Approximation of the expected value of the harmonic mean and some applications

Significance The harmonic mean (HM) filter is better at removing positive outliers than the arithmetic mean (AM) filter. There are especially difficult issues when an accurate evaluation of expected HM is needed such as, for example, in image denoising and marginal likelihood evaluation. A major challenge is to develop a higher-order approximation of the expected HM when the central limit theorem is not applicable. A two-term approximation of the expected HM is derived in this paper. This approximation enables us to develop a new filtering procedure to denoise the noisy image with an improved performance, and construct a truncated HM estimator with a faster convergence rate in marginal likelihood evaluation.