A new approach for solving sinusoid extraction problem in presence of distortions is proposed. Formulation of considered problem contains assumptions that sinusoidal signal is single and pulses are strictly finite in the time, but parameters of sinusoid as well as locations, durations and amplitudes of pulses are unknown a priori. We show that standard least squares criterion, based on the minimization of approximation error square, is inapplicable for parameter determination problem in presence of distorting pulses. The criterion of the minimum of the "duration" of approximation error is used to effectively solve the considered problem. Results of numerical simulations of the proposed method are presented. Developed approach is applied afterwards for the problem of restoration of distorted vibration data signal, collected by microwave measurement facility.