components. A high degree of correlation was observed between the
bands (Table II). The results of applying the KL transformation
using the eigenvectors were observed by the seven prineipal
components. Of these the last three components (5-7) were found to
contain mostly noise. Further confirmation of this and the
efficient compaction is evident from Table III. This table gives a
comparison of variances of the original and transformed 7 bands.
Note the very low variance in the transformed bands 5-7 indicating
noise.
Principal components 5-7 were dropped in the reconstruction (inverse
KL) process. In other words they were set to 0.0 . The results of
the forward-inverse KL transformation with components 5-7 dropped
indicate reduced noise level. Due to limited space, all the
original and reconstructed images are not shown here.’ Figures 1-3
show zoomed areas over water in bands 1, 2 and 7. Note the reduced
detector-to-detector and band noise. Most of the errors in
difference images were -1, 0 or +1. There were very few pixels with
absolute errors greater than 2.
Table IV shows the various quantitative measures, MSE, mean of
absolute error (MAE), peak-to-peak signal to noise ratio (SNR) and
the correlation coefficient. Measures were computed for all seven
bands of the reconstructed image with the original as the reference.
Note that the MAE for any single band does not exceed 1.6. The
results agree with the observation by other researchers that the
stripe noise and band noise introduce errors that are in this range
of gray level or digital number (DN) [3,4,18]. Also note the very
high correlation and the SNR.
Instead of retaining the high variance principal components (1-1) in
the reconstruetion process, the low variance components (5-7) can be
retained. Such a reconstructed 7-band data will enable to observe
what is being stripped from the original bands by the noise removal
process. One expects to see mostly the noise in these reconstructed
images. The stripe noise and band noise are clearly visible in
these images. Figures 4-6 show reconstructed bands 1, 2 and 7 with
the high variance principal components 1-4 set to 0.0 instead of 5-7
being set to 0.0. The images have been scaled for better visual
effects. As expected, note that these figures show strongly the
banding, stripes and very little image structure.
Conelusions
Noise removal in TM images has been shown through spectral filtering
using the KL transform. The results are very encouraging. The
processed images are expected to yield better results for
classification in land use, crop inventory, forestry studies etc.
Additionally since the process is a spectral filter, a failed
detector response or a dropout is inherently rectified by the
process. It has been found by other researchers that interpolation
of failed detector values from adjacent bands is better than using
ad jacent detector values from the same band. The KLT processing
replaces the failed detector values by a weighted average of the
same detector from all the bands. The results have been found to be
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