Reconstruction of blurred orbits under finite resolution

Techniques to retrieve information about orbits of dynamical systems lost in the process of making measurements due to discretization, sampling, or noise are developed. A general method of reprocessing the experimentally obtained data to effectively increase its information content (the accuracy of measurements) is proposed. Potential applications include many areas of applied mathematics such as inverse problems, time series analysis, ill posed problems, etc. The method can also be used to help construct new highly accurate measuring devices.