IEEE Trans Image Process. 2017 Jun;26(6):3002-3015. doi: 10.1109/TIP.2017.2686014. Epub 2017 Mar 22.
Sequential dictionary learning via the K-SVD algorithm has been revealed as a successful alternative to conventional data driven methods, such as independent component analysis for functional magnetic resonance imaging (fMRI) data analysis. fMRI data sets are however structured data matrices with notions of spatio-temporal correlation and temporal smoothness. This prior information has not been included in the K-SVD algorithm when applied to fMRI data analysis. In this paper, we propose three variants of the K-SVD algorithm dedicated to fMRI data analysis by accounting for this prior information. The proposed algorithms differ from the K-SVD in their sparse coding and dictionary update stages. The first two algorithms account for the known correlation structure in the fMRI data by using the squared Q, R-norm instead of the Frobenius norm for matrix approximation. The third and last algorithms account for both the known correlation structure in the fMRI data and the temporal smoothness. The temporal smoothness is incorporated in the dictionary update stage via regularization of the dictionary atoms obtained with penalization. The performance of the proposed dictionary learning algorithms is illustrated through simulations and applications on real fMRI data.
通过 K-SVD 算法的顺序字典学习已被证明是一种成功的替代传统数据驱动方法的方法，例如用于功能磁共振成像 (fMRI) 数据分析的独立成分分析。然而，fMRI 数据集是具有时空相关性和时间平滑性概念的结构化数据矩阵。在将 K-SVD 算法应用于 fMRI 数据分析时，没有考虑到这种先验信息。在本文中，我们提出了三种变体的 K-SVD 算法，专门用于 fMRI 数据分析，考虑到了这种先验信息。所提出的算法在其稀疏编码和字典更新阶段与 K-SVD 有所不同。前两种算法通过使用 Q、R-范数代替矩阵逼近的 Frobenius 范数来考虑 fMRI 数据中的已知相关结构。第三种也是最后一种算法同时考虑了 fMRI 数据中的已知相关结构和时间平滑性。通过对通过惩罚获得的字典原子进行正则化，将时间平滑性纳入字典更新阶段。通过在真实 fMRI 数据上的模拟和应用说明了所提出的字典学习算法的性能。
