For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting (NLSF) method and the linear regression of the sum (LRS) method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.

The problem of multiplicative noise removal has been widely studied in recent years. Many methods have been used to remove it, but the final results are not very excellent. The total variation regularization method to solve the problem of the noise removal can preserve edge well, but sometimes produces undesirable staircasing effect. In this paper, we propose a variational model to remove multiplicative noise. An alternative algorithm is employed to solve variational model minimization problem. Experimental results show that the proposed model can not only effectively remove Gamma noise, but also Rayleigh noise, as well as the staircasing effect is significantly reduced.

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