A multi-touch system includes a panel for conducting signals, e.g. by FTIR, from incoupling points to outcoupling points, to define detection lines across the panel. A signal processor operates in a repeating sequence of iterations to obtain an output signal from a detector coupled to the outcoupling points and generate a formatted signal value for each detection line, and operate a reconstruction algorithm on the formatted signal values to determine an interaction pattern on the panel. The signal processor also, at least intermittently in the sequence of iterations, operates compensation data on the formatted signal values to compensate for contaminations on the panel, and calculates updated compensation data based on an interference pattern determined as a function of the interaction pattern, the interference pattern being a 2D representation of contamination-induced signal interferences. The influence of contaminations in the interaction pattern is thereby suppressed.