A novel technique based on the statistical autoregressive (AR) model has recently been developed as a solution to estimate the signal-to-noise ratio (SNR) in scanning electron microscope (SEM) images. In another research study, the authors also developed an algorithm by cascading the AR model with the Lagrange time delay (LTD) estimator. This technique is named the mixed Lagrange time delay estimation autoregressive (MLTDEAR) model. In this paper, the fundamental performance limits for the problem of single-image SNR estimation as derived from the Cramer-Rao inequality is presented. We compared the experimental performances of several existing methods--the simple method, the first-order linear interpolator, the AR-based estimator as well as the MLTDEAR method--with respect to this performance bound. In a few test cases involving different images, the efficiency of the MLTDEAR single-image estimation technique proved to be significantly better than that of the other three methods. Study of the effect of different SEM setting conditions that affect the autocorrelation function curve is also discussed.
In this paper, we propose to use the autoregressive (AR)-based interpolator with Wiener filter and apply the idea to scanning electron microscope (SEM) images. The concept for combining the AR-based interpolator with Wiener filtering comes from the essential requirement of Wiener filtering for accurate and consistent estimation of the power of the noise in images prior to filter implementation. The resultant filter is called AR-Wiener filter. The proposed filter is embedded onto the frame grabber card of the scanning electron microscope (SEM) for real-time image processing. Different images are captured using SEM and used to compare the performances of the conventional Wiener and the proposed AR-Wiener technique.
A new technique based on the statistical autoregressive (AR) model has recently been developed as a solution to signal-to-noise (SNR) estimation in scanning electron microscope (SEM) images. In the present study, we propose to cascade the Lagrange time delay (LTD) estimator with the AR model. We call this technique the mixed Lagrange time delay estimation autoregressive (MLTDEAR) model. In a few test cases involving different images, this model is found to present an optimum solution for SNR estimation problems under different noise environments. In addition, it requires only a small filter order and has no noticeable estimation bias. The performance of the proposed estimator is compared with three existing methods: simple method, first-order linear interpolator, and AR-based estimator over several images. The efficiency of the MLTDEAR estimator, being more robust with noise, is significantly greater than that of the other three methods.