MR/1 is 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. The MR/1 software components include almost all applications presented in the book Image and Data Analysis: the Multiscale Approach . Descriptions of these applications can also be found in many published papers . The goal of MR/1 is not to replace existing image processing packages, but to complement them, offering the user a complete set of multiresolution tools. These tools are executable programs, which work on a wide range of platforms, independently of current image processing systems. They allow the user to perform various tasks using multiresolution, such as wavelet transforms, filtering, deconvolution, and so on. Programs can also be called from a Java interface. A set of IDL (Interactive Data Language, by Research Systems Inc.) and PV-Wave (Visual Numerics Inc.) routines are included in the package which interface the executables to these image processing packages. MR/1 is an important package, introducing front-line methods to scientists in the physical, space and medical domains among other fields; to engineers in such disciplines as geology and electrical engineering; and to financial engineers and those in other fields requiring control and analysis of large quantities of noisy data.

Wavelet and Multiscale Transform

Many 1D and 2D wavelet transforms and other multiscale methods, such the Pyramidal Median Transform or the lifting scheme, have been inplemented in MR/1 .

Noise Modeling

Our noise modeling in the wavelet space is based on the assumption that the noise in the data follows a distribution law, which can be:

a Gaussian distribution

a Poisson distribution

a Poisson + Gaussian distribution (noise in CCD detectors)

Poisson noise with few events (galaxy counts, X-ray images, point patterns)

Speckle noise

Correlated noise

Root Mean Square map: we have a noise standard deviation of each data value.

If the noise does not follow any of these distributions, we can derive a noise model from any of the following assumptions:

it is stationary, and we have a subimage containing a realization of the noise,

it is additive, and non-stationary,

it is multiplicative and stationary,

it is multiplicative, but non-stationary,

it is undefined but stationary,

it is additive, stationary, and correlated.

Applications

Descriptions of these applications can also be found in many published papers .

General tools: data conversion, simulation, statistic, Fourier analysis, mathematical morphology, principal component analysis, …

1D and 2D wavelet transform and reconstruction.

Multiscale object manipulation: statistic, band extraction, comparison, …

Multiresolution support detection.

1D and 2D filtering taking into account the different noise models. Many methods have been implemented (11 in 1D and 18 in 2D) including standards like K-Sigma thresholding, SURE, MAD, Universal thresholding, Multiscale Wiener filtering, …

Image background subtraction.

Image deconvolution: nine standard deconvolution methods are available (MEM, Lucy, Landweber, MAP, …), and five wavelet based methods.

Image registration.

Lossy and lossless image compression. the PMT (median based compression method) and the bi-orthogonal wavelet transform allows both the user to reconstruct an image (or a part of an image) at a given resolution. Lossless image compression is based on the lifting scheme.

Object detection and extraction in 1D and 2D data set using the Multiscale Vision Model.

Edge detection and image reconstruction from the multiscale edges. Many standard edge detection methods are available (15) and two wavelet based methods.

1D Wavelet Transform Modulus Maxima (WTMM) representation and reconstruction.

1D Multifractal analysis.

Examples

Many examples can be found at www.multiresolution.com.