On the Construction of Invertible Filter Banks on the 2-Sphere

The theories of signal sampling, filter banks, wavelets and "overcomplete wavelets" are well-established for the Euclidean spaces and are widely used in the processing and analysis of images. While recent advances have extended some filtering methods to spherical images, many key challenges remain. In this paper, we develop theoretical conditions for the invertibility of filter banks under continuous spherical convolution. Furthermore, we present an analogue of Papoulis's generalized sampling theorem on the 2-Sphere. We use the theoretical results to establish a general framework for the design of invertible filter banks on the sphere and demonstrate with examples of self-invertible spherical wavelets and steerable pyramids.

• Type: Journal
• Year: 2008
• Where: TIP
• Authors: B. T. Thomas Yeo, Wanmei Ou, Polina Golland
• Keywords: Continuous Spherical Convolution, Filter Banks, TIP 2008, Wavelets