This paper presents a new approach for the optimization of a dictionary used in ECG signal compression and reconstruction systems, based on Compressed Sensing (CS). Alternatively to fully data driven methods, which learn the dictionary from the training data, the proposed approach uses an over complete wavelet dictionary, which is then reduced by means of a training phase. Moreover, the alignment of the frames according to the position of the R-peak is proposed, such that the dictionary optimization can exploit the different scaling features of the ECG waves. Therefore, at first, a training phase is performed in order to optimize the overcomplete dictionary matrix by reducing its number of columns. Then, the optimized matrix is used in combination with a dynamic sensing matrix to compress and reconstruct the ECG waveform. In this paper, the mathematical formulation of the patient-specific optimization is presented and three optimization algorithms have been evaluated. For each of them, an experimental tuning of the convergence parameter is carried out, in order to ensure that the algorithm can work in its most suitable conditions. The performance of each considered algorithm is evaluated by assessing the Percentage of Root-mean-squared Difference (PRD) and compared with the state of the art techniques. The obtained experimental results demonstrate that: (i) the utilization of an optimized dictionary matrix allows a better performance to be reached in the reconstruction quality of the ECG signals when compared with other methods, (ii) the regularization parameters of the optimization algorithms should be properly tuned to achieve the best reconstruction results, and (iii) the Multiple Orthogonal Matching Pursuit (M-OMP) algorithm is the better suited algorithm among those examined.

中文翻译：

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压缩感知后心电信号重建的字典优化方法


本文提出了一种基于压缩感知（CS）的心电信号压缩和重建系统中使用的字典优化的新方法。除了从训练数据中学习字典的完全数据驱动方法之外，所提出的方法使用超完整的小波字典，然后通过训练阶段来减少字典。此外，还提出了根据 R 峰位置进行帧对齐，以便字典优化可以利用 ECG 波的不同缩放特征。因此，首先执行训练阶段，以便通过减少其列数来优化过完备字典矩阵。然后，将优化后的矩阵与动态传感矩阵结合使用来压缩和重建心电波形。本文提出了针对特定患者的优化的数学公式，并对三种优化算法进行了评估。对于每一个，都对收敛参数进行了实验调整，以确保算法能够在最合适的条件下工作。通过评估均方根差值百分比 (PRD) 来评估每个考虑的算法的性能，并与最先进的技术进行比较。 获得的实验结果表明：（i）与其他方法相比，使用优化的字典矩阵可以在心电信号的重建质量方面达到更好的性能，（ii）优化算法的正则化参数应为适当调整以实现最佳重建结果，并且 (iii) 多重正交匹配追踪 (M-OMP) 算法是所检查的算法中更适合的算法。