دانلود رایگان ترجمه مقاله ارزیابی نویز MRI و حذف نویز با استفاده از PCA غیر موضعی (نشریه الزویر ۲۰۱۵)

برآورد نوفه MRI و نوفه زدایی MRI با بکارگیری PCA غیر موضعی

MRI noise estimation and denoising using non-local PCA

Abstract

This paper proposes a novel method for MRI denoising that exploits both the sparseness and self-similarity properties of the MR images. The proposed method is a two-stage approach that first filters the noisy image using a non local PCA thresholding strategy by automatically estimating the local noise level present in the image and second uses this filtered image as a guide image within a rotationally invariant non-local means filter. The proposed method internally estimates the amount of local noise presents in the images that enables applying it automatically to images with spatially varying noise levels and also corrects the Rician noise induced bias locally. The proposed approach has been compared with related state-of-the-art methods showing competitive results in all the studied cases.

۱ Introduction

Magnetic resonance (MR) imaging has very important role on current medical and research procedures. However, these images are inherently noisy and thus filtering methods are required to improve the data quality. This denoising process is usually performed as a preprocessing step in many image processing and analysis tasks such as registration or segmentation. There is a large amount of bibliography related to the denoising topic that highlights the relevance of this issue for the scientific community. A large review of MRI denoising methods can be found at Mohan et al. (2014). Currently, most denoising methods can be classified on those that use the intrinsic pattern redundancy of the data and those exploiting their sparseness properties. On the first class, the well known non-local means (NLM) filter (Buades et al., 2005) is maybe the most representative method. This method reduces the noise by exploiting the self-similarity of the image patterns by averaging similar image patterns. In MRI, early works using the NLM method are from Coupé et al. (2008) and Manjón et al. (2008). The bibliography related to this method is quite extensive (Tristán-Vega et al., 2012; Coupé et al., 2012; Manjón et al., 2009, 2010, 2012; Wiest-Daesslé et al., 2008; He and Greenshields, 2009; Rajan et al., 2012, 2014). On the other hand, sparseness-based methods try to reduce the noise naturally present in the images by assuming that the noisy data can be represented in a lower dimensionality space. In such methods, it is considered that most of the signal can be sparsely represented using few bases that enables to discard the noise related components or simply approximate noisy patterns by their corresponding noise free patterns. An example of these techniques are for instance those based on FFT or DCT transforms where standard bases such as sin or cosine functions are used to represent the images (Guleryuz, 2003; Yaroslavsky et al., 2000). In this case, noise reduction is achieved by removing noise related coefficients in a transform domain using either soft or hard thresholding techniques. More recently, techniques that learn the bases from the images to be denoised have received much attention (Elad and Aharon, 2006; Mairal et al., 2008; Protter and Elad, 2009). These techniques learn a set of bases from the images to be denoised or from a set of similar noise free images to create a dictionary to sparsely represent image patches as a linear combination of dictionary entries (Aharon et al., 2006). The advantage of these dictionaries over standard ones such those used on DCT or FFT transforms is the fact they are better adapted to the images to be processed that enables a sparser representation and therefore a better signal/noise separation. In MRI, sparse theory has been used in many recent methods (Bao et al., 2008, 2013; Patel et al., 2011). Principal Component Analysis (PCA) and related approaches have been also used for noise reduction in images (Muresan and Parks, 2003; Bydder et al., 2003; Deledalle et al., 2011). This type of technique falls in the second category since it takes benefit from the fact that original signal can be projected into an orthogonal space where most of the variance of the signal is accumulated in few components while the noise being not sparse is uniformly spread over all the components. Noise reduction using PCA normally requires 3 main steps: (1) decomposing a set of selected signals into their principal components, (2) shrinking noise related components, and finally (3) reconstructing back the signals by inverting the PCA decomposition. This approach was first used by Muresan and Parks (2003) by applying PCA decomposition over a local set of image patches. Zhang et al. (2010) improved this approach by grouping similar patches before PCA decomposition and iterated the process to obtain a higher noise reduction. PCA has been also used to robustly compute patch similarities within a non-local means framework (Van de Ville and Kocher, 2010; Zhang et al., 2013, 2014). PCA based denoising has been also used for MRI filtering. In Manjón et al. (2009) PCA was used as a postprocessing step to remove remaining noise after the application of a multicomponent non-local means filter for multimodal MRI. Recently, a nonparametric PCA based filter was proposed for 2D MR images where patch similarities are estimated using rank limited PCA coefficients (Kim et al., 2011). Also recently, PCA based approaches have been proposed for diffusion weighted image (DWI) denoising (Bao et al., 2013; Fan Lam et al., 2013; Manjón et al., 2013). In this paper, we present a novel denoising approach based on the application of PCA decomposition over a set of similar patches using a sliding window scheme. The resulting filtered image is used as a guide image to accurately estimate the voxel similarities within a rotationally invariant NLM (PRI-NLM) strategy as done in Manjón et al. (2012). The increased quality of this guide image resulting from the proposed PCA-based noise removal method significantly improves the application of the PRI-NLM filter boosting the overall denoising performance. We must remark that our guided PRI-NLM filter shares some similarities with methods like the one proposed by Salmon et al. (2012) where a Yaroslavsky filter is applied using information from a pre-filtered image to improve denoising performance or also CANDLE filter (Coupé et al., 2012) which uses a median filtered image. Our approach is also related the method proposed by Zhang et al. (2010) to filter natural images with stationary Gaussian noise but in our case our patch selection is performed on a pre-filtered image to obtain a more robust patch groping on very noisy conditions. Furthermore, we deal with nonstationary Rician noise and the thresholding step is performed by automatically estimating the local noise level from the eigenvalues of the PCA decomposition. The three main contributions in this paper are: (1) a new collaborative filter using a PCA based strategy to compute a improved guide image, (2) an automatic spatially varying noise estimation method fully integrated in the denoising pipeline and (3) a new Rician bias correction method.