This work presents a mathematical model of a fast-acting single-layer artificial neural network applied to the task of image reconstruction after noise.For research purposes, this algorithm was implemented in the Python and C++ programming languages.The numerical simulation of the recovery efficiency of the described neural network was performed for different values of the noise factor, the MAGNESIUM + GABA number of samples required to train elements in the sample and the dimensionality of the coupling coefficients, w.The study of the mathematical model of this neural network is presented; as Quinoa a result, it is possible to identify its essence, to reduce the number of operations required to recover a single element and to increase recovery accuracy by changing the order of calculation of coupling coefficients, w.