What Is the IDL Wavelet Toolkit?

The IDL Wavelet Toolkit consists of a set of graphical user interfaces (GUI) and IDL routines for wavelet analysis of multi-dimensional data.

Motivation

Wavelet analysis is becoming a popular technique for data and image analysis. By decomposing a signal using a particular wavelet function, one can construct a picture of the energy within the signal as a function of both spatial dimension (or time) and wavelet scale (or frequency). The wavelet transform is used in numerous fields such as geophysics (seismic events), medicine (EKG and medical imaging), astronomy (image processing), and computer science (object recognition and image compression). The technique is flexible and robust, yet it is fast enough to be used in real-time image processing.

A set of standard wavelet techniques have been developed which make it possible for the average user to apply the wavelet method with confidence. Recent advances in significance testing and cross-wavelet analysis have also enhanced the acceptability of wavelet analysis within the scientific community. Nevertheless, the calculation of the wavelet transform and the display of the output requires considerable experience.

Users

The IDL Wavelet Toolkit is designed for a wide audience, ranging from the casual user who wishes to explore the possibilities of wavelet analysis, to the scientist or engineer who wants to produce robust and complex results.

Potential users and their applications include:

Students— introduction to wavelets, graphical analysis;

Engineers— data analysis, signal processing, data compression;

Scientists— data analysis, filtering and denoising, cross-wavelet;

Computer scientists— image compression, speed of operations;

Mathematicians— explore wavelet families, test out new analysis techniques.

Applications

Examples of specific applications are:

Time-series analysis— time-scale power spectrum, noise filtering, multiresolution analysis;

Self-similar series— fractals, long-memory processes;

Turbulence— detection of coherent structures;

Signal processing— filtering and denoising;

Image processing— edge detection, compression, enhancement.

Features

The IDL Wavelet Toolkit has the following features:

Wavelet Applet

The Toolkit Applet lets you manage your projects, import data and wavelets, visualize the results, and add your own user tools.

Continuous Wavelet Transform

Allows you to compute the continuous wavelet transform on one-dimensional vectors. This routine is written in IDL .pro code.

Discrete Wavelet Transform

Allows you to compute the discrete wavelet transform (partial or full) on multi-dimensional data. These routines are written in C and contained in the IDL wavelet dlm.

Wavelet Functions

The Toolkit comes with several wavelet functions that are accessible both inside the Applet and from your own programs. You can easily add your own wavelet functions to the Toolkit.

3D Wavelet Power Spectrum

Callable from within the Applet and from your own programs, the visualizer plots the wavelet power as a three-dimensional surface, with optional contour lines. You can rotate, translate, and find the power at a particular location.

Multiresolution Analysis

Stand alone or callable from the Applet, this routine produces plots for the smooth (low pass), detail (band-pass), and rough (high-pass) components of your data.

Denoise Tool

This widget tool enables you to denoise your vector or image array by thresholding (hard or soft) either by cumulative power or coefficient number.

Dataset Viewer

Manage the datasets within each project by importing new data, viewing data values, and customizing the data fields.

Import Data

You can import data from a variety of file formats: ASCII, binary, image (BMP, JPEG, PNG, PPM, SRF, TIFF, DICOM), and WAV audio. Image files can be either indexed color (8- or 16-bit) or TrueColor (24-bit). You can also import data directly from the IDL> command prompt.