The Wavelet Transform

• Introduction
• The continuous wavelet transform
• Examples of Wavelets
  • Morlet's Wavelet
    • Mexican Hat
• The discrete wavelet transform
  • Introduction
  • Multiresolution Analysis
  • The à trous algorithm
  • Pyramidal Algorithm
    • The Laplacian Pyramid
    • Pyramidal Algorithm with one Wavelet
  • Multiresolution with scaling functions with a frequency cut-off
    • The Wavelet transform using the Fourier transform
    • The Reconstruction
• Visualization of the Wavelet Transform
  • Visualisation of the first class
  • Visualisation of the second class
  • Visualisation of the third class
• Noise reduction from the wavelet transform
  • The convolution from the continuous wavelet transform
  • The Wiener-like filtering in the wavelet space
  • Hierarchical Wiener filtering
  • Adaptive filtering from the wavelet transform
  • Hierarchical adaptive filtering
• Comparison using a multiresolution quality criterion
• Deconvolution
  • Introduction
  • Regularization in the wavelet space
  • Tikhonov's regularization and multiresolution analysis
  • Regularization from significant structures
    • Regularization of Van Cittert's algorithm
    • Regularization of the one-step gradient method
    • Regularization of Lucy's algorithm
    • Convergence
• The wavelet context in MIDAS
  • Introduction
  • Commands Description
    • TRANSF/WAVE
    • RECONS/WAVE
    • HEADER/WAVE
    • INFO/WAVE
    • EXTRAC/WAVE
    • ENTER/WAVE
    • VISUAL/WAVE
    • VISUAL/CUB
    • VISUAL/CONT
    • VISUAL/SYNT
    • VISUAL/PLAN
    • VISUAL/PERS
    • FILTER/WAVE
    • COMPAR/WAVE
    • PLOT/SNR
    • PLOT/COR
    • DIRECT/WAVE
    • CITTERT/WAVE
    • GRAD/WAVE
    • LUCY/WAVE
    • TUTORIAL/WAVE
    • TRAN1D/WAVE
    • REC1D/WAVE