We present a method which allows for the blind source separation of sparse overcomplete mixtures. In this method, linear filters are used to find a new representation of the data and to enhance the signal-to-noise ratio. Further, “Deconfusion”, a method similar to the independent component analysis, decorrelates the filter outputs. In particular, the method was developed to extract neural activity signals from extracellular recordings. In this sense, the method can be viewed as a combined spike detection and classification algorithm. We compare the performance of our method to those of existing spike sorting algorithms, and also apply it to recordings from real experiments with macaque monkeys.