Fast wavelet estimation of weak biosignals

Wavelet-based signal processing has become commonplace in the signal processing community over the past decade and wavelet-based software tools and integrated circuits are now commercially available. One of the most important applications of wavelets is in removal of noise from signals, called denoising, accomplished by thresholding wavelet coefficients in order to separate signal from noise. Substantial work in this area was summarized by Donoho and colleagues at Stanford University, who developed a variety of algorithms for conventional denoising. However, conventional denoising fails for signals with low signal-to-noise ratio (SNR). Electrical signals acquired from the human body, called biosignals, commonly have below 0 dB SNR. Synchronous linear averaging of a large number of acquired data frames is universally used to increase the SNR of weak biosignals. A novel wavelet-based estimator is presented for fast estimation of such signals. The new estimation algorithm provides a faster rate of convergence to the underlying signal than linear averaging. The algorithm is implemented for processing of auditory brainstem response (ABR) and of auditory middle latency response (AMLR) signals. Experimental results with both simulated data and human subjects demonstrate that the novel wavelet estimator achieves superior performance to that of linear averaging.