We present a new method for component separation aimed to extract Sunyaev-Zeldovich (SZ) galaxy clusters from multifrequency maps of Cosmic Microwave Background (CMB) experiments. This method is designed to recover non-Gaussian, spatially localized and sparse signals. We first characterize the cluster non-Gaussianity by studying it on simulated SZ maps. We the apply our estimator on simulated observations of the Planck and Atacama Cosmology Telescope (ACT) experiments. The method presented here outperforms multi-frequency Wiener filtering both in the reconstructed average intensity for given input and in the associated error. In the absence of point source contamination, this technique reconstructs the ACT (Planck) bright (big) clusters central y parameter with an intensity which is about 84 (43) per cent of the original input value. The associated error in the reconstruction is about 12 and 27 per cent for the 50 (12) ACT (Planck) clusters considered. For ACT, the error is dominated by beam smearing. In the Planck case the error in the reconstruction is largely determined by the noise level: a noise reduction by a factor 7 would imply almost perfect reconstruction and 10 per cent error for a large sample of clusters. We conclude that the selection function of Planck clusters will strongly depend on the noise properties in different sky regions, as well as from the specific cluster extraction method assumed.
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