We present a new impulse noise removal technique based on Support Vector Machines (SVM). Both classification and regression were used to reduce the "salt and pepper" noise found in digital images. Classification enables identification of noisy pixels, while regression provides a means to determine reconstruction values. The training vectors necessary for the SVM were generated synthetically in order to maintain control over quality and complexity. A modified median filter based on a previous noise detection stage and a regression-based filter are presented and compared to other well-known state-of-the-art noise reduction algorithms. The results show that the filters proposed achieved good results, outperforming other state-of-the-art algorithms for low and medium noise ratios, and were comparable for very highly corrupted images.