Edge Preserving Image Denoising in Reproducing Kernel Hilbert Spaces

TL;DR

This paper introduces a novel image denoising method using Reproducing Kernel Hilbert Spaces, which outperforms wavelet techniques especially in impulse or mixed noise scenarios.

Contribution

The paper develops a new RKHS-based approach for noise removal, leveraging semi-parametric regularization and the Representer Theorem for improved denoising performance.

Findings

Performs well with Gaussian noise

Outperforms wavelet methods with impulse noise

Effective in mixed noise conditions

Abstract

The goal of this paper is the development of a novel approach for the problem of Noise Removal, based on the theory of Reproducing Kernels Hilbert Spaces (RKHS). The problem is cast as an optimization task in a RKHS, by taking advantage of the celebrated semiparametric Representer Theorem. Examples verify that in the presence of gaussian noise the proposed method performs relatively well compared to wavelet based technics and outperforms them significantly in the presence of impulse or mixed noise. A more detailed version of this work has been published in the IEEE Trans. Im. Proc. : P. Bouboulis, K. Slavakis and S. Theodoridis, Adaptive Kernel-based Image Denoising employing Semi-Parametric Regularization, IEEE Transactions on Image Processing, vol 19(6), 2010, 1465 - 1479.