Behind MR/Signal is MR, a set of software components developed by CEA (Saclay, France) and Nice Observatory. This project originated in astronomy, and involved the development of a range of innovative methods built around multiscale analysis. Multiresolution techniques have been developed in recent years, and furnish a powerful and insightful representation of the data. By means of multiresolution or multiscale analysis, a signal can be decomposed into a set of signals (or scales), each scale containing only structures of a given size. This data representation, associated with noise modeling, has been applied to very different applications such as data filtering, deconvolution, compression, feature detection, and so on. Results are enhanced in all such processing because the multiresolution approach allows a better understanding of how the data values are distributed in a signal, and how the signal can be separated from the noise.
Documentation on MR is available as PDF files at the address http://www.multiresolution.com Background references are: JL Starck, F Murtagh and A Bijaoui, Image and Data Analysis: The Multiscale Approach, Cambridge University Press, 1998; and JL Starck and F Murtagh, Astronomical Image and Data Analysis, Springer-Verlag, 2002. A large number of published articles are also available: see www.multiresolution.com for details.
The programs themselves are written in C++. They are provided as executables. All functionality is available for signals of length 512. Signals of greater length are supported if a license file is available. The graphical user interface is not license-protected. So, at a minimum, you can at all times use it to carry out processing on any signal of length 512.
Various data formats are supported: a text format with a single column of data values, one per line, with file extension .dat; a .csv format, allowing comma separated fields (e.g. a date field preceding the data value: the date itself is not taken into account) which is readable by Microsoft Excel; and the astronomy FITS (Flexible Image Transport System) binary file format.
If you wish to run MR programs in batch mode (for example, filtering,
followed by prediction) then the
programs can be accessed independently of the MR1D graphical
user interface. All programs can be run in a command prompt or DOS
window. Typically a program has a set of options (with defaults in all
cases), an input signal file, an output signal file. To see these options,
just give the command name in the command prompt or DOS window.
License Installation
Contact info@multiresolution.com to get a license. Other than the fact that
you are using a Windows PC and that you are using this software, you
will need to provide your PC identifier (see menu item under "File") and
the period of validity of your use of the software ("unlimited" or a
date). This will allow a 20-character key to be generated.
Under menu item "File"/"Register License", give your expiry date (or "unlimited") and the 20-character key. This allows your license file to be created.
The licensing works as follows.
A license file is created, called "cea_lic". This is a text file
(with no extension). This file is located in (or copied into)
the bin subdirectory where you installed the programs.
Sample Signals
A range of sample signals are provided, in different formats.
The futures512 data is of length which is acceptable for processing
without a license. Other data are related to FTSE-100 values,
euro and US dollar foreign exchange rates, Nile river
levels, Mississippi water levels, eye-gaze tracking data,
and sunspot occurrences.
File Management
PC ID: Determine your computer's host identifier
(Program used: mrhost*)
The 3-character identifier is used to generate a license key (which is
used from the text file called cea_lic).
Take Part of Signal
Extract a subset or interval from the displayed signal.
Export Signal As...
Supported formats: .DAT, .CSV, .FITS.
Install License
You need to provide your PC identifier (see above) and the expiry
date (or "unlimited") to Multi Resolutions. You will be given a 20-character
key which must be entered, in conjunction with the expiry date. This sets
up the license file (located with the executable programs).
Filtering
Signal Statistics (Program used: im1d_info)
Autocorrelation function for a given number of lags, and autoregressive
model fit with AIC, AICC or BIC model fit criteria.
Multiresolution Transform (Program used: mr1d_trans)
A large number of wavelet and other (e.g. multiresolution
median, multiresolution morphological) multiresolution transforms.
The output is saved to file, for display in Excel or other processing.
One signal is displayed: it is either a single user-selected scale,
or a combination of scales approximating the input signal.
Multiresolution Filtering (Program name: mr1d_filter)
Filtering in wavelet transform space, and rebuilding the cleaned up signal.
A very wide range of wavelet and other multiresolution transforms is
supported. In addition, a wide range of noise models is supported. For
full details, the MR documetation should be consulted (available at
http://www.multiresolution.com).
Multiresoluton Entropy Filtering (Program name: mw1d_filter)
The program filters a signal using the multiscale entropy method
(N2-MSE approach). An entropy measure is used to balance signal and
noise and, in this framework, noise is optimally determined and
removed.
Prediction
Nowcast (Program name: mr1d_nowcast)
Based on a B3 spline à trous wavelet transform, and
a number of alternative noise models, estimate significant scalewise
change in movement.
Trend (Program used: im1d_tend)
Estimate the signal trend.
Forecast (Program used: mr1d_fcast)
Based on a B3 spline à trous wavelet transform,
determine an autoregressive model fit, to the signal, per scale or
taking account of multiresolution scale-based sampling. Model fit
can use AIC, AICC or BIC criteria. Signal non-stationarity can be taken
into account. A user-specified number of values is predicted and
displayed in different color.
Multiresolution
Multiresolution Transform (Program used: mr1d_transform)
A wide range of wavelet and other multiresolution transforms, with
plotting of one scale or reconstruction of the signal. The transform
itself is saved to file, for display or processing in Excel or other
system.
Autocorrelation Function (Program used: mr1d_acor)
Based on a B3 spline à trous wavelet transform,
determine and display the autocorrelation function.
Multifractal
Devil's Staircase (Program used: mf1d_create_ds)
Create a Devil's Staircase fractal signal.
Multifractal Analysis (Programs used: mr1d_chain, mf1d_repart and
mf_analyse)
Carry out a multifractal analysis and plot scaling exponents and
the singularity spectrum.
Trouble Shooting