  Suppose $K_{_Y}$ and $K_{_X}$ are large sets of observed and reference
signals, respectively, each containing $N$ signals. Is it possible to construct
a filter $F$ that requires a priori information only on few signals, $p\ll N$,
from $K_{_X}$ but performs better than the known filters based on a priori
information on every reference signal from $K_{_X}$? It is shown that the
positive answer is achievable under quite unrestrictive assumptions. The device
behind the proposed method is based on a special extension of the piecewise
linear interpolation technique to the case of random signal sets. The proposed
technique provides a single filter to process any signal from the arbitrarily
large signal set. The filter is determined in terms of pseudo-inverse matrices
so that it always exists.
