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| A useful representation of the intensity is the logarithmic transformation to the [[http://en.wikipedia.org/wiki/Decibel| decibel unit]] {{{#!python img_dB=10*log10(img) }}} The PDF of the image above can be estimated from the number of occurrence of grey levels in the ''B'' intervals between ''q'' and ''q+dq'' and displayed using {{{#!python hist(img,bins=50) }}} with the resolution ''B'' for 50 ''bins'' (intervals). {{attachment:seaice_histogram.png}} The measurements that form an image show statistical fluctuations. The image is characterised by a probability density function (PDF). The PDF ''f'' describes the probability of the occurrence of a discrete grey level ''q'' in the range of grey levels ''Q''. {{{#!latex $\sum_{q=1}^Qf_q=1$ }}} |
Radar backscatter statistics
The received power (intensity) of a radar system is proportional to the (normalized) radar backscatter coefficient
latex error! exitcode was 2 (signal 0), transscript follows:
as a function of frequency and incidence angle. The backscatter coefficient describes how much of the transmitted energy is backscattered from the surface media.
A (calibrated) ASAR image img(y,x)=I is made of the measured intensities I which can be directly related to the backscatter coefficient. A value of zero means that no energy is reflected from the surface whereas a value of one means the total reflection.
Exercise
This ASAR image shows different sea ice types. Investigate the statistic of normalized backscatter value. What is the mean for the two prevalent sea ice types? Try to fit the image PDF with a superposition of two gamma distributions (ADVANCED EXERCISE).
from pylab import *
img=reshape(fromfile('ASAR_seaice_mixed_20080421_f32_1000x1000.dat',dtype=float32),(1000,1000))
close('all')
ql(img,vmin=0,vmax=0.3)
colorbar()
title('Sea ice radar backscatter intensity')