Adaptive multiple subtraction using regularized nonstationary regression

Match filtering

If the slave signals are translates of the same signal $s(\mathbf{x})$, the regression problem corresponds to the problem of match filtering between $s(\mathbf{x})$ and $m(\mathbf{x})$. In the 1-D case, one can take, for example,

$$s_k(x)=s(x-k+N/2)\;,$$

which turns the sum in equation 1 into a convolution with an unknown matching filter.