Deep Learning Approaches to Autocorrelation Function and Signal-to-Noise Ratio Estimation in Noisy Images

Accurate estimation of signal-to-noise ratio (SNR) in Scanning Electron Microscopy (SEM) is crucial because it evaluates the image quality. SEM images faced a challenge whereby Gaussian noise commonly appears in the images. Thus, researchers have developed several methods to estimate the SNR value. With the introduction of deep learning, most of the limitations in the classical methods can be addressed. This paper proposes a novel deep learning, CNN-based Calibration Map Network (CalibNet) to estimate the SNR value from SEM images using a calibration map between classical SNR and autocorrelation function SNR. The architecture consists of convolutional layers, rectified linear unit (ReLU) activations, max-pooling layers, adaptive pooling, and a regression head to predict the SNR value correctly. The proposed model is trained, validated and tested on two SEM images, the Biofilm SEM dataset (67 images) and the NFFA-EUROPE SEM dataset (961 images). Each image was artificially corrupted with Gaussian noise variance ranging from 0.001 to 0.01 to simulate realistic SEM imaging conditions. The proposed model was compared with Classical SNR, Autocorrelation Function (ACF), Nearest Neighbour (NN)-ACF, First-Order Linear Interpolation (LI)-ACF, and Quadratic-Sigmoid (Quarsig)-ACF methods. The results show that CalibNet outperformed all the classical methods in terms of mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) and R-squared (R²). Statistical analyses further confirmed that CalibNet predictions closely align with the Classical SNR values. Future work includes exploring more advanced model architectures, alternative calibration techniques, and real-time SNR estimation applications.