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首页> 外文期刊>IEEE Transactions on Medical Imaging >Basis Expansion Approaches for Regularized Sequential Dictionary Learning Algorithms With Enforced Sparsity for fMRI Data Analysis
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Basis Expansion Approaches for Regularized Sequential Dictionary Learning Algorithms With Enforced Sparsity for fMRI Data Analysis

机译：fMRI数据分析的具有稀疏性的正则化顺序字典学习算法的基础扩展方法

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摘要

Sequential dictionary learning algorithms have been successfully applied to functional magnetic resonance imaging (fMRI) data analysis. fMRI data sets are, however, structured data matrices with the notions of temporal smoothness in the column direction. This prior information, which can be converted into a constraint of smoothness on the learned dictionary atoms, has seldomly been included in classical dictionary learning algorithms when applied to fMRI data analysis. In this paper, we tackle this problem by proposing two new sequential dictionary learning algorithms dedicated to fMRI data analysis by accounting for this prior information. These algorithms differ from the existing ones in their dictionary update stage. The steps of this stage are derived as a variant of the power method for computing the SVD. The proposed algorithms generate regularized dictionary atoms via the solution of a left regularized rank-one matrix approximation problem where temporal smoothness is enforced via regularization through basis expansion and sparse basis expansion in the dictionary update stage. Applications on synthetic data experiments and real fMRI data sets illustrating the performance of the proposed algorithms are provided.
机译：顺序词典学习算法已成功应用于功能磁共振成像（fMRI）数据分析。但是，fMRI数据集是结构化的数据矩阵，具有沿列方向的时间平滑度的概念。可以转换为对学习的字典原子的平滑性约束的先验信息在应用于fMRI数据分析时很少包含在经典字典学习算法中。在本文中，我们通过提出两种新的顺序字典学习算法来解决此问题，这些算法专用于通过考虑此先验信息来进行fMRI数据分析。这些算法在字典更新阶段与现有算法不同。此阶段的步骤是作为计算SVD的幂方法的变体而得出的。所提出的算法通过左正则化秩一矩阵逼近问题的解决方案生成正则化字典原子，在字典更新阶段，通过基础扩展和稀疏基础扩展通过正则化来强制实现时间平滑。提供了在合成数据实验和真实fMRI数据集上的应用，这些数据说明了所提出算法的性能。

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