Department of Informatics and Telecommunications, University of Athens, Greece.
IEEE Trans Image Process. 2010 Jun;19(6):1465-79. doi: 10.1109/TIP.2010.2042995. Epub 2010 Mar 15.
The main contribution of this paper is the development of a novel approach, based on the theory of Reproducing Kernel Hilbert Spaces (RKHS), for the problem of noise removal in the spatial domain. The proposed methodology has the advantage that it is able to remove any kind of additive noise (impulse, gaussian, uniform, etc.) from any digital image, in contrast to the most commonly used denoising techniques, which are noise dependent. The problem is cast as an optimization task in a RKHS, by taking advantage of the celebrated Representer Theorem in its semi-parametric formulation. The semi-parametric formulation, although known in theory, has so far found limited, to our knowledge, application. However, in the image denoising problem, its use is dictated by the nature of the problem itself. The need for edge preservation naturally leads to such a modeling. Examples verify that in the presence of gaussian noise the proposed methodology performs well compared to wavelet based technics and outperforms them significantly in the presence of impulse or mixed noise.
本文的主要贡献在于提出了一种新的方法，该方法基于再生核希尔伯特空间（RKHS）理论，用于解决空间域中的噪声去除问题。所提出的方法的优点在于，它能够从任何数字图像中去除任何类型的加性噪声（脉冲、高斯、均匀等），与最常用的依赖于噪声的去噪技术形成对比。该问题通过利用半参数表示中的著名表示定理，将其作为 RKHS 中的优化任务来解决。尽管在理论上是已知的，但到目前为止，据我们所知，这种半参数表示形式的应用有限。然而，在图像去噪问题中，其使用是由问题本身的性质决定的。边缘保持的需要自然导致了这种建模。实例验证了在高斯噪声存在的情况下，与基于小波的技术相比，所提出的方法表现良好，并且在存在脉冲或混合噪声的情况下，性能明显优于它们。
