Two-dimensional Perfect Reconstruction Research Articles

Shift Unitary Transform for Constructing Two‐Dimensional Wavelet Filters

Due to the difficulty for constructing two‐dimensional wavelet filters, the commonly used wavelet filters are tensor‐product of one‐dimensional wavelet filters. In some applications, more perfect reconstruction filters should be provided. In this paper, we introduce a transformation which is referred to as Shift Unitary Transform (SUT) of Conjugate Quadrature Filter (CQF). In terms of this transformation, we propose a parametrization method for constructing two‐dimensional orthogonal wavelet filters. It is proved that tensor‐product wavelet filters are only special cases of this parametrization method. To show this, we introduce the SUT of one‐dimensional CQF and present a complete parametrization of one‐dimensional wavelet system. As a result, more ways are provided to randomly generate two‐dimensional perfect reconstruction filters.

Two-dimensional perfect reconstruction FIR filter banks with triangular supports

We present a theory and design of two-dimensional (2-D) perfect reconstruction (PR) filter banks (FBs) (PRFBs) in which the supports of the analysis and synthesis filters consist of two triangulars. The two-triangular FB can be realized by designing an appropriate 2-D complex prototype whose passband support is a triangle that is a half of a parallelepiped-shaped passband support defined by the sampling matrix. Then a complex prototype filter is modulated by the DFT, and each analysis filter is derived by taking the real part of the modulated output. We show that the two-triangular FB satisfies the condition of permissibility. A necessary and sufficient condition for 2-D PRFBs is derived. Moreover, we present a design method of the 2-D PRFB that minimizes the cost function consisting of the frequency constraint and PR condition. Finally, a design example is presented to confirm the validity of the proposed method.

Two-dimensional perfect reconstruction analysis/synthesis filter bank system with very high computational efficiency

An effective design structure for 2-D analysis/synthesis filter banks with high computational efficiency are proposed. The system involves a 2-D single-sideband (SSB) system, which is developed in terms of a 2-D separable weighted overlap-add (OLA) method of analysis/ synthesis and enables overlap between adjacent spatial domain windows. This implies that spatial domain aliasing introduced in the analysis is canceled in the synthesis process and provides perfect reconstruction. Achieving perfect reconstruction, each individual analysis/synthesis filter bank with SSB modulation is satisfied to be a cosine modulated version of a common baseband filter. Since a cosine-modulated structure is imposed in the design procedure, the system can reduce the number of parameters required to achieve the best computational efficiency. It can be shown that the resulting cosine-modulated filters are very efficient in terms of computational complexity and are relatively easy to design. Moreover, this design approach can be imposed on the system with relatively low reconstruction delays.

Theory of cosine-modulated two-dimensional perfect reconstruction filter banks

This paper considers a cosine-modulated, two-dimensional (2-D) perfect reconstruction (PR) filter banks theory. First, a 2-D digital filter with half-pass-band obtained by the sampling matrix had to be designed. Next, 2-D analysis filter banks are realized by cosine-modulating this prototype 2-D digital filter so that 2-D analyzed signals become real. It is shown that the modulation in the 2-D frequency plane is equivalent to 1-D modulation. A necessary and sufficient condition for 2-D perfect reconstruction filter banks is derived. If the polyphase filter pairs of the prototype filter doubly complement, the resulting 2-D filter bank satisfies the condition of perfect reconstruction.