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Efficient Digital Pre-filtering for Least-Squares Linear Approximation

  • Marco Dalai
  • Riccardo Leonardi
  • Pierangelo Migliorati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3893)

Abstract

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.

Keywords

Linear Interpolation Reconstruction Function Discrete Time Signal Optimal Analog Successive Rotation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Blu, T., Unser, M.: Quantitative Fourier analysis of approximation techniques: part I– interpolators and projectors. IEEE Trans. Signal Process. 47(10), 2783–2795 (1999)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Unser, M.: Sampling-50 years after Shannon.Proc. IEEE. 88 (4), pp. 569–587 (2000)Google Scholar
  3. 3.
    Blu, T., Unser, M.: Approximation error for quasi-interpolators and (multi)-wavelet expansions. Appl. Comput. Harmon. Anal. 6(2), 219–251 (1999)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Blu, T., Thvenaz, P., Unser, M.: How a simple shift can significantly improve the performance of linear interpolation. In: Proc. IEEE Int’l Conf. on Image Proc., pp. III. 377–III. 380 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marco Dalai
    • 1
  • Riccardo Leonardi
    • 1
  • Pierangelo Migliorati
    • 1
  1. 1.University of BresciaBresciaItaly

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