Wavelet Toolbox

Key Features

  • Standard wavelet families, including Daubechies wavelet filters, complex Morlet and Gaussian, real reverse biorthogonal, and discrete Meyer
  • Wavelet and signal processing utilities, including a function to convert scale to frequency
  • Methods for adding wavelet families
  • Lifting methods for constructing wavelets
  • Customizable presentation and visualization of data
  • Wavelet Design and Analysis app for continuous and discrete wavelet analysis
  • Wavelet packets, implemented as MATLAB objects
  • One-dimensional multisignal analysis, compression, and denoising
  • Multiscale principal component analysis
  • Multivariate denoising

Wavelet Toolbox authors are Michel Misiti, École Centrale de Lyon; Georges Oppenheim, Université de Marne-La-Vallée; Jean-Michel Poggi, Université René Descartes, Paris 5 Université; and Yves Misiti, Université Paris-Sud.

Applying Wavelet Methods

Wavelet methods provide functions and an app for analyzing, encoding, compressing, reconstructing, and modeling signals and images. They are useful in capturing, identifying, and analyzing local, multiscale, and nonstationary processes, enabling you to explore aspects of data that other analysis techniques miss, such as trends, breakdown points, discontinuities in higher derivatives, and self-similarity.

wa_wavelet_packet

Wavelet decomposition using wavelet packet analysis.

Wavelet Toolbox supports a full suite of wavelet analysis and synthesis operations. You can use it to:

  • Enhance edge detection in image processing
  • Achieve high rates of signal or image compression with virtually no loss of significant data
  • Restore noisy signals and degraded images
  • Discover trends in noisy or faulty data
  • Study the fractal properties of signals and images
  • Extract information-rich features for use in classification and pattern recognition applications
  • Perform multivariate denoising of signals with multiscale principal component analysis
wa_fingerprints

Image from the U.S. Federal Bureau of Investigation fingerprint database. The automatic thresholding feature of Wavelet Toolbox produces a compressed image with about 72% zeros and 98% of the original signal.

Analyzing Signals and Images

The Wavelet Design and Analysis app enables you to perform wavelet analysis, wavelet packet analysis, denoising, and compression on 1D and 2D signals. For 1D signals, you can:

  • Perform discrete wavelet analysis of signals
  • Perform continuous wavelet analysis of real signals using complex wavelets
  • Denoise signals
  • Estimate wavelet-based density
  • Perform wavelet reconstruction schemes based on various wavelet coefficient selection strategies
  • Randomly generate fractional Brownian motion
  • Perform 1D signal extension and truncation using periodic, symmetric, smooth, and zeropadding methods
  • Perform 1D signal clustering and classification using wavelet analyses (with Statistics Toolbox, available separately)

For 2D signals, you can:

  • Perform discrete wavelet analysis of images
  • Fuse two images
  • Perform translation-invariant denoising of images, using the stationary wavelet transform
  • Reconstruct wavelet schemes based on various wavelet coefficient selection strategies
Wavelet denoising, with instant visualization of the results.

Wavelet denoising, with instant visualization of the results. Threshold settings can be applied using the denoising and compression tools in the Wavelet Design and Analysis app.

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