Separable Complex-Valued Graph Filter Banks for Graph Signals

Abstract

This paper proposes the design of orthogonal and biorthogonal separable complex-valued filter banks on graphs. The proposed filter banks adopt the structure of two channel real-valued filter banks on graphs, and the filters in it are designed as separable complex filters composed of existing real filters. In this paper, the orthogonal complex-valued filter banks satisfying aliasing cancellation, perfect reconstruction and orthogonality, and the biorthogonal complex-valued filter banks satisfying aliasing cancellation and perfect reconstruction are stated respectively. The real filters based on Bernstein polynomial with good performance are selected in the final simulation to construct the complex filter banks. Instead of designing filters directly in complex valued domain, this method can avoid the complex operation of the complex valued domain. Both the amplitude and phase of the complex wavelet coefficients of the complex filter banks can describe the edge structure of the image, which can be used in applications such as image edge detection.