Evaluation and Bias Removal of Multi-Look Effect on Entropy/Alpha /Anisotropy
Jong-Sen Lee(1) and Thomas L. Ainsworth(2)
(1) Naval Research Laboratory, Remote Sensing Division, Washington DC, 20375-5351, United States
(2) National Central University, Center for Space and Remote Sensing Research, Chung-Li, Taiwan, China
Entropy, alpha angle and anisotropy (H//A), introduced by Cloude and Pottier , have become an effective and widely applicable tool for analyzing polarimetric SAR images. Recently, anisotropy is also found effective for measuring surface roughness, and entropy and alpha angle for soil moisture estimation . It is well known that multi-look (pixel average) processing can severely alter the values of entropy and anisotropy [3, 4]. Consequently, accurate estimation of these parameters is of paramount importance for geophysical parameter inversion. Lopez-Martinez et al.  derived probability density functions of eigenvalues from the multi-look coherency matrix, and assessed the asymptotic behavior of entropy and anisotropy, but the averaged alpha angle could not be evaluated because of the difficulty of deriving the probability density function for eigenvectors.
In this paper, a Monte Carlo procedure is used to simulate multi-look coherency matrices from various seed areas of interest, such as urban, forest, and rough surface. Multi-look simulations are processed for 1x3, 3x3, 3x5, 5x5, 5x7, 7x7, 7x9, 9x9, 9x11, 11x11, 11x13, and 13x13 independent sample averages. Then entropy, anisotropy and alpha angle are computed. The advantage of this procedure is multifold: 1) Both the mean and its standard deviation can be easily computed for all size of average, 2) Statistical behavior of averaged alpha angle can be assessed, 3) The effect of pixel correlation can be evaluated, and 4) The bias for entropy, anisotropy and alpha angle can be calculated that leads to the development of procedures for unbiased estimation of entropy and anisotropy.
Due to insufficient averaging, entropy is underestimated and anisotropy is overestimated. We found that the bias in Alpha angle can be either under or overestimated depending on scattering mechanisms. Based on simulation results, efficient bias removal procedures have been developed. In particular, the entropy bias can be precisely compensated independent of radar frequency and SAR systems. Data from L-band DLR/E-SAR and L-band JPL/AIRSAR, and X-band PI-SAR data are used for demonstration.
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