A Unified Approach to Noniterative Linear Signal Restoration

The main goal of this paper is to describe a unified frame-work for several noniterative algorithms for signal extrapolation reported in the literature. This unification is achieved through integral equation and Hilbert space theories. The importance of this unification is that we can bring to bear the vast body of techniques in these theories to the solution of the extrapolation problem. We will show that the so-called two-step procedures for extrapolation with different underlying models can be unified by means of non-iterative algorithms for solving optimization problems in Hilbert spaces. In particular, we show that two-step procedures under a discrete-con-tinuous model [1], [2] belong to a general class of well-known algorithms for solving linear integral equations of the first kind.