Influence of noise and sampling rate on the discrete image representation error

Abstract

Introduction: Digital registration of images is accompanied not only by an error caused by finite spatial resolution of the photo matrix, but also by the effect of noise whose contribution to the total error decreases with an increase in the aperture of the photosensors in the matrix. Thus, changing the sampling rate has the opposite effect on the sampling error and on the error caused by the noise. Purpose: Finding the optimal image sampling rate which would provide the minimum sampling error in the presence of noise.  Results: We have studied how an image discrete representation error depends on the sampling frequency and noise level. The image sampling process in the presence of noise was simulated in the MATLAB environment. The dependencies of the root-mean-square deviation of the sampling error caused by spectrum truncation (decrease in the passband of the low-pass filter) and the noise component of the error on the sampling frequency were plotted. A theorem is formulated on the upper bound of the sampling theorem: when sampling a function of finite duration in the presence of noise, there is a finite minimum value of the sampling error which is determined by the shape of the spectrum of the function and the noise level. Practical relevance: It is advisable to use the research results when choosing a photomatrix by the number of pixels for recording images in the presence of noise, as well as when choosing a low-pass filter passband for primary processing of a digital image.