Efficient Digital Pre-filtering for Least-Squares Linear Approximation

In this paper we propose a very simple FIR pre-filter based method for near optimal least-squares linear approximation of discrete time signals. A digital pre-processing filter, which we demonstrate to be near-optimal, is applied to the signal before performing the usual linear interpolation. This leads to a non interpolating reconstruction of the signal, with good reconstruction quality and very limited computational cost. The basic formalism adopted to design the pre-filter has been derived from the framework introduced by Blu et Unser in [1]. To demonstrate the usability and the effectiveness of the approach, the proposed method has been applied to the problem of natural image resampling, which is typically applied when the image undergoes successive rotations. The performance obtained are very interesting, and the required computational effort is extremely low.