Image processing using singularities and wavelets

The paper develops a singularity image model as an alternative to linear models for processing many complicated but important images. The model is effective because it provides image characterization, image decomposition, and image reconstruction. For a given measure, one can nonlinearly transform an image into a singularity domain, where each pixel has a singular coefficient. For everywhere singular images, the coefficients are equivalent to fractal dimensions. The image can be decomposed (or partitioned) into subimages such that pixels in each subimage have the same singularity coefficients. Since each subimage is fractal, the overall image can have singularity spectrum. For a wavelet-based measure, it is possible to reconstruct the image from the singularity information. The paper shows application examples including image denoising, image compression, and analysis of natural and biomedical images