Phase Preserving Denoising of Images

In recent years wavelet shrinkage denoising has become the method of choice for the denoising of images. However, despite much research a number of questions remain. Which of the many wavelets that exist should one use? How should the threshold be set? and How are features in the image affected by the thresholding operation? This paper explores these issues and argues for the use of non-orthogonal, complex valued, log-Gabor wavelets, rather than the more usual orthogonal or bi-orthogonal wavelets. Thresholding of wavelet responses in the complex domain allows one to ensure that perceptually important phase information in the image is not corrupted. It is also shown how appropriate threshold values can be determined automatically from the statistics of the wavelet responses to the image.