CSAIL Event Calendar: Previous Series
On the Construction of Invertible Filter Banks on the 2-Sphere
Speaker: Boon Thye Thomas Yeo , Medical Vision Group
Relevant URL: http://people.csail.mit.edu/ythomas/IFB_ICIP2006.pdf
The theories of signal sampling, filter banks, wavelets and steerable pyramids are well-established for the Euclidean spaces and 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 talk, we will present 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, which to the best of our knowledge, is the first generalized sampling theorem on the sphere. We use the two theoretical results to establish a general framework for the design of invertible filter banks on the sphere. We demonstrate with examples of self-invertible spherical wavelets and steerable pyramids.