We have developed a new theory for correcting track irregularities by applying their restored waveforms and carried out experimental levelling an lining work. In this theory, the optimum shifting/lifting values are obtained as solutions for a typical quadratic programming problem. Restrictions on shifting rails are formulated as constraint conditions of the optimization problem. Furthermore, in the case of levelling work, a designed cross level can be achieved. From experimental work on ballasted and slab tracks, the effectiveness of this theory has been confirmed. In the range of wavelength up to 50 m, the amplitude of track irregularity has decreased.