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A secondary index, independent of I ref , considers the radiometric errors :
∆ s [j] =m Is [j] − m Isj−1[j]
∆ e [j] =mÎ[j] − mÎ[j − 1]
The second order radiometric improvement factor is then given by :
(∑ )
j
IF 2 = 10log ∆2 s[j]
10 ∑
j ∆2 e[j]
(3.61)
(3.62)
3.8.3 Conclusion
Destriping techniques presented in this chapter can be classified in two major categories.
The first class is composed of statistical or radiometric equalization techniques such
as moment matching, histogram matching and the OFOV method. All these approaches
rely on the acquisition principle of pushbroom imaging systems to equalize the response of
individual detectors. Their application to MODIS data illustrates a significant amount of
residual stripes. Figure 3.20 shows that even after destriping, rapid fluctuations can still
be seen in the cross-track profiles of the denoised data. The analysis of column ensemble
averaged power spectrums (figure ) indicates that the amplitude of peaks related to periodic
stripes is reduced. To improve visual analysis of noise reduction, power spectrums
are plotted with a logarithmic scale, as a function of normalized frequency.
Equalization techniques do not account for non linear effects which are predominant in
MODIS data. Residual stripes in the images affect its power spectrum in two ways. Strong
non linear effects result in poor detector-to-detecotr stripes reduction and appear as persisting
peaks with a lower magnitude located at the same frequencies of 0.1, 0.2, 0.3, 0.4 and
0.5 pixels per cycles. Random stripes translate as strong variations of the power spectrum
in the high frequency range. Despite residual stripes, equalization techniques maintain the
image distortion index close to 1.
Alternative approaches to equalization are based on filtering techniques. The periodicity
of stripes can be exploited by a band-pass filter that cuts-off stripe related frequencies.
This can be achieved by placing narrow wells in the fourier response of the filter, centered
on the coordinates associated with periodic stripes. As seen in figure e, periodic peaks
are properly removed from the power spectrums. However, the overall shape of the column
power spectrum is strongly distorted. This is even more visible on the line ensemble
averaged power spectrum, which should be identical for both noisy and destriped images.
Wavelet analysis also offers an interesting perspective on the striping issue. The multdirectional
representation provided by wavelet transform is well suited to process striping
since only horizontal wavelet coefficients are contaminated with stripes. Setting to zero the
wavelet coefficients of the m highest resolution scales prior to wavelet reconstruction can
reduce the visual impact of stripe noise. The choice of the parameter m is fixed according
to the NR and ID indexes values and highly depends on the number of vanishing moments