I've got observed data $Y_1,\ldots, Y_n $ which consists of real values $X_1,\ldots, X_n$ and additive high-frequency noise $e_1,\ldots, e_n$, so $Y_i=X_i+e_i$. I know, that indicies $i_1,\ldots, i_m, m<n$, refer to those samples in which $e_j=0$ if $j\in(i_1,\ldots,i_m)$.
I'm trying to implement baseline detecting using that information about points which should have zero amplitude of noise. The filter should has a $Y$ series as input, and it should has output $Z$ like the follows: $Z$ - filtered data without high-frequency noise with $Z_j=Y_j$ if $j\in(i_1,\ldots,i_m)$. That is not strict limitation so it could be $Z_j\approx Y_j$
Which filters could I use for that purposes? I've seen cubic splines, which interpolate baseline by that points, but they are strictly depend on them, since I want filter to be able working even without points but with using them for correction.