Abstract: Methods, systems, and devices are disclosed for removing non-stationary and/or non-stereotypical artifact components from multi-channel signals. In one aspect, a method for processing a signal includes obtaining a first signal decomposition of a multi-channel baseline signal in a first matrix including nominal non-artifact signal components and a second signal decomposition of a multi-channel data signal in a second matrix including artifact components, in which the first and second matrices are complimentary matrices, forming a linear transform by non-linearly combining the complementary matrices, and producing an output signal corresponding to the multi-channel data signal by applying the formed linear transform to one or more samples of the multi-channel data signal to remove artifacts and retain non-artifact signal content in the output signal.