NOISE REMOVAL BY THE KARHUNEN LOEVE TRANSFORM 
Ram Srinivasan 
International Imaging Systems 
R&D 
1500 Buckeye Drive 
Milpitas, CA 95035 
Abstract 
The Karhunen-Loeve transformation (KLT) or the principal components 
analysis has been used to minimize the number of feature sets in 
remotely sensed images for better and easier classification. The 
KLT compacts most of the energy distributed over several bands in 
the data domain to fewer bands in the transform domain. This 
process decorrelates the information in the data domain. In this 
process it has been observed that the higher frequency components 
contain very low variance information, mostly of noise. Mostly the 
stripes and banding alone are visible in these components. 
The KLT is an orthogonal transformation and its inverse exists. 
This paper attempts to remove noise in the KLT domain by dropping 
the noisy or low variance components. The remaining components are 
used to bring the signal back to the spatial domain. Resultant 
images reveal that this process is successful in removing different 
kinds of noise (stripe, band noise etc.) that are uncorrelated 
between the bands. TM Images have been studied for this spectral 
noise removal procedure. Because of the spectral filtering that 
this algorithm employs it is expected that this will also 
effectively compensate for failed detectors. 
roduction 
The quality of Landsat MSS and TM images have been analyzed recently 
to quite a good extent under the Landsat-D Image Data Quality 
Analysis (LIDQA) [1-4] program. One of the major problems reported 
and researched by several researchers is the detector and scanning 
noise in the images known as striping and  banding [3,1]. Several 
algorithms have been proposed by researchers to remove the 
undesirable noise from the images. The proposed algorithms have 
been in the data domain and in the Fourier domain as well. Research 
analysts have also been concerned with the problem of failed 
detectors [5-6] that results in a null value along a scan line. The 
TM sensor has 100 detectors, 16 each in the reflective bands and 4 
in the thermal infrared band. In this paper, a method of noise 
removal is proposed in the KLT domain. This approach is expected to 
yield other benefits in the way of correcting for failed detectors. 
The Karhunen Loeve Transformation 
In the remote sensing area, the KLT [7-10] is probably better known 
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