Adaptive multiple subtraction using regularized nonstationary regression

Line fitting

Let $\mathbf{x}$ be one-dimensional (denoted by $x$), $N=2$, $s_1(x)=1$, and $s_2(x)=x$. The problem of minimizing $e(x)$ amounts to fitting a straight line $a_1 + a_2\,x$ to the master signal.