We have developed a method for suppressing coherent noise from seismic data by using the morphological differences between the noise and the signal. This method consists of three steps: First, we applied a dictionary learning method on the data to extract a redundant dictionary in which the morphological diversity of the data is stored. Such a dictionary is a set of unit vectors called atoms that represent elementary patterns that are redundant in the data. Because the dictionary is learned on data contaminated by coherent noise, it is a mix of atoms representing signal patterns and atoms representing noise patterns. In the second step, we separate the noise atoms from the signal atoms using a statistical classification. Hence, the learned dictionary is divided into two subdictionaries: one describing the morphology of the noise and the other one describing the morphology of the signal. Finally, we separate the seismic signal and the coherent noise via morphological component analysis (MCA); it uses sparsity with respect to the two subdictionaries to identify the signal and the noise contributions in the mixture. Hence, the proposed method does not use prior information about the signal and the noise morphologies, but it entirely adapts to the signal and the noise of the data. It does not require a manual search for adequate transforms that may sparsify the signal and the noise, in contrast to existing MCA-based methods. We develop an application of the proposed method for removing the mechanical noise from a marine seismic data set. For mechanical noise that is coherent in space and time, the results show that our method provides better denoising in comparison with the standard FX-Decon, FX-Cadzow, and the curvelet-based denoising methods.