Sparse reconstruction is an important aspect of modern medical imaging, reducing the acquisition time of relatively slow modalities such as magnetic resonance imaging (MRI). Popular methods are based mostly on compressed sensing (CS), which relies on the random sampling of Fourier coefficients ($k$-space) to produce incoherent (noise-like) artefacts that can be removed via convex optimisation. Hardware constraints currently limit Cartesian CS to one dimensional (1D) phase-encode undersampling schemes, leading to coherent and structured artefacts. Reconstruction algorithms typically deploy an idealised and limited 2D regularisation for artefact removal, which increases the difficulty of image recovery. Recognising that phase-encode artefacts can be separated into contiguous 1D signals, we develop two decoupling techniques that enable explicit 1D regularisation. We thereby leverage the excellent incoherence characteristics in the phase-encode direction. We also derive a combined 1D + 2D reconstruction technique that further takes advantage of spatial relationships within the image, leading to an improvement of existing 2D deep-learned (DL) recovery techniques. Performance is evaluated on a brain and knee dataset. We find the proposed 1D CNN modules significantly improve PSNR and SSIM scores compared to the base 2D models, demonstrating a superior scaling of performance compared to increasing the size of 2D network layers.

翻译：稀疏重建是现代医学成像的一个重要方面，它能够缩短磁共振成像等相对缓慢模态的采集时间。主流方法主要基于压缩感知，该技术通过随机采样傅里叶系数（k空间）产生不相干（类噪声）伪影，并借助凸优化消除这些伪影。当前硬件限制将笛卡尔压缩感知局限于一维相位编码欠采样方案，导致产生相干且结构化的伪影。重建算法通常采用理想化且受限的二维正则化进行伪影去除，这增加了图像恢复的难度。考虑到相位编码伪影可分解为连续的一维信号，我们开发了两种解耦技术，实现了显式的一维正则化。由此，我们充分利用了相位编码方向上的优异不相干特性。我们还推导出一种结合一维与二维的重建技术，该技术进一步利用了图像内部的空间关系，从而改进了现有的二维深度学习重建技术。在脑部和膝盖数据集上评估了性能。我们发现，与基础二维模型相比，所提出的一维卷积神经网络模块显著提升了峰值信噪比和结构相似性指数得分，展现出相较于增加二维网络层规模更优的性能扩展性。