Signal-to-noise ratio estimation on SEM images using cubic spline interpolation with Savitzky–Golay smoothing
Article first published online: 24 OCT 2013
© 2013 The Authors Journal of Microscopy © 2013 Royal Microscopical Society
Journal of Microscopy
Volume 253, Issue 1, pages 1–11, January 2014
How to Cite
SIM, K.S., KIANI, M.A., NIA, M.E. and TSO, C.P. (2014), Signal-to-noise ratio estimation on SEM images using cubic spline interpolation with Savitzky–Golay smoothing. Journal of Microscopy, 253: 1–11. doi: 10.1111/jmi.12089
- Issue published online: 6 DEC 2013
- Article first published online: 24 OCT 2013
- Manuscript Accepted: 6 SEP 2013
- Manuscript Received: 24 JUN 2013
- Additive white Gaussian noise;
- electron microscope;
- signal-to-noise ratio
A new technique based on cubic spline interpolation with Savitzky–Golay noise reduction filtering is designed to estimate signal-to-noise ratio of scanning electron microscopy (SEM) images. This approach is found to present better result when compared with two existing techniques: nearest neighbourhood and first-order interpolation. When applied to evaluate the quality of SEM images, noise can be eliminated efficiently with optimal choice of scan rate from real-time SEM images, without generating corruption or increasing scanning time.
A new estimation technique, cubic spline interpolation with Savitzky-Golay smoothing (CSISG), to estimate the signal-to-noise ratio (SNR) from a single scanning electron microscope (SEM) image is developed. The cubic spline interpolation is a proven technique to interpolate among known data points, and the Savitzky-Golay noise reduction filtering based on unweighted linear least-squares regression and third order of polynomial is used to estimate central of the fitted point polynomial curve as a new smoothed data set. The new technique gives the flexibility to carefully obtain the desired span level by generating a third degree polynomial curve fitting to attain an expression for span level estimation. This autocorrelation-based technique requires image details to be correlated over a few pixels, while the noise is assumed to be uncorrelated from pixel to pixel. Different images with edges, high curvature points, extremities of periodic pattern and gradient estimation are used in this paper. The noise component is derived from the difference between the image autocorrelation at zero offset and the estimation of the corresponding original image autocorrelation. In relation to this new SNR estimation technique, the performance for the problem of single image SNR estimation is presented. The new technique is found to demonstrate better when compared with different existing estimators as well as first order interpolation method (FOM) and the nearest neighborhood method (NNM) on different SEM sample images with different specifications and magnifications. The sample images are selected based on their well-known and explicit objective description. In a few test cases involving different images, the efficiency of Savitzky-Golay noise reduction filtering single image estimation technique is shown to be significantly better than those of the other two methods, where noise variance (NV) ranges from 0.001 to 0.010. In order to study the quality of SEM images, noise can be eliminated efficiently with optimal choice of scan rate from real-time SEM images, without generating corruption or increasing scanning time.