Analyzing the time-frequency features of seismic traces plays an important role in seismic stratigraphy analysis and hydrocarbon detection. The current popular time-spectrum analysis methods include short-time Fourier transform, continuous wavelet transform, S-transform, and matching pursuit (MP), among which MP is the most tolerant of the window/scalar effect. However, current MP algorithms do not consider the interfering effects of seismic events on the estimation of optimal wavelets in each decomposition iteration. The interfered reflection seismic events may result in inaccurate estimation of optimal wavelets during the whole decomposition procedure. We have developed a hybrid basis MP workflow to minimize the effect of event interference on the estimation of optimal wavelets. Our algorithm assumes that the wavelet features remain constant in a user-defined small time window. The algorithm begins with identifying the strongest reflection waveform. Next, we estimate the optimal wavelet and the corresponding reflectivity model for the selected waveform by using a basis pursuit algorithm. Then, we subtract the seismic traces from the waveform computed from the optimal wavelet and estimated reflectivity model. We repeat this procedure until the total energy of seismic traces falls below a user-defined value. We have determined the effectiveness of our algorithm by first applying it to a synthetic model and then to a real seismic data set.