Dynamic magnetic resonance imaging (DMRI) is an effective imaging tool for
diagnosis tasks that require motion tracking of a certain anatomy. To speed up
DMRI acquisition, k-space measurements are commonly undersampled along spatial
or spatial-temporal domains. The difficulty of recovering useful information
increases with increasing undersampling ratios. Compress sensing was invented
for this purpose and has become the most popular method until deep learning
(DL) based DMRI reconstruction methods emerged in the past decade.
Nevertheless, existing DL networks are still limited in long-range sequential
dependency understanding and computational efficiency and are not fully
automated. Considering the success of Transformers positional embedding and
"swin window" self-attention mechanism in the vision community, especially
natural video understanding, we hereby propose a novel architecture named
Reconstruction Swin Transformer (RST) for 4D MRI. RST inherits the backbone
design of the Video Swin Transformer with a novel reconstruction head
introduced to restore pixel-wise intensity. A convolution network called
SADXNet is used for rapid initialization of 2D MR frames before RST learning to
effectively reduce the model complexity, GPU hardware demand, and training
time. Experimental results in the cardiac 4D MR dataset further substantiate
the superiority of RST, achieving the lowest RMSE of 0.0286 +/- 0.0199 and 1 -
SSIM of 0.0872 +/- 0.0783 on 9 times accelerated validation sequences.

提出了一种名为 Reconstruction Swin Transformer (RST) 的新型架构，用于 4D MRI 重建，该架构继承了视频 Swin Transformer 的骨干设计，并引入了新的重建头部来恢复像素级强度，通过在卡片 4D MR 数据集中的实验结果进一步证实了 RST 的优越性。

基于卷积网络辅助重建 Swin Transformer 的动态 MRI 重建学习

Learning Dynamic MRI Reconstruction with Convolutional Network Assisted  Reconstruction Swin Transformer

Support recovery of sparse signals from compressed linear measurements is a
fundamental problem in compressed sensing (CS). In this paper, we study the
orthogonal matching pursuit (OMP) algorithm for the recovery of support under
noise. We consider two signal-to-noise ratio (SNR) settings: i) the SNR depends
on the sparsity level $K$ of input signals, and ii) the SNR is an absolute
constant independent of $K$. For the first setting, we establish necessary and
sufficient conditions for the exact support recovery with OMP, expressed as
lower bounds on the SNR. Our results indicate that in order to ensure the exact
support recovery of all $K$-sparse signals with the OMP algorithm, the SNR must
at least scale linearly with the sparsity level $K$. In the second setting,
since the necessary condition on the SNR is not fulfilled, the exact support
recovery with OMP is impossible. However, our analysis shows that recovery with
an arbitrarily small but constant fraction of errors is possible with the OMP
algorithm. This result may be useful for some practical applications where
obtaining some large fraction of support positions is adequate.

本文研究压缩感知领域的稀疏信号恢复问题，通过对正交匹配追踪算法在噪声情况下的研究，分析了两种信噪比设置情况下的恢复效果及最低信噪比要求，同时比较了在不同条件下算法的精确恢复率，结果可用于某些实际应用场景。