Blades vibrations must be measured in operations to validate blade design. Tip-timing is one of the classical measurement methods but its main drawback is the generation of sub-sampled and non-uniform sampled signals. Consequently tip-timing signals cannot be processed with conventional methods. Assuming that blade vibration signals yield to line spectra, we introduced a sparse signal model that uses speed variation of the engine. The usual solutions of inverse problems are given with the LASSO method. This paper presents a new approach based on a ℓ 0-regularization. It is solved with the OMP algorithm adapted to our model. Results from synthetic and real signals are presented to illustrate the efficiency of this method, including a real blade crack test case. The main advantages of the proposed method are to provide accurate estimations with a computational cost drastically reduced with respect to existing methods. Besides, the method does not need to set up regularization parameters while taking into account the speed variation of the engines. Finally, results show that this approach greatly reduces frequency aliasings caused by the low sampling frequency of the measured signals.