A Dictionary Optimization Method for Reconstruction of ECG Signals after Compressed Sensing

Abstract

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.

Keywords

• compressed sensing
• dictionary learning
• ECG
• OMP