In this paper we discuss the use of a time-frequency representation, the Wigner distribution, for the decomposition and characterization of seismic signals. The advantage of the Wigner distribution over other representations, such as the wavelet and sliding window Fourier transform, is its sharp localization properties in the time-frequency plane. However, the Wigner distribution is a not a linear transformation. This non-linearity complicates the use of the Wigner distribution for time-frequency filtering and decomposition. We present an optimization method for the reconstruction of a time signal from its Wigner distribution. The reconstruction technique enables a decomposition of a signal into its time-frequency components, where the reconstructed components are stripped off from the signal one by one. The method is illustrated a real data example. We also demonstrate how the decomposition can be used for suppression and enhancement of events in the time-frequency plane.