Multigrid Image Reconstruction from Arbitrarily Spaced Samples
M. Arigovindan, M. Sühling, P. Hunziker, M. Unser
Proceedings of the 2002 Ninth IEEE International Conference on Image Processing (ICIP'02), Rochester NY, USA, September 22-25, 2002, pp. III.381-III.384.
We propose a novel multiresolution-multigrid based signal reconstruction method from arbitrarily spaced samples. The signal is reconstructed on a uniform grid using B-splines basis functions. The computation of spline weights is formulated as a variational problem. Specifically, we minimize a cost that is a weighted sum of two terms: (i) the sum of squared errors at the specified points; (ii) a quadratic functional that penalizes the lack of smoothness. The problem is equivalent to solving a very large system of linear equations, with the dimension equal to the number of grid points. We develop a computationally efficient multiresolution-multigrid scheme for solving the system. We demonstrate the method with image reconstruction from contour points.
Errata
-
p. III-382, the regularization filter is lacking some first-order difference operators Δ. It should read P(z1, z2) = −(hy ⁄ hx) B3(z1) Δ2(z2) − (hx ⁄ hy) Δ2(z1) B3(z2).
-
p. III-382, in the final expression of the regularization filter, a term β should be replaced by B. After introduction of the missing first-order difference operators, it should read P(z1, z2) = (hy ⁄ hx3) B7(z1) B3(z2) Δ4(z2) + (1 ⁄hx hy) Δ2(z1) B5(z1) Δ2(z2) B5(z2) + (hx ⁄ hy3) B7(z2) B3(z1) Δ4(z1).
@INPROCEEDINGS(http://bigwww.epfl.ch/publications/arigovindan0201.html,
AUTHOR="Arigovindan, M. and S{\"{u}}hling, M. and Hunziker, P. and
Unser, M.",
TITLE="Multigrid Image Reconstruction from Arbitrarily Spaced Samples",
BOOKTITLE="Proceedings of the 2002 Ninth {IEEE} International Conference
on Image Processing ({ICIP'02})",
YEAR="2002",
editor="",
volume="{III}",
series="",
pages="381--384",
address="Rochester NY, USA",
month="September 22-25,",
organization="",
publisher="",
note="")