| Wavelets appear today in a variety of advanced signal processing applications, including medical diagnostics, compression, transmission, storage, and noise reduction. The goal of this research is to demonstrate a new method for image and signal denoising which is based on wavelets combined with higher order statistics. The primary contribution of this work is to develop a 2-d third order image denoising algorithm. We begin with the existing 1-d version of the algorithm, and then we extend it to two dimensions. The performance of the third order denoising algorithm is compared with two well known second order algorithms, Visushrink and Bayesshrink.;This approach is unique because unlike other wavelet denoising techniques that are second order in nature, it uses the triple correlation coefficient of the wavelet-signal cross correlation. The threshold, applied in the third order domain, is a key component of denoising algorithms. Clean reference signals are used to determine the optimum threshold for the third order algorithm.;Two methods are used to compare the performance of the third order and second order algorithms. One method is based on traditional Mean Squared Error (MSE) metrics and the second is based on a new concept known as a Task Specific Metric (TSM). TSM is unlike traditional MSE metric because it measures local errors, those near impulse-like features of a signal. This research shows that the third order algorithm maintains these impulse-like features better than the second order ones. The improved denoising provided by the third order algorithm is demonstrated by applying it to Electroencephalograph (ECG) signals as well as images of a wide variety. |
