Regularized Interpolation for Noisy Images

Abstract—Interpolation is the means by which a continuouslydefined model is fit to discrete data samples. When the data samples are exempt of noise, it seems desirable to build the model by fitting them exactly. In medical imaging, where quality is of paramount importance, this ideal situation unfortunately does not occur. In this paper, we propose a scheme that improves on the quality by specifying a tradeoff between fidelity to the data and robustness to the noise. We resort to variational principles which allow us to impose smoothness constraints on the model for tackling noisy data. Based on shift-, rotation-, and scaleinvariant requirements on the model, we show that the Lpnorm of an appropriate vector derivative is the most suitable choice of regularization for this purpose. In addition to Tikhonovlike quadratic regularization, this includes edge-preserving totalvariation-like (TV) regularization. We give algorithms to recover the continuously-defined model from noisy samp...

• Type: Journal
• Year: 2010
• Where: TMI
• Authors: Sathish Ramani, Philippe Thévenaz, Michael Unser
• Keywords: Data Samples, Model, Quadratic Regularization, TMI 2010