Sparse reconstruction is an important aspect of MRI, helping to reduce acquisition time and improve spatial-temporal resolution. Popular methods are based mostly on compressed sensing (CS), which relies on the random sampling of k-space to produce incoherent (noise-like) artefacts. Due to hardware constraints, 1D Cartesian phase-encode under-sampling schemes are popular for 2D CS-MRI. However, 1D under-sampling limits 2D incoherence between measurements, yielding structured aliasing artefacts (ghosts) that may be difficult to remove assuming a 2D sparsity model. Reconstruction algorithms typically deploy direction-insensitive 2D regularisation for these direction-associated artefacts. Recognising that phase-encode artefacts can be separated into contiguous 1D signals, we develop two decoupling techniques that enable explicit 1D regularisation and leverage the excellent 1D incoherence characteristics. We also derive a combined 1D + 2D reconstruction technique that takes advantage of spatial relationships within the image. Experiments conducted on retrospectively under-sampled brain and knee data demonstrate that combination of the proposed 1D AliasNet modules with existing 2D deep learned (DL) recovery techniques leads to an improvement in image quality. We also find AliasNet enables a superior scaling of performance compared to increasing the size of the original 2D network layers. AliasNet therefore improves the regularisation of aliasing artefacts arising from phase-encode under-sampling, by tailoring the network architecture to account for their expected appearance. The proposed 1D + 2D approach is compatible with any existing 2D DL recovery technique deployed for this application.

翻译：稀疏重建是磁共振成像的重要方面，有助于缩短采集时间并提高时空分辨率。常用方法主要基于压缩感知（CS），其依赖于k空间的随机采样以产生非相干（类噪声）伪影。由于硬件限制，一维笛卡尔相位编码欠采样方案在二维CS-MRI中较为流行。然而，一维欠采样限制了测量间的二维非相干性，产生结构化混叠伪影（鬼影），在假设二维稀疏模型时可能难以去除。重建算法通常针对这些方向相关的伪影采用方向不敏感的二维正则化。鉴于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，能够实现显式一维正则化并利用一维非相干性的优越特性。我们还推导了一种结合一维与二维的重建技术，充分利用图像内部的空间关系。在回顾性欠采样脑部和膝部数据上开展的实验表明，将所提出的一维AliasNet模块与现有二维深度学习（DL）重建技术相结合，可提升图像质量。同时发现，与单纯扩展原始二维网络层尺寸相比，AliasNet能实现更优的性能缩放。因此，AliasNet通过定制网络结构以适配预期伪影形态，改善了相位编码欠采样引起的混叠伪影的正则化。所提出的一维与二维联合方法可与应用于该场景的任何现有二维深度学习重建技术兼容。