Software Maarten Jansen

• ThreshLab: Matlab algorithms for sparse models (wavelets, multiscale local polynomials) and sparse model selection

  Version 6.1.3, released June 2024

  • Multiscale transforms for sparse data representations
    • First generation discrete wavelet transforms (DWT)
      • 1D (equispaced signals), 2D (images)
      • Fast (FWT - critcally downsampled) - Redundant - Nondecimated (RWT, aka cycle spinning, stationary WT, translation-invariant, a-trous, maximum overlap)
      • Orthogonal (Coiflet, Daubechies, Haar, Symmlet) - Biorthogonal (CDF spline, CDF with less dissimilar lengths)
    • Second generation discrete wavelet transforms (lifting) for nonequispaced data (ThreshLab2)
      • 1D Deslauriers-Dubuc wavelets (i.e., multiscale interpolating polynomial prediction), average interpolating prediction
      • 1D, CDF spline wavelets on nonequispaced knots
      • 1D wavelets based on broken basis refinement (i.e., generalised B-spline construction)
      • 1D, 2D, multiscale kernel and local polynomial transforms (MLPT) (cfr. Laplacian pyramid)
      • 2D transforms for scattered data
    • Wavelets for specific models and applications
      • Wavelet-Fisz or CVS - Conditional Variance Stabilisation for Poisson data
      • Continuous Unbalanced Haar Transform for Change Point Detection
  • Thresholds and other sparse variable selection methods
    • Variable selection and estimation routines based on thresholds
      • Soft and Hard thresholding
      • Iterative soft- and hard-thresholding with step dependent thresholds for inverse problems
      • Lasso
    • Threshold and model size assessment
      • Exact Risk or PE - Prediction Error (for soft- and hard thresholding)
      • SURE - Stein Unbiased Risk Estimator (for soft- and hard thresholding)
      • GCV - Generalized Cross Validation, (for soft- and hard thresholding)
      • Ebayesthresh (Bayesian model)
    • Structured/grouped variable selection
      • Best subtree selection

  • Other routines
    • MRF - Markov Random Fields (geometrical prior for Bayesian image denoising)

  Also see these test images
  

• Additional software

  • LiftVor

    Liftvor is a matlab implementation of the routines discussed in
    M. Jansen, G. Nason, and B. Silverman. Multiscale methods for data on graphs and irregular multidimensional situations. Journal of the Royal Statistical Society, series B, 71(1), pages 97-125, 2009.
    
    This software uses ThreshLab routines, so install ThreshLab first, then unzip this file
    
    This software is not maintained actively. The ultimate goal is (of coarse; and obviously when time permits, i.e., after my retirement, I guess) to fully integrate this into ThreshLab. Sorry for possible inconveniences
    
    The file testfileLiftVor.m is a test routine which may help you navigating through the set of files
    
    There is also R software for this paper. The R software is not a mere translation of the matlab version (or vice versa). Check with Guy Nason for more info.
  
  

• See publication list for more info