Abstract
Recently, we have developed a new analysis method for multi-spectral satellite data called " Pattern Decomposition Method" based on linear mixing of three universal spectral pattern of ground objects, namely water, vegetation and soil. In this method, the spectral reflectance of each pixel in a satellite image is decomposed into the three components. We study the application of the method to continuos spectra of ground objects and the relationship between the method and the principle component analysis method in terms of information transformation. The continuous spectral reflectance of land cover objects in the 350-2,500 nm wavelength band could be decomposed by the universal spectral patterns and 95% of the information of the spectral reflectance is transformed on average. This result is very important general rule for analyzing the hyper-multispectral satellite data. Mixing ratio of land cover objects in a pixel could be evaluated with good accuracy using the linear mixing three decomposition coefficients.

1. Introduction
Reflecting the process of technology, recent satellite sensors can provide hyper multi-spectral data. Several analysis methods have been developed for these data. The methods are generally classified into two groups. One is the class of principle components transformation [Gonzalez 1997, Merembeck and Turner 1980]. The principle component analysis method is mathematically pleasing, but the new coordinate system have no physical meaning. The other is spectral mixing analysis (end members method) [Adams et. Al. 1995]. In this analysis, the spectrum of each pixel is approximated as the linear sum of a spectrum for each classification category. The coefficients of that linear sum express the belongings ratios of each pixel to those categories.

We have developed a new analysis method for multi-spectral satellite data called the "Pattern decomposition Method" (PDM) [Fujiwara et. Al. 1996]. The PDM is a kind of spectral mixing analysis but the spectrum of each pixel is expressed as the linear sum of three universal spectral patterns, namely the spectral patterns of three representative land objects, water, vegetation and soil. The usage of universal spectral patterns make possible the comparison of data of different time and also of different sensor with the same criteria.

According to the application of the PDM to LANDSAT/Tm data and simulated ADEOS-II/GLI data, it can be said that reflect light from most land cover objects can be approximated with a linear combination of the three universal patterns of water, vegetation and soil with good accuracy [Hayashi et. al. 1998]. In a sense, the universal patterns in the PDM are one kind of three principal axes in n-dimensional space but have universal physical meaning.

In this paper, the applicability of the PDM to nearly continuous spectrum data are presented. For this study, we used radio-spectrometer data measured in the field.

2. The Pattern decomposition method
In the PDm, the data for each pixel is a set of reflectance data converted from a set of brightness data of n-bands. The set of reflectance of each pixel is approximated as follows:
A_i®C_w P_iw + C_v P_iv + C_s P_is,               (1)
Where A_i is the reflectance of band i,P_iw, P_iv, P_is are water, vegetation and soil universal standard spectral pattern and is normalized as S_i=1ⁿ|P_ik|=1 (k=w,v,s) and C_w,C_v,C_s are three pattern decomposition coefficients with the condition of C_w>0, C_v>0, and C_s>0. the three pattern decomposition coefficients Cw, Cv, and Cs are evaluated using the least squares method.

Using the remainder of I band's reflectance,
R_i=A_i-(C_wP_iw+C_vP_iv+C_sP_is).             (2)
and the squared sum of the reminders, X= S_i=1ⁿ R_i², the relative error of all bands is defined as follows:
E=(X)^1/2/ S_i=1ⁿ A_i             (3)
The error index of reduced -c² is also defined as follows:
c_n-3² = X/ degree of freedom = R_i²/(n-3)          (4)
The denominator (n-3) is the degree of freedom for a data set of n-bands.

To study information transfer from original data by the PDM, the information defined by Shannon in bit unit
I=-cp_ilog₂(p_i) ,           (5)
was used, where p_i is a probability of event i. for satellite data, p_k (x) is probability of frequency distribution of reflectance x for band k.