Wavelet-based information theory in quantitative assessment of AFM images' quality

The quantitative assessment of the image quality produced by atomic force microscopy (AFM) is an ongoing and challenging task. In our study, we demonstrate Shannon's application of information theory for measuring image quality. Specifically, we propose quantifying the loss of image information due to the various distortion processes by exploring the relationship between image information based on the information channel capacity (ICC), spectral image representation, and visual quality. Since the ideal image is unavailable, the power and noise spectrum, the critical input information for the image quality evaluation, must be robustly estimated in the proposed method. The classical, most popular Welch method for spectral estimation uses an average of several windowed periodograms and can produce biased spectrum estimates. Therefore, in our work, we discuss an alternative technique based on the wavelet transform that can be applied to solve this challenging problem, specifically in the case of noisy, uncertain AFM measurements. Finally, we validate the performance of the enhanced ICC-wavelet-based algorithm with noisy measurement AFM data.