Wavelet singularity detection for image processing

The idea of wavelet singularity detection (WSD) can be traced back to the work of Jaffard. He showed that the local regularity of an n-dimensional signal (which is measured through its Lipschitz exponent) can be estimated by analyzing its n+1-dimensional scale-space. Mallat further showed that the Lipschitz exponent of a singularity can be estimated by tracing its wavelet transform modulus maxima (WTMM). Nevertheless, the tracing of WTMM is not just a tedious procedure computationally; ambiguity is often resulted in determining the correspondence of a modulus maximum to a singularity. In that light, the wavelet transform modulus sum (WTMS) approach was proposed. In this paper, the applications of WTMS in image denoising, compressed image deblocking, and scalable image coding are described. They show that WSD is a valuable tool for image processing and has widespread applications.