The mixed Lagrange time-delay estimation autoregressive (MLTDEAR) model is proposed as a solution to estimate image noise variance. The only information available to the proposed estimator is a corrupted image and the nature of additive white noise. The image autocorrelation function is calculated and used to obtain the MLTDEAR model coefficients; the relationship between the MLTDEAR and linear prediction models is utilized to estimate the model coefficients. The forward-backward prediction is then used to obtain the predictor coefficients; the MLTDEAR model coefficients and prior samples of zero-offset autocorrelation values are next used to predict the power of the noise-free image. Furthermore, the fundamental performance limit of the signal and noise estimation, as derived from the Cramer-Rao inequality, is presented.
A new filter is developed for the enhancement of scanning electron microscope (SEM) images. A mixed Lagrange time delay estimation auto-regression (MLTDEAR)-based interpolator is used to provide an estimate of noise variance to a standard Wiener filter. A variety of images are captured and the performance of the filter is shown to surpass the conventional noise filters. As all the information required for processing is extracted from a single image, this method is not constrained by image registration requirements and thus can be applied in real-time in cases where specimen drift is presented in the SEM image.