Factoring two‐dimensional two‐channel non‐separable stripe filter banks into lifting steps

Abstract

Since the division with remainder cannot be implemented in multivariable polynomials, the two-dimensional non-separable wavelet transform cannot be lifted by using a similar way as that of univariate wavelet transforms. To solve this problem, a general lifting factoring method of two-dimensional two-channel non-separable stripe filter banks is presented. The constructing form of the polyphase matrices of the stripe filter banks is deduced and the general factoring of the polyphase matrices is given. Compared with the separable lifting wavelet transform, the proposed lifting factoring method can extract better texture information. The lifting form is more succinct than that of the tensor product lifting wavelet transform. The computation amount of the proposed factoring method for image decomposition is a quarter of the two-dimensional two-channel non-separable stripe filter bank and the original two-dimensional two-channel non-separable wavelet system is quickened. Moreover, the proposed lifting factorising method is faster than the traditional two-dimensional two-channel non-separable wavelet transform based on the Fourier transformation framework in which the size of each filter is greater than N + 1 . The proposed lifting factorising method has better sparsity than that of the original wavelet transform and the famous two-dimensional two-channel biorthogonal symmetric non-separable wavelet transform.