This work presents a noise attenuation technique based upon applying a sparsity constraint to a time-frequency transform. It is demonstrated that the solution obtained from applying the sparsity constraint rather than the more common minimum norm constraint produces a superior noise attenuated signal. The sparsity constrained transformation is achieved by finding a sparse representation of the input data in terms of a dictionary of complex Ricker wavelets. The utilization of a complex wavelet dictionary possesses the advantage that signals with arbitrary phase can be represented with enhanced sparsity. Examples with synthetic and real microseismicity data illustrate the capacity of the technique to attenuate ambient noise in microseismic records with low signal-to-noise ratio.