MATHEMATICAL MODEL AND RECOGNITION ALGORITHMS FOR IMAGE PROCESSING

Chasovskikh Viktor Petrovich, Koch Elena Viktorovna

The article discusses the possibility of increasing the speed of algorithms when processing information technology images, including artificial intelligence technologies. A mathematical model is proposed as a nonlinear tensor product. This model is presented in the form of fast algorithms. It has been proven that various types of fast Fourier transform can be represented in a nonlinear, generalized form and represented by a set of two rules defining nonlinearity for fast algorithms. For image processing algorithms, relationships are formed from several operations of fast algorithms. Three iterations are defined. In the first iteration, the nonlinearity of the transformation is determined. In the second iteration, the nonlinearity of sparse transformations of direct sums of nonlinear transformations is formed. At the third iteration, a fast nonlinearity transformation is formed as a result of combining nonlinear sparse transformations. A new approach to transformations with nonlinear dependencies and the use of a fast algorithm has been created. The applied recursion rules for nonlinear transformation models create new opportunities for regular viewing of implicit fast transformations with nonlinearity. Thus, the authors formulated a new property of transformations, defined as the result of a superposition of “sparse” transformations with nonlinearity, and a new (with fewer computational operations) fast algorithm was created.

Keywords:model, pixels, image, fast algorithms. information Technology.