Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, IL 61801, USA.
IEEE Trans Med Imaging. 2011 May;30(5):1028-41. doi: 10.1109/TMI.2010.2090538. Epub 2010 Nov 1.
Compressed sensing (CS) utilizes the sparsity of magnetic resonance (MR) images to enable accurate reconstruction from undersampled k-space data. Recent CS methods have employed analytical sparsifying transforms such as wavelets, curvelets, and finite differences. In this paper, we propose a novel framework for adaptively learning the sparsifying transform (dictionary), and reconstructing the image simultaneously from highly undersampled k-space data. The sparsity in this framework is enforced on overlapping image patches emphasizing local structure. Moreover, the dictionary is adapted to the particular image instance thereby favoring better sparsities and consequently much higher undersampling rates. The proposed alternating reconstruction algorithm learns the sparsifying dictionary, and uses it to remove aliasing and noise in one step, and subsequently restores and fills-in the k-space data in the other step. Numerical experiments are conducted on MR images and on real MR data of several anatomies with a variety of sampling schemes. The results demonstrate dramatic improvements on the order of 4-18 dB in reconstruction error and doubling of the acceptable undersampling factor using the proposed adaptive dictionary as compared to previous CS methods. These improvements persist over a wide range of practical data signal-to-noise ratios, without any parameter tuning.
压缩感知（CS）利用磁共振（MR）图像的稀疏性，能够从欠采样的 k 空间数据中实现精确重建。最近的 CS 方法采用了分析稀疏变换，如小波、曲波和有限差分。在本文中，我们提出了一种从高度欠采样的 k 空间数据中自适应学习稀疏变换（字典）并同时重建图像的新框架。该框架中的稀疏性是通过强调局部结构的重叠图像块来实现的。此外，字典可以适应特定的图像实例，从而有利于更好的稀疏性，进而可以采用更高的欠采样率。所提出的交替重建算法学习稀疏字典，并在一步中使用它去除混叠和噪声，然后在另一步中恢复和填充 k 空间数据。在具有各种采样方案的几种解剖结构的 MR 图像和真实 MR 数据上进行了数值实验。结果表明，与以前的 CS 方法相比，使用所提出的自适应字典可以将重建误差提高 4-18dB，并且可以将可接受的欠采样因子提高一倍。这些改进在广泛的实际数据信噪比范围内都能持续存在，而无需进行任何参数调整。
