Bayesian False Discovery Rate Wavelet Shrinkage: Theory and Applications

Dual tree complex wavelet transform-based signal denoising method exploiting neighbourhood dependencies and goodness-of-fit test

A novel signal denoising method is proposed whereby goodness-of-fit (GOF) test in combination with a majority classifications-based neighbourhood filtering is employed on complex wavelet coefficients obtained by applying dual tree complex wavelet transform (DT-CWT) on a noisy signal. The DT-CWT has proven to be a better tool for signal denoising as compared to the conventional discrete wavelet transform (DWT) owing to its approximate translation invariance. The proposed framework exploits statistical neighbourhood dependencies by performing the GOF test locally on the DT-CWT coefficients for their preliminary classification/detection as signal or noise. Next, a deterministic neighbourhood filtering approach based on majority noise classifications is employed to detect false classification of signal coefficients as noise (via the GOF test) which are subsequently restored. The proposed method shows competitive performance against the state of the art in signal denoising.

EMAT noise suppression using information fusion in stationary wavelet packets

An important issue in ultrasonic nondestructive testing is the detection of flaw echoes in the presence of background noise created by instrumentation and by clutter noise. Signal averaging, autoregressive analysis, spectrum analysis, matched filtering, and the wavelet transform have all been used to filter noise in ultrasonic signals. Widely-used wavelet threshold estimation algorithms are not designed for electromagnetic acoustic transducer (EMAT) pulse-echo signals, and therefore do not exploit their unique impulse nature. The approach to ultrasonic signal filtering proposed in this paper is based on stationary wavelet packet denoising with a threshold influenced by several information sources: a statistical echo detection, the amplitude distribution of the wavelet transform coefficients, and a priori known system frequency characteristics. The proposed method was evaluated on signals measured with EMAT probes and under various SNR conditions; it outperforms the wavelet transform with the Stein unbiased risk estimate (SURE) threshold estimation method and split-spectrum processing (SSP). The results indicate SNR enhancement of 19 dB with real EMAT data.