Application of dictionary learning in compressed sensing of data in MRI

Himanshu Padole, S. Joshi
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Abstract

In recent years, it is now well established that for the data like MRI images that admit the sparse representation in some transformed domain, Compressed Sensing (CS) approach is well suited for the accurate restoration tasks. Various analytical sparsifying transforms such as wavelets, finite differences and curvelets are used extensively in many CS methods. In this paper, a general framework for the adaptive learning of the sparsifying transform (dictionary) and reconstruction of the MR image from undersampled k-space data simultaneously is proposed. Here, we also propose the supervised dictionary learning framework adapted to specific task of MR image reconstruction and an efficient algorithm to solve the corresponding optimization problem. In this framework, overlapping image patches are used to exploit the local structure in the image to enforce the sparsity. Dictionary is trained using training images corresponding to particular class the given image belongs to. This results in better sparsities hence the higher undersampling rate. In this alternating reconstruction algorithm, firstly the sparsifying dictionary is learnt to remove aliasing effect and then restoring and filling of the k-space data is performed in the other step. Experiments are conducted on the brain MR image data set with different sampling methods. Results of these experiments show the improvement of around 2.5 dB in PSNR and improvement of around 0.1 in the HFEN value of the reconstructed image. Performance with various sampling schemes is evaluated and the results show that 2D variable density random undersampling scheme is best suited for the MRI application.
字典学习在MRI数据压缩感知中的应用
近年来,对于像MRI图像这样在某些变换域中具有稀疏表示的数据,压缩感知(CS)方法非常适合于精确恢复任务。各种解析稀疏化变换,如小波变换、有限差分变换和曲线变换,广泛应用于许多CS方法中。本文提出了一种从欠采样k空间数据中同时进行稀疏化变换(字典)自适应学习和磁共振图像重建的通用框架。在此,我们还提出了适用于特定任务的MR图像重建的监督字典学习框架和解决相应优化问题的高效算法。在该框架中,使用重叠的图像补丁来利用图像中的局部结构来增强稀疏性。字典使用与给定图像所属的特定类相对应的训练图像进行训练。这导致了更好的稀疏性,因此更高的欠采样率。在交替重建算法中,首先学习稀疏字典去除混叠效应,然后对k空间数据进行恢复和填充。采用不同的采样方法对脑磁共振图像数据集进行了实验。实验结果表明,重构图像的PSNR提高了2.5 dB左右,HFEN值提高了0.1左右。对不同采样方案的性能进行了评价,结果表明二维变密度随机欠采样方案最适合于MRI应用。
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