results: 该方法可以提供更加细节和结构保持的图像恢复结果，并且比 convex 方法更加稳定。Abstract
Total Variation regularization (TV) is a seminal approach for image recovery. TV involves the norm of the image's gradient, aggregated over all pixel locations. Therefore, TV leads to piece-wise constant solutions, resulting in what is known as the "staircase effect." To mitigate this effect, the Hessian Schatten norm regularization (HSN) employs second-order derivatives, represented by the pth norm of eigenvalues in the image hessian, summed across all pixels. HSN demonstrates superior structure-preserving properties compared to TV. However, HSN solutions tend to be overly smoothed. To address this, we introduce a non-convex shrinkage penalty applied to the Hessian's eigenvalues, deviating from the convex lp norm. It is important to note that the shrinkage penalty is not defined directly in closed form, but specified indirectly through its proximal operation. This makes constructing a provably convergent algorithm difficult as the singular values are also defined through a non-linear operation. However, we were able to derive a provably convergent algorithm using proximal operations. We prove the convergence by establishing that the proposed regularization adheres to restricted proximal regularity. The images recovered by this regularization were sharper than the convex counterparts.
摘要
全Variation正规化（TV）是一种杰出的方法 для图像恢复。TV通过图像梯度的norm，在所有像素位置上进行积分，因此TV会导致piece-wise常数解，这被称为“阶梯效应”。为了 mitigate这些效应，使用第二 derivatives，表示图像Hessian的pth norm的 eigenvalues，在所有像素位置上进行积分。HSN表现出比TV更好的结构保持性。然而，HSN解决方案通常是过度熔化。为了解决这个问题，我们引入了非CONvex shrinkage penalty，应用于图像Hessian的 eigenvalues。这个 penalty不是直接定义的closed form，而是通过其proximal操作定义。这使得构建可提供 garantía de convergencia的算法变得困难，因为singular values 也是通过非线性操作定义。然而，我们成功地 derivated a provably convergent algorithm using proximal operations。我们证明了这种正则化的 convergencia by establishing that the proposed regularization adheres to restricted proximal regularity。图像recovered by this regularization were sharper than the convex counterparts。
Motion Compensated Unsupervised Deep Learning for 5D MRI
results: 在5D bSSFP数据上进行了验证，并实现了更高的数据效率和质量。Abstract
We propose an unsupervised deep learning algorithm for the motion-compensated reconstruction of 5D cardiac MRI data from 3D radial acquisitions. Ungated free-breathing 5D MRI simplifies the scan planning, improves patient comfort, and offers several clinical benefits over breath-held 2D exams, including isotropic spatial resolution and the ability to reslice the data to arbitrary views. However, the current reconstruction algorithms for 5D MRI take very long computational time, and their outcome is greatly dependent on the uniformity of the binning of the acquired data into different physiological phases. The proposed algorithm is a more data-efficient alternative to current motion-resolved reconstructions. This motion-compensated approach models the data in each cardiac/respiratory bin as Fourier samples of the deformed version of a 3D image template. The deformation maps are modeled by a convolutional neural network driven by the physiological phase information. The deformation maps and the template are then jointly estimated from the measured data. The cardiac and respiratory phases are estimated from 1D navigators using an auto-encoder. The proposed algorithm is validated on 5D bSSFP datasets acquired from two subjects.
摘要
我们提议一种无监督深度学习算法，用于从3D辐射式获取的5D心脏MRI数据进行运动补做重建。无门限自由呼吸5D MRI简化扫描计划，提高了患者的 COMFORT，并提供了许多临床优势，包括均匀的空间分辨率和可以在任意视图下重新构成数据。然而，目前的5D MRI重建算法需要很长的计算时间，其结果受到数据的划分方式的均匀性影响很大。我们的算法是一种更高效的替代方案。这种运动补做方法模型了数据在每个心脏/呼吸期中的变换为Fourier样本的扭曲版本的3D图像模板。变换地图是由基于生物频率信息的卷积神经网络驱动。模板和变换地图然后从测量数据中共同估计。心脏和呼吸频率是通过1D导航器使用自动Encoder来估计。我们的算法在5D bSSFP数据集上进行验证，从两个试验者中获得了 validate。