A non-iterative estimator for the concentration parameter of the relative phase distribution

In this paper, we propose an approximation of the relative phase probability function (RP pdf) and use it to find a non-iterative estimator for the concentration parameter of the pdf. In particular, we approximate the log-likelihood equation which is highly nonlinear by another equation where we can use the proposed pdf's approximation to solve for the estimator. To illustrate the effectiveness of the proposed estimator, the comparisons between the proposed method and the maximum likelihood (ML) estimation method are displayed in terms of both numerical accuracy and computational saving in the estimation. The results show that the proposed method yields a good and comparable estimator with the ML estimator but with less computational time in estimating the parameters from the simulated samples, and also works well in histogram fitting of the relative phase samples of complex wavelet coefficients extracted from several standard test images.