Denoising of single and multidimensional signals using a higher-order statistics wavelet-based approach

This dissertation presented a new denoising scheme in which a higher-order correlation wavelet-based approach has been used to reduce the effect of the noise. The new method was used to identify the wavelet coefficients of noisy signals uncorrupted by noise. A mathematical analysis has been provided, and examples in one-dimensions have been given. The denoising results were analyzed and compared with a previously known denoising technique. The effect of using the new method on the performance of signal identification and probability of detection of some chemical spectra was also studied. The new technique was extended to 2-D, and it was used in denoising noisy images. In this research, many experiments were done to test the performance of the new technique. In general, the new method results at low input signal-to-noise ratio, compared favorably and was less sensitive to the threshold selection when compared to a more common denoising method. The new method improved the probability of detection of noisy spectra at low values of signal-to-noise ratio. The denoising of a multispectral image using a 2-D and a 3-D approaches was also studied in this research. It was found that for multispectral imagery the 3-D denoising algorithm worked better.