FRACTIONAL SPLINE WAVELET SOFTWARE FOR MATLAB
Thierry Blu
The Chinese University of Hong Kong
June 2014
A. TEST PROGRAMS
DEMO1D: Demonstration program that exemplifies the use of the 1D Fractional Spline Wavelet transform
and the associated helper functions
DEMO2D: Demonstration program that exemplifies the use of the 2D Fractional Spline Wavelet transform
and the associated helper functions
B. CORE WAVELET TRANSFORM FUNCTIONS
FFTFRACTSPLINEFILTERS: Computes the frequency responses of the wavelet analysis and synthesis filters
(lowpass and highpass) for various types ('ortho','bspline','dual') of orthonormal or semi-orthonormal
fractional spline wavelet transforms, and for various parameters (alpha,tau) as described in Ref. [3].
FFTWAVELETANALYSIS1D : Performs an FFT-based computation of the 1D wavelet transform of a signal to a given depth J.
FFTWAVELETSYNTHESIS1D: Performs an FFT-based computation of the 1D inverse wavelet transform.
FFTWAVELETANALYSIS2D : Performs an FFT-based computation of the 2D wavelet transform of an image to a given depth J.
FFTWAVELETSYNTHESIS2D: Performs an FFT-based computation of the 2D inverse wavelet transform.
C. OTHER ROUTINES
WEXTRACT1D : Extraction of a subband of a 1D wavelet transform.
WAVELETPLOT1D: Show the 1D wavelet transform as several staged plots.
WEXTRACT2D : Extraction of a subband of a 2D wavelet transform.
WAVELETPLOT2D: Show the 2D wavelet transform using a standard quadrant image.
FRACTSPLINEFUNCTION : Computes a scaling function with the input (alpha,tau) parameters
FRACTSPLINEWAVELETFUNCTION: Computes a wavelet function with the input (alpha,tau) parameters
FRACTSPLINEAUTOCORR: Frequency domain computation of fractional spline autocorrelation function.
References:
[1] Unser, M. & Blu, T.,"Fractional Splines and Wavelets", SIAM Review, Vol. 42 (1), pp. 43-67, March 2000.
[2] Blu, T. & Unser, M.,"The Fractional Spline Wavelet Transform: Definition and Implementation", Proc. IEEE International
Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), Istanbul, Turkey, Vol. {I}, pp. 512-515, June 5--9, 2000.
[3] Blu, T. & Unser, M.,"A Complete Family of Scaling Functions: The $($-Fractional Splines", Proc. IEEE International
Conference on Acoustics, Speech, and Signal Processing (ICASSP'03), Hong Kong, China, Vol. {VI}, pp. 421-424, April 6--10, 2003.
Demo at http://bigwww.epfl.ch/demo/jfractsplinewavelet/