提高噪声恢复能力，支持不同的编码策略，同时提高稳健性 潜在的生理和系统变化。我们在快速高分辨率成像方面的发展包括 改进了笛卡尔成像中k空间内插重建的策略，以及新的自适应重建算法。 用于三维非笛卡尔成像的校准技术。对于前者，我们延长了班轮移位- 用于以两种方式重建多线圈数据的不变卷积内插方法：i)特定于扫描 同时用于丢失k空间数据的非线性估计的无训练数据库的深度学习 多层、并行和部分傅立叶成像，II)区域特定的移位变化的线性核 加速体积并行成像。对于非笛卡尔收购，我们的自我校准用于估计 半径和旋转特定的插值核，没有额外的ACS数据。我们还解决了以下问题 改进非傅立叶编码捕获，例如时空编码，并设计快速矩阵 稀疏化方法，能够在不增加计算负担的情况下进行正则化重建。为了进一步 在多维采集中提高重建保真度，我们提出了局部使用高阶张量 模型，以及无参数正则化的信息论方法。最后，我们认为 在存在生理和系统变化的情况下成像，例如运动和B0不均匀，其 在超高场强下尤其明显，并开发了一个基于自洽的框架 非线性反转，它利用来自外部传感器或序列元素的改进的初始化。

Project Summary/Abstract Image reconstruction from raw measurements is an inverse problem of fundamental importance in MRI. The basic formulation for such reconstructions involve a k-space sampled uniformly on a Cartesian grid at greater than the Nyquist rate, which is Fourier transformed to generate the desired image. However, this acquisition- reconstruction strategy is often difficult to perform in practical research and clinical settings, as it leads to long scan times, necessitating trade-offs in spatial and temporal resolutions. This observation has led to the development of multiple reconstruction strategies over the last few decades, including partial Fourier imaging, parallel imaging, non-Cartesian acquisitions and compressed sensing, where the reconstruction goes beyond a simple Fourier transform, and often involves careful mathematical modeling of the MR system and images. The aforementioned developments aim to address a continuous need for faster imaging, improved resolutions and robustness, both in clinical and research settings. However, as the existing methods reach the limits of resolution and acceleration achievable in the presence of system and physiological limitations, new reconstruction strategies are needed to improve image quality for various acquisition strategies. In this TRD, we seek to develop new image reconstruction techniques for enabling fast high-resolution acquisitions, improving noise resilience, allowing for different encoding strategies, while increasing robustness to underlying physiological and system variations. Our developments for fast high-resolution imaging include improved strategies for k-space interpolation reconstruction in Cartesian imaging, as well as new self- calibrated techniques for three-dimensional non-Cartesian imaging. For the former, we extend the liner shift- invariant convolutional interpolation approaches for reconstructing multi-coil data in two ways: i) Scan-specific deep learning without training databases for non-linear estimation of missing k-space data, in simultaneous multi-slice, parallel and partial Fourier imaging, ii) Region-specific shift-variant linear kernels for highly- accelerated volumetric parallel imaging. For non-Cartesian acquisitions, our self-calibration is used to estimate radius- and rotation-specific interpolation kernels, without additional ACS data. We also tackle the problem of improving non-Fourier encoded acquisitions, such as spatiotemporal encoding, and devise fast matrix sparsifying approaches to enable regularized reconstructions without high computational burden. To further improve reconstruction fidelity in multi-dimensional acquisitions, we propose the local use of high-order tensor models, along with an information theoretic approach for parameter-free regularization. Finally, we consider imaging in the presence of physiological and system variations, such as motion and B0 inhomogeneities, which are especially pronounced at ultrahigh field strengths, and develop a self-consistency based framework for nonlinear inversion, which utilizes improved initialization from external sensors or sequence elements.