Nonlinear image filtering in the wavelet transform domain

In this dissertation, a new technique for multiplicative noise image denoising in the wavelet transform domain is presented. Unlike most existing techniques, the approach does not require prior modeling of either the image or the noise statistical characteristics. Instead, the approach explicitly accounts for the signal dependent nature of the noise. This is considered by attempting to use the variances of the detail wavelet coefficients to decide whether to smooth or preserve these coefficients. The approach takes advantage of wavelet transform property in generating three detail sub-images each providing separate information with certain image features directivity. This allows the ability to combine information provided by different detail sub-images to direct the filtering operation. The algorithm uses the analysis of variance statistical approach to decide whether detail wavelet coefficients are due to image related features or they are due to noise. Most existing techniques use orthogonal transforms in order to preserve statistical characteristic of the noise i.e., additive white gaussian noise. Results of our approach show the effectiveness of the technique whether we use orthogonal or biorthogonal mother wavelets. Thus suggesting that preserving statistical characteristic of the noise is not critical in the smoothing operation as long as the noise is signal dependent.