IEEE Trans Image Process. 2014 Dec;23(12):5007-19. doi: 10.1109/TIP.2014.2360122. Epub 2014 Sep 24.
We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRIs) from highly undersampled k -space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov chain Monte Carlo for the Bayesian model, and use the alternating direction method of multipliers for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.
我们开发了一种贝叶斯非参数模型，用于从高度欠采样的 k 空间数据中重建磁共振图像 (MRI)。我们在图像重建过程中执行字典学习。为此，我们使用β过程作为非参数字典学习先验，将图像块表示为字典元素的稀疏组合。除了其他字典学习变量外，字典的大小和特定于补丁的稀疏模式也从数据中推断出来。字典学习直接在压缩图像上执行，因此针对正在考虑的 MRI 进行了调整。此外，我们还研究了与字典学习模型相结合的全变差惩罚项，并展示了字典学习的去噪特性如何在噪声环境下消除对正则化参数的依赖。我们为贝叶斯模型推导了基于马尔可夫链蒙特卡罗的随机优化算法，并使用交替方向乘子法有效地执行全变差最小化。我们在几个 MRI 上展示了实验结果，结果表明，所提出的正则化框架可以提高重建准确性，优于其他方法。
