Design of multi-parameter steerable functions using cascade basis reduction

A new cascade basis reduction method of computing the optimal least-squares set of basis functions to steer a given function is presented. The method combines the Lie group-theoretic and the singular value decomposition approaches such that their respective strengths complement each other. Since the Lie group-theoretic approach is used, the set of basis and steering functions computed can be expressed in analytic form. Because the singular value decomposition method is used, this set of basis and steering functions is optimal in the least-squares sense. Most importantly, the computational complexity in designing basis functions for transformation groups with large numbers of parameters is significantly reduced. The efficiency of the cascade basis reduction method is demonstrated by designing a set of basis functions to steer a Gabor function under the four-parameter linear transformation group.