Kernel regression based feature extraction for 3D MR image denoising

Abstract

Kernel regression is a non-parametric estimation technique which has been successfully applied to image denoising and enhancement in recent times. Magnetic resonance 3D image denoising has two features that distinguish it from other typical image denoising applications, namely the tridimensional structure of the images and the nature of the noise, which is Rician rather than Gaussian or impulsive. Here we propose a principled way to adapt the general kernel regression framework to this particular problem. Our noise removal system is rooted on a zeroth order 3D kernel regression, which computes a weighted average of the pixels over a regression window. We propose to obtain the weights from the similarities among small sized feature vectors associated to each pixel. In turn, these features come from a second order 3D kernel regression estimation of the original image values and gradient vectors. By considering directional information in the weight computation, this approach substantially enhances the performance of the filter. Moreover, Rician noise level is automatically estimated without any need of human intervention, i.e. our method is fully automated. Experimental results over synthetic and real images demonstrate that our proposal achieves good performance with respect to the other MRI denoising filters being compared.

Introduction

Magnetic Resonance Imaging (MRI) techniques have an ever increasing importance in current medical diagnosis, due to the fact that they are non-invasive and are able to produce accurate three dimensional representations of the internal structures of the human body. Nevertheless, practitioners must attain a balance between image quality and patient comfort, since the image generation process yields more exact images as the acquisition time increases. Moreover, there could be other temporal constraints, such as physiological or organizational limitations. Hence, many MR images suffer from noise, which disturbs the diagnosis.

In an attempt to remedy this problem, many researchers have devoted to the task of developing MRI denoising techniques. A necessary condition for these methods is that they do not remove useful anatomical information. That is, they should not delete real structures in their intent to clean the noise. An additional difficulty comes from the nature of the noise present in this kind of images, which is Rician distributed. This is not usual in image processing, where other noise types are more common, such as Gaussian or impulsive. Consequently, specific techniques must be developed for Rician noise in order to manage MR images properly, since general image denoising algorithms produce suboptimal results.

There is a wide range of methods which have been proposed to accomplish these goals. The so called conventional approach (McGibney and Smith, 1993, Sijbers et al., 1998b, Sijbers and den Dekker, 2004) starts by obtaining an estimation of the Rician noise level present in the acquired image, and then looks for maximum likelihood estimators of the original noiseless pixel values.

Anisotropic diffusion (Perona and Malik, 1990, Gerig et al., 1992, Samsonov and Johnson, 2004) reduces image noise by considering a scale space where the input image generates a succession of progressively more blurred images. It has been adapted to reduce the speckle (Yu and Acton, 2002, Aja-Fernández and Alberola-López, 2006) and suit the need of unbiasing of the Rician noise (Krissian and Aja-Fernández, 2009). Moreover, it has been used for MRI denoising in conjunction with the Wiener filter (Martín-Fernández et al., 2007), which spatially averages pixels by studying their correlation structure.

Wavelet domain methods have produced a large number of algorithms for cleaning magnetic resonance images (Wink and Roerdink, 2004, Pizurica et al., 2006). Early works (Nowak, 1999, Zaroubi and Goelman, 2000) were followed by multiscale products thresholding (Bao and Zhang, 2003), which uses adjacent wavelet subbands to separate the edges from noise. These techniques can also be used to enhance the performance of other approaches. This is demonstrated in (Wu et al., 2003), where wavelets are used to remove the noise in the background areas (those with zero noiseless value), which follows a Rayleigh distribution. Bilateral filtering has been shown to preserve the edges efficiently (Anand and Sahambi, 2010); the proposal works on the squared values of the noisy image, so that the noise is more easy to distinguish from the useful signal.

Other methodologies include Expectation-Maximization based Bayesian estimation (Awate and Whitaker, 2007), median filtering (Liévin et al., 2002, Ling and Bovik, 2002) and modeling of the noisy image as a random field (He and Greenshields, 2009).

Finally, the non-local means filter has been recently proposed, and has received considerable attention (Coupé et al., 2008, Liu et al., 2010, Manjón et al., 2008, Manjón et al., 2010, Buades et al., 2005a, Buades et al., 2005b, Wiest-Daesslé et al., 2008). It builds an estimation of the noiseless pixel value by weighted averaging over a large portion of the input image, where the weights are based on the relative similarities among the neighbor pixels and that one to be estimated. Its capabilities go beyond MRI denoising, since it has been successfully applied to super-resolution reconstruction Protter et al., 2009.

In this work our aim is to adapt to MRI denoising an image denoising framework which has been successful in other applications, such as kernel regression (Takeda et al., 2007, Takeda et al., 2009, López-Rubio, 2010). Kernel regression is a non-parametric estimation method to find the conditional expectation of a variable (the noiseless pixel value) with respect to another (the pixel coordinates in the image). Here we propose a MRI restoration system which uses the local directional information from a second order kernel regressor to guide the operation of a zeroth order kernel regression.

The structure of this paper is as follows. First we describe our proposed restoration system (Section 2), which is made up of four modules. Then we explain our experimental methodology and present the results with both synthetic and real benchmark images (Section 3). After that we discuss the features of our approach, and we outline future lines of research (Section 4). Finally, Section 5 is devoted to conclusions.