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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
An example of the actual signature of one pixel for 195 bands
of the California 94 AVIRIS dataset and different level of
lowpass component of wavelet decomposition of this spectral
signature is shown in figure3. As s seen from this figure as the
number of wavelet decomposition levels increases, the
structure of the spectral signature becomes smoother than the
structure of original signature.
250. “Original Signature el À
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13008 CU bas
401 8 30 10 1x | 160 Le 70
Band Number
: ‘wavelet Coefficient:
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Band. Number Band Number:
Figure3. Example of a pixel spectral signature and different levels of
wavelet decomposition for the low pass component
In the algorithm of wavelet reduction we need to reconstruct
the spectral signature to automatically select the number of
levels of wavelet decomposition.
While wavelet decomposition involves filtering and down
sampling the wavelet reconstruction involve up sampling and
filtering. The up sampling process lengthens decomposed
spectral data by inserting zeros as high pass component
between each element.
3. WAVELET- BASED DIMENSION REDUCTION
3.1 General Description of Algorithm
Wavelet-Based reduction can be effectively applied to
hyperspectral imagery. Performance d? wavelet reduction can
be better for larger dimensions (Kaewpijit et al, 2003). This
property is due to very nature wavelet compression, where
significant feature of the signal might be lost when the signal is
under sampled. The general description of the wavelet
reduction algorithm follows;
1. For each pixel in a hyperspectral scene, the 1-D signal
corresponding to its spectral signature is decomposed using
Daubechies wavelet.
2. For each hyperspectral pixel, approximation the original
spectral is reconstructed using IDWT. The needed level of
decomposition for a given pixel is the one that corresponds to
producing an acceptable correlation whit the original signature.
3. Combining results from all pixels, the number of the level of
decomposition (L) is automatically computed as the lowest
level needed after discarding outliers.
63
4. Using the number of L computed in (3) the reduced output
data are composed of all pixels decomposed to level L.
Therefore, if the original number of bands was N the output
number of bands is N/2*.
3.2 Automatic Decomposed Level Selection
The correlation between the original spectral signature and the
reconstructed spectral approximation is an indicator, which
measures the similarity between two spectral signatures and
used for selecting how many levels of decomposition can be
applied while steel yielding good classification accuracy. The
correlation function between the original spectral signature (x)
and its reconstructed approximation (y) is shown in (Kaewpijit
et al, 2003)
1
Yur rind x). (4)
po y) ;
: (ES = CS XY y A »)
where N is the original dimension of the signal.
Table.! shows the similarity between the original spectral
signature and its reconstructed approximation of one class for
the scene in our image. As seen from the table, as the number
of levels of decomposition increases and the signal become
more different from the original data, a proportionate decrease
in correlation is observed. For each pixel in the hyperspectral
scene and for each level of decomposition the correlation
between original and reconstructed signal is computed. All
correlation higher than the user-specified threshold contributes
to the histogram for that level of decomposition. When all
pixels are processed, the lowest level of wavelet decomposition
needed to produce such correlation is used for the remainder of
the algorithm.
Correlation
Level
.9974
.9936
.9804
.9558
.9224
Tablel. Similarity Measures Between The Original
Versus the Reconstructed Spectral Signature for one
Class in our image.
4. WAVELET-BASED REDUCTION AND
CLASSIFICATION ACCYRACY
We have experimentally validated the Wavelet Based
dimension reduction by using remotely sensed image test from
a hyperspectral scene, using the ENvironment for Visualizing
Images (ENVI) as a tool for classification accuracy assessment.
Using the wavelet-reduced data, an error (confusion) matrix of
several classification methods for the same level of
decomposition between the Wavelet and PCA was calculated.
