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1. Introduction
The recent development of more sophisticated remote sensing systems enable the measurement of radiation in many more spectral interval than possible previously. An example of this technology is the AVIRIS system, which collects image data in 220 bands.

The increased dimensionality of such hyperspectral data provides a challenge to the current techniques for analyzing such data.

Supervised classification techniques use labeled samples in order to terrain the classifier. Fukunaga(1989) proved that the required number of training samples is linearly related to the dimensionality for a linear classifier and to the square of dimensionality for a quadratic classifier. It has been estimated that as the number of dimensions increases the training samples size need to increases exponentially in order to have an effective estimate of the multivariate densities needed to perform a non-parametric classification.

This suggests the need for reducing the dimensionality via a preprocessing method, which takes into consideration high dimensional spaces properties. Dimension reduction is the transformation that brings data from a high order dimension to a low order dimension, similar to lossy compression method, dimension reduction reduced the size of the data but unlike compression, dimension is applicant-driven.

A number of techniques have been developed to reduce dimensionality. One of these techniques is Principle Component Analysis (PCA) .PCA is effective at compression information in multivariate data sets by computing orthogonal projections that maximize the amount of data variance. It is typically performed through the egin-decompositopn of the spectral covariance matrix of an image cube.

The information can then be presented in the form of component images, which are projections of the image cube on to the eigenvectors, the component images corresponding to the large eigenvalues are presumed to preserve the majority of the information about the scene. Unfortunately information content in hyperspectral images dose not always coincide with such projections for several reasons.

1) PCA is optimal when the background associated with signal sources is Gaussian white noise. This is often not the case in hyperspectral images, where the clutter includes contributions from interface sources such as natural background signatures as well as structured (nonrandom) noise such as stripping, when the Gaussian assumption dose not hold, the background clutter can become indistinguishable from signal source.

2) The objects of interests are often small relative to the size of the scene, and therefore contribute a small amount to the overall variance. PCA often fails to capture the variability associated with small objects unless their spectra are nearly orthogonal to the background spectra.

An alternative to PCA that can alleviate some these problems is Minimum Noise Fraction (MNF) transform. This transform, also known as noise-adjusted principle components, was designed to produce orthogonal component images that are ordered by image quality as measured by the SNR, rather than the data variance.

The MNF transform is equivalent to sequence of two orthogonal transformations where the first rotates the data such that the noise covariance matrix is diagnolized, thus “whitening” the noise, followed by a standard PCA transform. PCA performance is improved because the noise effects on signal source are minimized by the whitening process, however the MNF transform still depend on “bulk” image properties, so it is not generally sensitive to small objects. For these reasons it is proposed a new dimension reduction method based on wavelet decomposition .The principle of this method is to apply a discrete wavelet transform to hyperspectral data in the spectral domain and at each pixel location. This dose not only reduce the data, volume but it also can preserve the characteristics of the spectral of signature. This is due to intrinsic property of wavelet transforms of preserving of high and low frequency during the signal decomposition, therefore preserving peaks and valleys found in typical spectra. In addition, some of subbands especially the low pass filter, can eliminate anomalies found in one of the bands. Our experimental results for representative sets of hyperspectral data have confirmed that the wavelet spectral reduction as compare to PCA provides better classification accuracy.

This paper is organized as follows. Section 2 provides an overview of the automatic multiresoluton wavelet analysis for dimension reduction of hyperspectral data. Section 3 discusses the automatic selection of level of decomposition. Section 4 presents results for the automatic wavelet reduction. This is accomplished by investigating the impact of the wavelet reduction on classification accuracies for different conventional classification methods and Section 5 provides our concluding remark for this work.

2. Automatic Multiresolution Wavelet Analysis
Multiresolution wavelet transform can provide a domain in which both time and scale information can be studied simultaneously giving a time-scale representation of the signal under observation. A wavelet transform can be obtained by projection the signal onto shifted and scaled version of a basic function. This function is known as the mother wavelet, Ψ (t), A “mother wavelet” must satisfy this condition


This condition implies that the wavelet has a zero average
And the shifted and scaled version of the mother wavelet forms a basis of functions. These basis functions can be represented as
Where “a” represents the scaling factor and “b” the translation factor.

Wavelet transforms may be either discrete or continuous. In this paper only discrete orthonormal based of wavelet are considered. For dyadic DWT the scale variables are power of 2 and the shift variables are non overlapping and discrete.

One property that most wavelet systems satisfy is the multiresolution analysis (MRA) property. In this paper Mallat algorithm is utilized to compute these transforms.

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