Properties for perfect reconstruction using multirate linear phase two-dimensional nonseparable filter banks and its implementation

Abstract

Nonexpansive symmetric extension is preferred over merely periodic extension because it leads to far fewer losses in boundaries and edges after compression. The generalization of the results in 1-D cases to arbitrary nonseparable multidimensional cases remain open problem. By properly classifying the symmetry of finite-supported 2-D signals and filters, we study the properties of decimation, interpolation, and convolution in the two-band nonexpansive symmetric extension of 2-D nonseparable filters, where the quincunx sampler and diamond-shaped linear phase filters are considered and the conditions for retaining symmetry during various operations are obtained, which are prerequisites for perfect reconstruction. According to these properties, we sketch out a detailed procedure for implementation and test its correctness on the real image. The strategies and results can be generalized for applications in dimensions higher than two.