BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Multigrid Adaptive Image Processing

M. Unser

Proceedings of the 1995 Second IEEE International Conference on Image Processing (ICIP'95), Washington DC, USA, October 23-26, 1995, vol. I, pp. 49–52.

We consider a general weighted least squares approximation problem with a membrane spline regularization term. The key parameters in this formulation are the weighting factors which provide the possibility of a spatial adaptation. We prove that the corresponding space-varying variational problem is well posed, and propose a novel multigrid computational solution. This multiresolution relaxation scheme uses three image pyramids (input data, weights, and current solution) and allows for a very efficient computation with an effective O(N) complexity, where N is the number of pixels. This general multigrid solver can be useful for a variety of image processing tasks. In particular, we propose new multigrid solutions for noise reduction in images (adaptive smoothing spline), interpolation/reconstruction of missing image data, and image segmentation using an adaptive extension of the K-means clustering algorithm. 

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