A 2D prediction step using multiquadric local interpolation with adaptive parameter estimation for image compression

Abstract

We present and analyze several prediction strategies in the 2D setting based on multiquadric radial basis function interpolation with either linear or Weighted Essentially Non Oscillatory (WENO) shape parameter approximation. When considered within Harten’s framework for Multiresolution, these prediction operators give rise to sparse multi-scale representations of 2D signals, whose compression capabilities are demonstrated through numerical experiments. It is well know that the accuracy of multiquadric interpolation depends on the choice of the shape parameter. In addition, in [6], it was shown that the use of data-dependent strategies in the selection of the shape parameter leads to more accurate reconstructions. We shall show that our local adaptive estimates of the shape parameters lead to non-separable, fully 2D, reconstruction strategies that lead, in turn, to efficient compression algorithms.