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access icon free Factoring two-dimensional two-channel non-separable stripe filter banks into lifting steps

  • Author(s): Bin Liu 1  and  Weijie Liu 2
    • View affiliations
  • Source: Volume 12, Issue 7, July 2018, p. 1185 – 1194
    DOI:  10.1049/iet-ipr.2017.0935 , Print ISSN 1751-9659, Online ISSN 1751-9667
© The Institution of Engineering and Technology
Received 26/08/2017, Accepted 18/02/2018, Revised 12/02/2018, Published 22/02/2018

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 . 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.

Inspec keywords: Fourier transforms; channel bank filters; matrix algebra; feature extraction; image filtering; image texture

Other keywords: image decomposition; univariate wavelet transforms; Fourier transformation framework; texture information extraction; multivariable polynomials; two-dimensional two-channel nonseparable wavelet system; two-dimensional two-channel biorthogonal symmetric nonseparable wavelet transform; two-dimensional two-channel nonseparable stripe filter bank factoring; two-dimensional nonseparable wavelet transform; general lifting factoring method; tensor product lifting wavelet transform; polyphase matrices

Subjects: Integral transforms; Algebra; Algebra; Filtering methods in signal processing; Integral transforms; Image recognition; Computer vision and image processing techniques

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