Software and Images

Chapter 2, The Wavelet Transform, Guided Numerical Experiments

  1. dwtdemo.m, demo of the 2D biorthogonal Discrete Wavelet Transform.
  2. cwtdemo.m, demo of the Continuous Wavelet Transform using a 1D signal.
  3. wpdemo.m, demo of the 2D wavelet packet transform.
  4. WaveLab 850, Matlab functions for wavelet analysis. Link to WaveLab 850 site. See too for Lena and Einstein images.
  5. CWT of a 1D piecewise smooth signal (Matlab code from section 2.9.2)
  6. Nonlinear approximation by DWT (Matlab code from section 2.9.3)
  7. Nonlinear approximation by wavelet packets (Matlab code from section 2.9.4)

Chapter 3, Redundant Wavelet Transform, Guided Numerical Experiments

  1. einstein.bmp, Einstein image.
  2. Denoising by UWT, undecimated wavelet transform (Matlab code from section 3.9.1)
  3. IDL Astronomical User Library. Link to IDLAstro site. See inter alia for FITS image format reading and writing.
  4. ngc2997.png, image of galaxy NGC 2997.
  5. HaleBopp256.fits, Hale-Bopp image.
  6. opthalmic.png, ophthalmology image.
  7. star1d.pro, starlet transform of a 1D signal.
  8. istar1d.pro, 1D signal reconstruction from its starlet transform.
  9. umt_ex.pro, simulate a 1D signal, add noise, and perform a starlet transform, a multiscale median transform and a median-wavelet transform on it.
  10. star_ex.pro, demo of transforms with the NGC 2997, Hale-Bopp and ophthalmology images.
  11. star2d.pro, starlet transform of a 2D image.
  12. istar2d.pro, 2D image reconstruction from its starlet transform.
  13. star2d_drc.pro, dynamic range compression using the starlet transform of an image.
  14. Dynamic range compression using the starlet transform (IDL code from section 3.9.2)

Chapter 4, Nonlinear Multiscale Transforms, Guided Numerical Experiments

  1. umt1d.pro, undecimated median transform of a 1D signal.
  2. umt2d.pro, undecimated median transform of a 2D image.
  3. Starlet, multiscale median, and median-wavelet transforms (IDL code from section 4.5.1)
  4. glitch.fits, image used in Fig. 4.3.

Chapter 5, The Ridgelet and Curvelet Transforms, Guided Numerical Experiments

  1. CurveLab, Curvelet Transform in Matlab. (Link to curvelet.org site.)
  2. For WaveLab 850, Matlab code for wavelet analysis, see Chapter 2 above.
  3. Matlab code comparing DCTG2 and UWT, the Second Generation Discrete Curvelet Transform and the Undecimated Wavelet Transform (Matlab code from section 5.6.2)
  4. Matlab code for denoising using DCTG2, Second Generation Discrete Curvelet Transform (Matlab code from section 5.6.3)
  5. fdctdemo.m, NLA demo with the DCTG2.

Chapter 6, Sparsity and Noise Removal, Guided Numerical Experiments

  1. DBlockToolbox100, a collection of Matlab programs that implements 2D block denoising under Gaussian noise. (Gzipped, tar file, for expansion when downloaded.)
  2. ImageJ, Image Processing and Analysis in Java site at the National Institutes of Health, for image used in Fig. 6.8.
  3. Matlab code discussed in section 6.7.1: the script Scripts/blockgenfigvisual.m available in the DBlockToolbox100.
  4. den2dTIdemo.m, translation-invariant denoising by the UWT and DWT.
  5. den2dfdctdemo.m, denoising by the DCTG2 and UWT.

Chapter 7, Linear Inverse Problems, Guided Numerical Experiments

  1. SplittingSolvers, a collection of Matlab programs that implements monotone operator splitting for solving sparsity-regularized linear inverse problems. (Gzipped, tar file, for expansion when downloaded.)
  2. Matlab code discussed in section 7.5.1: the script 1D/Demos/testsApprox1DEx7.m in the SplittingSolvers toolbox.
  3. Matlab code discussed in section 7.5.2: the script 1D/Demos/testsDeconv1D.m in the SplittingSolvers toolbox.

Chapter 8, Morphological Diversity, Guided Numerical Experiments

  1. MCALab, Signal and Image Decomposition and Inpainting. (Link to MCALab site.) For architecture of the MCALab Package, see section 8.8.2.
  2. All figures in the book in sections 8.6.5 (texture and cartoon separation), 8.7.4 (inpainting) and 8.8.7 (including the cleaning of an EEG signal from fMRI magnetic resonance contamination, and composite riser signal cleaning in oil exploration) can be reproduced using the MCALab software. Refer to Table 8.1 for the parameters used in creating the figures.

Chapter 9, Sparse Blind Source Separation, Guided Numerical Experiments

  1. GMCALab100, a collection of Matlab programs that implements Generalized Morphological Component Analysis for sparsity-regularized multichannel signal/image bind source separation. (Gzipped, tar file, for expansion when downloaded.)
  2. Matlab code discussed in section 9.10.1: the script sparse_noisy_examples.m in the GMCALab package.

Chapter 10, Multiscale Geometric Analysis on the Sphere, Guided Numerical Experiments

  1. HEALPix software for pixelization, hierarchical indexation, synthesis, analysis, and visualization of data on the sphere. (Link to sourceforge.net site.)
  2. HEALPix home page. (Link to healpix.jpl.nasa.gov site.)
  3. MRS: Multi-Resolution on the Sphere, IDL software and documentation. (Link to external site.)
  4. Image mars_topo_mola_hpx_128.fits, Mars image. (For FITS image format handling, see IDL Astro library under Chapter 3 above.)
  5. Image earth_healpix_128.fits, earth image.
  6. Image sync_res128.fits, synchrotron image.
  7. Undecimated wavelet transform on the sphere, (IDL code from section 10.9.2)
  8. Pyramidal wavelet transform on the sphere, (IDL code from section 10.9.3)
  9. Denoising on the sphere using wavelet, curvelet and combined transforms, (IDL code from section 10.9.4)

Chapter 11, Compressed Sensing, Guided Numerical Experiments

  1. See the SplittingSolvers Matlab package used in Chapter 7.
  2. Matlab code discussed in section 11.8, with results in Table 11.3: the script 1D/Demos/testsCS1times.m in the SplittingSolvers package.
  3. Matlab code also discussed in section 11.8 and used for Figure 11.3: the script 2D/Demos/testsCS2DimplicitEx2.m in the SplittingSolvers package.

End