Estimation of the Equivalent Number of Looks in Polarimetric SAR Imagery

We present two new estimators for the equivalent number number of looks (ENL) designed for polarimetric synthetic aperture radar data. These are the first known estimators to utilise the full multilook polarimetric covariance matrix, and both are derived from moments of the Wishart distribution. The first estimator is obtained from the second-order trace moment, which provides a multivariate generalisation of the conventional ENL definition. The second estimator is found from the log-determinant moment, and is also shown to be the maximum likelihood estimator. The latter estimator proves to have superior statistical properties to any other known ENL estimator. These properties are decisive for the good performance obtained with a proposed procedure for unsupervised estimation. We demonstrate on airborne AIRSAR data how a robust ENL estimate can be extracted from the distribution of small sample estimates collected over the whole scene.