Towards Image Processing Based on System of Difference Equations

In the last few years image processing and analysis, particularly, video and image compression became very important due to immense development of new multi-media products, surveillance systems, automotive industry, etc, and the shortage of bandwidth and storage space of the memory. In the paper we consider a mathematical model as an approach to image processing, compression and restoration. We use edge detection algorithm to construct infinite system of difference equations, which is encoded by means of given family of functions, i.e. low degree polynomials, piece-wise linear functions or Heaviside step functions. Corresponding encoding and decoding algorithm is proposed, along with comprehensive theoretical background. The existence and uniqueness of decoded image is considered. This paper presents some preliminary study of the advantages and drawbacks of the approach and indicates areas of possible further research.