Compressed Sensing Recovery using Modified Newton Gradient Pursuit Algorithm and its Application to ECG with Denoising

摘要

Compressed sensing (CS) is a novel sampling paradigm which states that with prior knowledge of the domain in which the signal is sparse, it is possible to reconstruct the signal with fewer measurements than required by the Nyquist Theorem. In this paper, we propose a novel iterative greedy algorithm called modified Newton Gradient Pursuit (m-NGP) for practical CS reconstruction. Empirical evidence suggests that this algorithm achieves improved performance with comparable computational complexity over the existing state of art greedy algorithms. The algorithm also does not require prior information about the sparsity, making it suitable in real world problems where exact sparsity information may not be available. Further, we demonstrate the advantages of our algorithm, in a practical scenario for recovering the denoised ECG signal from 25% compressive measurements. By using a suitable sparsifying dictionary, the noisy components due to base line wander (BW), power line interference (PLI) and high frequency noises can be removed from the signal. Our algorithm outperforms other greedy algorithms in recovering the ECG signal and is able to achieve a PSNR of 71.72 dB compared with 68.23 dB obtained using OMP for record 104 from the MIT-BIH Arrhythmia database corrupted with BW and PLI.