Research Seminar - May 14, 1999

Abstract

Denoising of images is typically done with the following process: The image is transformed into some domain where the noise component is more easily identified, a thresholding operation is then applied to remove the noise, and finally the transformation is inverted to reconstruct a (hopefully) noise-free image. In recent years the wavelet transform has become popular for the denoising of images. However, a number of questions arise:

• Which of the many wavelets that exist should one use?
• What form of thresholding should be used?
• How should the threshold be set? and
• How are features in the image affected by the thresholding operation?

In this talk I will explore these issues and argue for the use of 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 phase information in the image is not corrupted. I will also show how appropriate threshold values can be determined from the statistics of the wavelet responses to the image.