The more important point to this paper is that, not only there are 
gain and bias variations within the band but also across the bands, 
This means, the gain and bias corresponding to a detector in band 1 
is not the same as the corresponding detector in band 2 and so on. 
From this, one can conclude that there is not only a mismatch of 
gains and biases between various detectors spatially, but also 
spectrally. This indicates that the various gains and biases are 
uncorrelated spectrally. The dynamic range of these biases and 
gains are very small and hence they contribute to low variance noise 
values. Hence this information is packed into the higher principal 
components. In contrast the true image information has a wide 
dynamic range which leads to high variance values and hence this 
information is packed into the lower principal components. 
To restate, applying the KLT in the spectral dimension would result 
in all kinds of this uncorrelated or poorly correlated noise 
information being packed into the higher principal components 
whereas the lower ones contain the information of interest. This 
has been verified by several researchers [2,5,11,15] on several 
Landsat MSS and TM scenes. It has also been consistently found that 
the higher order principal components have very low variance or 
energy in them. For example, a typical KLT on a TM scene could 
reveal about 1-2 $ of the total energy being contained in the 
principal components 5 through 7. Note that this noise energy is 
part of the original data energy and can be dropped in the KL domain 
by setting the respective components to zero. Visual inspection of 
the principal components of the TM and MSS scenes clearly illustrate 
these facts. It is a primary reason why remote sensing researchers 
pick the first three principal components from the TM or MSS scenes 
for image classification and land use studies. 
The KLT is an invertible transformation as was seen before. 
Performing an inverse KL transformation, taking only the useful 
components into account rejecting the noise or low variance 
components (by setting them to zero values), then one could expect 
the reconstructed image to be free from all unwanted noisy 
information. Such a reconstruction also preserves vital image 
information. The reconstructed image with the insignficant 
components dropped, obviously does not have the same data variance 
as the original noisy data. There is some loss of energy which is 
contributed mostly by noise and very little (if any) by useful 
information. A quantitative measure of such a loss can be obtained 
through (4). This spectral filter operates on each pixel across the 
bands and hence can remove noise spatially as well as spectrally. 
Such a spectral filtering procedure in the KL domain also offers 
some flexibility. Based on the variances of each component it 
should be easy to find out a priori as to how much loss of energy 
takes place by the filtering procedure. 
Experimental Results 
A 512 X 512 TM scene of the San Francisco bay area has been chosen 
for the study. Statistics were then collected on the T-band data. 
Table I provides the eigenvalues of the data. This indicates that 
the KLT can pack 98.3 % of the total data energy into the first 
three principal components and 99.5 % into the first four 
266