Software

Variance of Tight Framelet Feature (VTFF)

Programming Language: MATLAB


Introduction:

A Noise Robustness Focus Measure Based on Tight Framelet Features

Related Papers:

  • Li Y.-R., Liu J., Ye Z., Shen L., and Zhuang X. A Noise Robustness Focus Measure Based on Tight Framelet Features.


    • Code Download: Focus Measure


    Appendix: VTFF

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    Multilevel non-stationary tight framelets for image restoration (MNTF)

    Programming Language: MATLAB


    Introduction:

    Regularization with multilevel non-stationary tight framelets for image restoration

    Related Papers:

  • Li Y.-R., Chan R. H., Shen L., and Zhuang X. Regularization with multilevel non-stationary tight framelets for image restoration. Applied and Computational Harmonic Analysis, 53 : 332-348 (2021).


    • Download: TNTF

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    Directional 3D Haar tight framelets

    Programming Language: MATLAB


    Introduction:

    Directional 3D Haar Tight Framelets.

    Related Papers:

  • Han B., Li T., and Zhuang X. Directional compactly supported box spline tight framelets with simple geometric structure, Applied Mathematics Letters. 91: 213 - 219 (2019).


    • Download: D3HaarTransforms

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    Directional Compactly Supported Tensor Product Complex Tight Framelets

    Programming Language: MATLAB


    Introduction:

    Directional compactly supported tensor product complex tight framelet filter banks and applications

    Related Papers:

  • Han B., Mo Q., Zhao Z., and Zhuang X. Directional Compactly Supported Tensor Product Complex Tight Framelets with Applications to Image Processing.


    • Download: cptTPCTF

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    Directional Bandlimited Tensor Product Complex Tight Framelets

    Programming Language: MATLAB


    Introduction:

    Directional bandlimited tensor product complex tight framelet filter banks and applications

    Related Papers:

  • Han B., Zhao Z., and Zhuang X. (2016) Directional tensor product complex tight framelets with low redundancy.


    • Download: bdTPCTF

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    Digital Affine Shear Filter Banks with 2-Layer Structure

    Programming Language: MATLAB


    Introduction:

    The digital affine filter banks with 2-layer structure and Theire applications.

    Related Papers:

  • Che, Z. and Zhuang, X. (2017) Digital affine shear filter banks with 2-layer structure..


    • Download: DAST-2

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    Digital Affine Shear Transforms

    Programming Language: MATLAB


    Introduction:

    The digital affine shear transform and its applications.

    Related Papers:

  • Zhuang, X. (2015) Digital affine shear transforms: fast realization and applications in image/video proccessing.


    • Download: DAST

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    ShearLab

    Programming Language: MATLAB


    Introduction:

    The digital shearlet transform and its applications.

  • PPFT: the pesudo-polar Fourier transform.
  • Weighting: weighting (preconditoning) on the pseudo-polar grid.
  • Windowing: digtial shearlet windowing on the pseudo-polar grid.
  • Denosing: application on denosing.


    • Related Papers:

  • Donoho, D.L., Kutyniok, G., Shahram, M., and Zhuang, X. (2010) A rational design of a digital shearlet transform. The 9th International Conference on Sampling Theory and Applications, Singapore, 2011.

  • Kutyniok, G., Shaharm, M., and Zhuang, X. (2012) ShearLab: A rational design of a digital parabolic scaling algorithm. SIAM Journal on Imaging Sciences. 5 (4):1291-1332.


    • Download: Please go to WWW.SHEARLAB.ORG for more details and updated version.

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    Wavelet Construction Package (Univariate, Almost Complete)

    Programming Language: MAPLE 10.0


    Introduction:

    This package contains rotinues developed for the design of univariate wavelets, multiwavelets, framelets, multiframelets having desirable properties such as symmetry, (bi)orthogonality, sum rule condition, vanishing moments, linear phase moments, and so on. This package contains the following subpackages, which are being developed or under development.

  • D1Utilities: commonly used rutines.
  • D1MatOrthExt: matrix extension with symmetry.
  • D1MatOrthExtAlgQ: matrix extension with symmetry in algebraic number fields.
  • D1DualChain: top-down and bottom-up dual chains construction of biorthogonal wavelets.
  • D1IntpFuncVect: interpolating function vectors.
  • D1MatBiorthExt: matrix extension with symmetry for birothogonal multiwavelets.
  • D1Complex: construction of complex tight framelets.
  • D1CBC: coset-by-coset construction of biorthogonal multiwavelets developed by Professor Bin Han, see here.
  • D1CriticalExponentV2.txt: the L2 smoothness of a mask.

    • For more details, see the help document in HTML format in this website or download maple .mws file format here.

    Related Papers:

  • Chui, C. K., Han, B., and Zhuang, X. (2010) A dual-chain approach for bottom-up construction of wavelet filters with any integer dilation.
  • Zhuang, X. (2010) Matrix extension with symmetry and construction of biorthogonal multiwavelets.
  • Zhuang, X. (2010) Construction of symmetric complex tight d-wavelet frames from pseudo splines via matrix extension with symmetry.
  • Zhuang, X. (2010) Matrix extension with symmetry and its applications. Approximation Theory XIII (San Antonio, TX, 2010), Springer.
  • Han, B. and Zhuang, X. (2010) Matrix Extension with symmetry and its applications to symmetric orthonormal multiwavelets. SIAM Journal on Matrix Analysis and Applications. 42(5): 2297-2317.
  • Han, B., Kwon, S. G. and Zhuang, X. (2009) Generalized interpolating refinable function vectors. Journal of Computational and Applied Mathematics. 227: 254-270.
  • Han, B. (2003) Vector cascade algorithms and refinable function vectors in Sobolev spaces, Journal of Approximation Theory, 124(1): 44-88.

    • Download: click HERE to download.

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    The L2 Critical Exponent of Masks

    Programming Language: MATLAB


    Introduction:

    Compute the L2 critical exponent of a matrix mask in 1D and 2D.

  • D1CriticalExponentV2: the L2 critical exponent of a mask (univariate).
  • D2CriticalExponentV2: the L2 critical exponent of a mask (bivariate).


    • Related Papers:

  • Bin Han, Vector cascade algorithms and refinable function vectors in Sobolev spaces , Journal of Approximation Theory, Volumn 124 (2003), Issue 1, 44-88.

    • Download:click HERE to download.

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    Plotting Graphs of Wavelet Masks

    Programming Language: C


    Introduction:

    Plot the graphs of wavelet masks in 1D and 2D.

  • plot1dvec: plot graphs of a mask (univariate).
  • plot2dvec: plot graphs of a mask (bivariate).


    • Related Papers:


    Download:click HERE to download.

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