EXTENSION OF REGULARIZATION THEORY-BASED ON GENERAL REGRESSION INTO MULTIVALUED FUNCTIONS AND A RECONSTRUCTION ALGORITHM FOR DISCONTINUOUS FUNCTIONS WITHOUT LINE PROCESSES

This paper considers the regularization theory based on the general re gression. The general regression does not require the measure for the smoothness, which plays the important role in the standard regularizat ion theory or its extension. The theory is extended so that the regula rization can be applied to the case where the data are multivalued. Ba sed on the extended theory, an algorithm is derived which can reconstr uct in a deterministicway the discontinuous function from the discrete data, without requiring the conventional line process, by regarding t he discontinuity as a boundary between different functions. The effect iveness of the derived algorithm and the robustness against the noise are demonstrated by a computer simulation.