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