Microseismic monitoring is an indispensable technique in characterizing the physical processes that are caused by extraction or injection of fluids during the hydraulic fracturing process. Microseismic data, however, are often contaminated with strong random noise and have a low signal-to-noise ratio (S/N). The low S/N in most microseismic data severely affects the accuracy and reliability of the source localization and source-mechanism inversion results. We have developed a new denoising framework to enhance the quality of microseismic data. We use the method of adaptive sparse dictionaries to learn the waveform features of the microseismic data by iteratively updating the dictionary atoms and sparse coefficients in an unsupervised way. Unlike most existing dictionary learning applications in the seismic community, we learn the features from 1D microseismic data, thereby to learn 1D features of the waveforms. We develop a sparse dictionary learning framework and then prepare the training patches and implement the algorithm to obtain favorable denoising performance. We use extensive numerical examples and real microseismic data examples to demonstrate the validity of our method. Results show that the features of microseismic waveforms can be learned to distinguish signal patches and noise patches even from a single channel of microseismic data. However, more training data can make the learned features smoother and better at representing useful signal components.