Extended conjugate polar fourier transforminconvolution network
This paper proposes an extended conjugate polar Fourier transform (ECPFT), to design iterated radial filter bank (RFB) and directional filter bank (DFB) convenient for accurate multiscale and multidirectional decomposition in discretization over a convolution network. With conjugated symmetric form, ECPFT would convert complex directional wavelets in original spatial domain to real ones in the inverse Fourier domain of ECPFT. Furthermore, it can contribute to changing the design of nonseparable RFB and DFB to decomposition in scales and directions with 1-D filter bank in each dimension separably in the ECPFT domain. The generated properties of conjugate symmetry and periodicity of 2π in both angular and radial dimensions, also guarantee convolution and sampling operations in both dimensions within the inverse Fourier domain of ECPFT. The fast algorithm for discretization is developed to reduce complexity.