Wreath products for image processing

We present a wreath product approach for matched filtering to detect rotated copies of a template in an image. We view the image as a homogeneous space for a wreath product, a noncommutative symmetry group. The corresponding Fourier analysis has a natural multiresolution structure and accompanying efficient algorithm which we explain and illustrate with an example. The associated matched filter is a new example of the use of a noncommutative convolution for image processing. Numerical experiments are described in which this noncommutative approach outperforms standard Fourier-based methods.