A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands

This paper deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function (or Power Spectral Density, PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of blind wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant, and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte-Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem

PCA Assisted DTCWT Denoising for Improved DOA Estimation of Closely Spaced and Coherent Signals

Performance of standard Direction of Arrival (DOA) estimation techniques degraded under real-time signal conditions. The classical algorithms are Multiple Signal Classification (MUSIC), and Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT). There are many signal conditions hamper on its performance, such as closely spaced and coherent signals caused due to the multipath propagations of signals results in a decrease of the signal to noise ratio (SNR) of the received signal. In this paper, a novel DOA estimation technique named CW-PCA MUSIC is proposed using Principal Component Analysis (PCA) to threshold the nearby correlated wavelet coefficients of Dual-Tree Complex Wavelet transform (DTCWT) for denoising the signals before applying to MUSIC algorithm. The proposed technique improves the detection performance under closely spaced, and coherent signals with relatively low SNR conditions. Also, this method requires fewer snapshots, and less antenna array elements compared with standard MUSIC and wavelet-based DOA estimation algorithms