Rotation of foveated image in the wavelet domain

An advantage of wavelet transform is its efficiency in representing natural images, that is, a natural image can be accurately represented by only a small number of retained wavelet coefficients. It is interesting to know whether some common image operations, e.g., rotation, can be performed very fast in wavelet domain. Preferably, the running time should depend only on the number of retained coefficients, not the size of the original image. However, it is not clear how this can be achieved. In this paper, we consider rotation and images with a special structure: foveated images. Wavelet coefficients of a foveated image vanish outside an arrangement of circles. We exploit this structure to derive algorithms that accurately approximate rotation. The running time is Θ(m) where m is the number of retained coefficients. Experiments show the accuracy of the approximation.