Efficient Maximum-Likelihood Estimation of Equivalent Number of Looks for PolSAR Image

The complex Wishart distribution is a widely used statistical model for multilook polarimetric synthetic aperture radar (PolSAR) image data, of which the equivalent number of looks (ENL) is a critical parameter. Over the past decades, various estimators have been developed to estimate the ENL of complex Wishart distribution, of which the maximum likelihood (ML) estimator is important since it is asymptotically unbiased and has a small variance. However, this estimator is very time-consuming since it has no analytical solution and is usually solved numerically. To address this problem, this letter proposes an efficient ML estimator of ENL by deriving an approximate closed-form solution. Moreover, to estimate the ENL map of a PolSAR image, we also develop an efficient way to compute the local sample statistics parallelly. The experimental results on two PolSAR images show that our method yields highly approximate ENL values as the traditional ML estimator while is much more efficient. It costs less than 0.8 s on a general laptop to estimate the ENL map of a PolSAR image with 900 × 1024 pixels.