Application of bootstrap techniques for the estimation of Target Decomposition parameters in RADAR polarimetry

Abstract

Abstract-The precise estimation of the eigenvalues of PolSAR reponses is essential in the derivation of Target Decomposition parameters such as the Cloude-Pottier parameters (Entropy, Anisotropy and average angle Alpha). However, sample eigenvalues are strongly biased for small sample sizes leading to underestimated Entropy and overestimated Anisotropy values. In this paper, we investigate the use of a particular bootstrap technique for the correction of the bias. Bootstrap techniques are attractive because they can deal with very small sample sizes under minimal assumptions on the signal distribution. Here, we are using the jackknife bias correction technique which has been successfully applied to various signal processing problems. Monte-Carlo simulations reveal that the jackknife bias correction directly applied on the Cloude-Pottier parameters lead to better bias reduction.

BIAS COMPENSATION IN H/a/Α POLARIMETRIC SAR DECOMPOSITION AND ITS IMPLICATION FOR THE CLASSIFICATION

“…, E) by 2 × 4, 3 × 6, 4 × 8 and 5 × 10 boxcar filter. As demonstrated in [18][19][20][21][22], we observe from Figs. 2(a) and (b) that sample entropy was always underestimated.…”

“…However, these techniques reduced the bias but altered the variances of sample values. As established in [22], Yahia/Aguili's technique decreased the noise whereas the techniques proposed in [18][19][20][21] amplified it. Consequently, both bias and speckle variance influenced the performances of the classification.…”

“…A variety of bias compensation procedures have been proposed in the literature [18][19][20][21][22]. However, these techniques reduced the bias but altered the variances of sample values.…”

“…The asymptotic quasi maximum likelihood estimator (AQ-MLE) of sample eigenvalues is derived from the eigenvalue pdfs [18]. Foucher et al [19] introduced a bootstrap technique to estimate eigenvalues, entropy, anisotropy, and α angle. The bootstrap on eigenvalues gives similar bias correction to AQ-MLE [19].…”

“…Foucher et al [19] introduced a bootstrap technique to estimate eigenvalues, entropy, anisotropy, and α angle. The bootstrap on eigenvalues gives similar bias correction to AQ-MLE [19]. Lee et al [20] exploited the linear dependence of the entropy bias on the entropy to its bias removal.…”