Development of a cascade mathematical model for digital image processing: a systems approach

Abstract

The object of this study is to preprocessing digital images degraded by additive Gaussian noise using cascaded Gaussian filtering. The scientific problem is to improve the output signal-to-noise ratio and reduce reference-based residual error of noisy digital images under additive Gaussian noise while preserving the informative structure required for subsequent image analysis. The model represents a noisy image as an additive combination of the reference image and a Gaussian noise component and describes two filtering stages through convolution of Gaussian kernels. The model is tested on the Lena benchmark image at noise levels from –10 dB to +10 dB and compared with median and bilateral filtering using signal-to-noise ratio and root mean square error. The results show that the cascade Gaussian model provides the highest signal-to-noise ratio over the studied range. At –10 dB the model increases SNR to 15.02 dB, whereas median and bilateral filters reach 4.21 dB and 1.26 dB. At +10dB, the cascade model achieves 28.19 dB. The model lowers RMSE at –10 dB to 45.25 pixels, while median and bilateral filtering give 81.95 and 115.16 pixels. This improvement comes from how Gaussian smoothing reduces random noise and how the Gaussian kernel creates a predictable filtering effect. The feature of the research results is that higher denoising accuracy is achieved together with mathematical transparency and simple implementation, without training data or a reference noise channel. Practical application of the model is possible as a preprocessing stage in machine vision, biomedical image analysis, robotic systems, monitoring, and other tasks with Gaussian-like noise