Although the matching pursuit algorithm can accurately decompose waveforms, its use in real applications is limited. This is because it can be computationally intensive as it is based on selecting elements from complete dictionaries spanning the time-frequency plane of interest. There is, therefore, a need for smaller dictionaries that can still result in accurate waveform decompositions. In this paper, we propose the particle filter matching pursuit algorithm that adapts the dictionary to the waveform structure. This algorithm uses particle filtering, a sequential Monte Carlo approach, to estimate the dictionary suitable for the decomposition of a given waveform, and then uses the matching pursuit algorithm to decompose the waveform. We demonstrate, using simulations, that the particle filtering matching pursuit can decompose waveforms faster than the matching pursuit.