Invertible Filter Banks on the 2-Sphere

Multiscale filtering methods, such as wavelets and steerable pyramids, are widely used in processing and analysis of planar images and promise similar benefits in application to spherical images. While recent advances have extended some filtering methods to the sphere, many key challenges remain. In this paper, we develop conditions for the invertibility of spherical filter banks for both continuous and discrete convolution and illustrate how such conditions can be incorporated into the design of self-invertible axis-symmetric wavelets. Self-invertibility is particularly desirable when modifying images in the wavelet domain.