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. This paper presents a new sparse method for tip-timing spectral analysis that makes use of engine rotation variations. Assuming that blade vibration signals yield to line spectra, a sparse signal model is introduced as a linear system. The solution to the problem is obtained by ADMM (Alternating Direction Method of Multipliers) with a ℓ 1-regularization. Results for simulated and real signals are given to illustrate the efficiency of this method. The main advantages of the proposed method are to provide a fast solution and to take into account the variations of the rotation speed. Results show that this approach reduces frequency aliasings caused by the low sampling frequency of the measured signals.