Subband-Adaptive Shrinkage for Denoising of ECG Signals

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Subband-Adaptive Shrinkage for Denoising of ECG Signals S. Poornachandra1 and N. Kumaravel2 1 Department 2 Department

of Biomedical Engineering, SSN College of Engineering, Anna University, Chennai 600025, India of Electronics and Communication Engineering, Anna University, Chennai 600025, India

Received 12 March 2005; Revised 8 September 2005; Accepted 28 September 2005 Recommended for Publication by Walter Kellermann This paper describes subband dependent adaptive shrinkage function that generalizes hard and soft shrinkages proposed by Donoho and Johnstone (1994). The proposed new class of shrinkage function has continuous derivative, which has been simulated and tested with normal and abnormal ECG signals with added standard Gaussian noise using MATLAB. The recovered signal is visually pleasant compared with other existing shrinkage functions. The implication of the proposed shrinkage function in denoising and data compression is discussed. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

1.

INTRODUCTION

Electrocardiogram (ECG) obtained by noninvasive technique is a harmless, safe, and quick method of cardiovascular diagnosis. The accuracy and content of information extracted from recording require proper characterization of waveform morphologies that needs better preservation of signals and higher attenuation of noise. Recently, wavelet transform has proved to be a useful tool for nonstationary signal analysis. Wavelets provide flexible prototyping environment that comes with fast computational algorithms. A shrinkage method compares empirical wavelet coefficient with a threshold. The coefficient sets it to zero if its magnitude is less than threshold value [1]. The threshold acts as an oracle, which distinguishes between significant and insignificant coefficients. Shrinkage of empirical wavelet coefficients works best when the underlying set of true coefficients of function f is sparse [4]. The wavelet shrinkage was conceptually inspired by the work of Donoho and Johnstone (1995) as well as by the work of Breiman and Bruce and Gao (1996). Donoho et al., developed wavelet shrinkage methods for denoising of function estimation [2]. Among wavelet shrinkage methods, SureShrink is an optimized hybrid scale dependent thresholding scheme based on Stein’s unbiased risk estimate (SURE) [5]. It combines universal threshold selection schemes and scale dependent adaptive threshold selection scheme that provide the best estimation results in the sense of l2 risk when true function is not known. However, since standard

soft shrinkage function is weakly differentiable only in the first order, it does not allow for gradient based optimization method to search for optimal solution for SURE risk [3]. Asymptotically both hard and soft shrinkage estimates are achieved within a factor log(n) of the ideal performance [1]. The wavelet coefficients at coarsest scale are left intact, while coefficients at all other scales are thresholded via soft shrinkage with universal thresholding 

λ = σ 2 log N,

(1)

where σ 2 is the