Two-dimensional (2D) spectroscopy is used to study the interactions between energy levels in both the field of optics and nuclear magnetic resonance (NMR).Conventionally,the strength of interaction between two levels is inferred from the value of their common off-diagonal peak in the 2D spectrum,which is termed the cross peak.However,stronger diagonal peaks often have long tails that extend into the locations of the cross peaks and alter their values.Here,we introduce a method for retrieving the true interaction strengths by using sparse signal recovery techniques and apply our method in 2D Raman spectroscopy experiments.