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

Regularized Interpolation for Noisy Data

S. Ramani, P. Thévenaz, M. Unser

Proceedings of the Fourth IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'07), Arlington VA, USA, April 12-15, 2007, pp. 612-615.

Interpolation is a vital tool in biomedical signal processing. Although there exists a substantial literature dedicated to noise-free conditions, much less is known in the presence of noise. Here, we document the breakdown of standard interpolation for noisy data and study the performance improvement due to regularized interpolation. In particular, we numerically investigate the Tikhonov (quadratic) regularization. On top of that, we explore non-quadratic regularization and show that this yields further improvements. We derive a novel bounded regularization approach to determine the optimal solution. We justify our claims with experimental results. 

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