Efficient digital pre-filtering for least squares linear approximation

In this paper we propose a very simple FIR pre-filter for near optimal least-squares linear approximation of discrete time signals. At first, a greedy least square approximation of the desired signal is derived using an efficient digital pre-processing filter, then the usual linear interpolation is applied to obtain the final result. 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. 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.