Original contributionDenoising 3D MR images by the enhanced non-local means filter for Rician noise☆
Introduction
Three-dimensional magnetic resonance (MR) imaging plays an important role in modern medical diagnosis and therapy because of their noninvasive, high-resolution and isotropic voxels. However, random noise usually appears during the process of obtaining MR images and degrades the quality of the images. The noise not only affects the medical diagnostic tasks, but also degrades many image processing and analysis tasks, such as registration, segmentation, super-resolution and visualization, etc. Thus, it is necessary to remove the noise from the images. In general, there are two ways to suppress the noise. One way is to improve the image acquisition techniques. For example, acquire several samples of the same data and average them. This usually leads to long acquisition time and additional motion artifacts, and becomes unrealistic. Another way is to denoise the acquired image by some image denoising techniques. It requires less time and is often as effective as improving the acquisition techniques. Thus, this method has been widely used.
Many image denoising methods have been proposed in prior research. Starting from the classic, e.g., Wiener filtering [1] and Gaussian filter [2], to the more recent, such as anisotropic diffusion filtering [3], total variation minimization [4], wavelet thresholding methods [5] and bilateral filter [6], etc. These methods have been extensively used in MRI denoising, e.g., Wiener filtering [7], Gaussian filter [8], anisotropic diffusion filtering [9], wavelet thresholding [10], [11], [12], [13] methods and trilateral filtering [14]. A good review of some of these methods can be seen in Ref. [15]. Most of the methods use the same approach, being that the new value of a pixel in the image is calculated by averaging the values of a set of other pixels. For example, the classic Gaussian filter denoises an image I by convoluting the image with a Gaussian kernel Gσ of width σ>0:where I(x,y) represents the value (intensity value) of pixel i at position (xi,yi) of I, u(xi,yi) represents the filtered value, and M and N represent the width and height of Gσ, respectively. It performs well on removing noise in the flat regions of the image. However, it also removes some detail and blurs the edges. Bilateral filter [6] updates the value of pixel i of image I by means of nonlinear combination of nearby image values I(j) based on their geometric closeness and photometric similarity:where I(i) represents the value of pixel i; N(i) represents a neighborhood centered at pixel i; d(i,j) and s(I(i),I(j)) represent the geometric closeness and photometric similarity between pixel i and pixel j, respectively; and k(i) is a normalizing constant.Since the similarities of the pixels' values are considered, the edges can be preserved. However, approaches like the bilateral filter are spatially local or semi-local. That is to say, only the pixels in a neighboring area of the pixel being processed have a significant impact on the new value of that pixel. As a result, large-scale structures are preserved, while small structures are considered as noise and are removed.
Actually, there are lots of repeated structures in the natural images and the medical images. Considering the redundancy property, Buades et al. [16] proposed a non-local means (NLM) filter. Unlike most existing techniques which mainly rely on local pixels within a small neighbor to remove the noise, the NLM filter finds repeated structures in the global area. The restored value of pixel i is calculated as the weighted average of all the pixels within the image:while the weight w(i,j) is computed as the similarity between the neighborhood of pixel i being processed and the neighborhood of the other pixel j in the whole image. Since the noise is removed by finding and averaging repeated structures in the global area, and the similarity is computed by comparing the patches instead of single points, the edges and detail can both be well preserved. Some research has demonstrated its superiority over other methods.
The original NLM filter was initially proposed for removing Gaussian noise. Considering the characteristic of Rician noise in MR images, Manjón et al. [17] and Wiest-Daesslé et al. [18] adapted the NLM filter and applied it to MRI denoising. Good performance was shown in their experiments. However, the performance of these two filters will decrease as the noise increases. In this article, we propose an enhanced NLM filter with pre-processing (PENLM) to improve the denoising effect. In the proposed filter, the squared magnitude image is first denoised by the NLM filter. Then, unbiased correcting is performed to remove the bias deviation. In the original NLM filter, the similarity of two pixels (or voxels) is computed based on the noisy image. Actually, the accuracy of the computation will be affected by the noise. As far as this problem is concerned, we denoise the image by the Gaussian filter first, then calculate the similarity of two pixels (or voxels) based on the filtered image. Another method we adopt to improve the computation accuracy is to utilize a group of a square and a line as neighbor to replace the original cubic neighbor for weight estimations. The proposed filter has been compared with several methods presented recently, showing an improved performance, especially in the circumstances where the noise is significant.
The rest of this article is organized as follows: Section 2 describes the NLM filter and presents a brief review of the prior work about the NLM filter. The proposed filter is introduced in Section 3. In Section 4, the influence of the parameters is first explored. Then, the proposed filter is compared with several existing filters in peak signal-to-noise ratio (PSNR) and by vision on the MR images from the BrainWeb database. Finally, the conclusion is presented in Section 5.
Section snippets
The NLM filter
Given a 2D noisy image I, the NLM filter computes the denoised value u(i) for pixel i of I by calculating the weighted average of all pixels within I. This can be represented as follows [16]:where I(j) is the value of pixel j and w(i,j) represents the similarity between pixel i and pixel j. It is defined as,where h is a degree of filtering; Ni and Nj are the square neighborhoods of pixel i and pixel j, respectively;
The characteristics of MR images
It is known that the magnitude of the MR image is computed from the real image and imaginary image which contain Gaussian distributed noise, and the noise contained in the magnitude MR image follows a Rician distribution [29]. The squared magnitude MR image (the value of each pixel in the image is the square of the value of the corresponding pixel in the original magnitude image) has a noise bias which is equal to 2σ2 and is signal independent [11], where σ is the standard deviation of the
Experiments
In this section, the performance of the proposed filter was investigated. To select the optimized parameters, we first studied the impact of the parameters for denoising. Then, the proposed method of estimating noise bias was compared with Nowak's [11] method. Finally, we compared the proposed filter with three other filters: the original NLM filter, the UNLM filter and the RNLM filter.
We defined two kinds of methods:
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Enhanced NLM (ENLM) filter. In this filter, the methods of unbiased
Conclusion
In this article, we proposed an enhanced NLM filter with preprocessing for 3D MR images. The contributions of the proposed filter mainly include (a) calculating similarity based on the Gaussian filtered image to reduce the disturbance of the noise, and (b) a new neighbor for more accurate computation of the similarity. Comparative experiments were performed on T1-weighted, T2-weighted and PD-weighted images from the BrainWeb Database to compare and analyze the proposed filter with the original
Acknowledgments
We would like to thank McConnell Brain Imaging Center (BIC) of the Montreal Neurological Institute, McGill University for providing access to the MR data in the BrainWeb Database (http://www.bic.mni.mcgill.ca/brainweb). We would also like to thank VisAGeS of the IRISA Institute, University of Rennes I for providing online applications (http://www.irisa.fr/visages/benchmarks/).
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2020, Smart HealthCitation Excerpt :Lu S et al. (Lu et al., 2016, pp. 1412–1417) proved that the pixel selection based NLM approach to be one of the best approaches for denoising. The method is further extended to a 3-dimensional MR image (Liu et al., 2010). However, all these denoising approaches are applicable for the MR images which are having equal noise distributions.
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This work was supported in part by the China International Science and Technology Cooperation Project (Grant No. 2009DFA12290).