Elsevier

Magnetic Resonance Imaging

Volume 55, January 2019, Pages 133-139
Magnetic Resonance Imaging

Original contribution
A simple and fast adaptive nonlocal multispectral filtering algorithm for efficient noise reduction in magnetic resonance imaging

https://doi.org/10.1016/j.mri.2018.08.011Get rights and content

Abstract

Purpose

We recently introduced a multispectral (MS) nonlocal (NL) filter based on maximum likelihood estimation (MLE) of voxel intensities, termed MS-NLML. While MS-NLML provides excellent noise reduction and improved image feature preservation as compared to other NL or MS filters, it requires considerable processing time, limiting its application in routine analyses. In this work, we introduced a fast, simple, and robust filter, termed nonlocal estimation of multispectral magnitudes (NESMA), for noise reduction in multispectral (MS) magnetic resonance imaging (MRI).

Methods

Through extensive simulation and in-vivo analyses, we compared the performance of NESMA and MS-NLML in terms of noise reduction and processing efficiency. Further, we introduce two simple adaptive methods that permit spatial variation of similar voxels, R, used in the filtering. The first method is semi-adaptive and permits variation of R across the image by using a relative Euclidean distance (RED) similarity threshold. The second method is fully adaptive and filters the raw data with several RED similarity thresholds to spatially determine the optimal threshold value using an unbiased criterion.

Results

NESMA shows very similar filtering performance as compared to MS-NLML, however, with much simple implementation and very fast processing time. Further, for both filters, the adaptive methods were shown to further reduce noise in comparison with the conventional non-adaptive method in which R is set to a constant value throughout the image.

Conclusions

NESMA is fast, robust, and straightforward to implement filter. These features render it suitable for routine clinical use and analysis of large MRI datasets.

Introduction

Image filtering for noise reduction has been broadly applied in magnetic resonance imaging (MRI) to improve diagnostic accuracy, quality of image registration and segmentation [1], and parameter estimation [[2], [3], [4], [5], [6]]. The enhancement in signal-to-noise ratio (SNR) can be used to improve temporal or spatial resolution. Local image filtering methods estimate the true intensity of a given voxel using neighboring voxels. A popular method of local filtering is based on local kernel convolution with the original image to provide a weighted-average estimate of the intensity for the voxel of interest (i.e. index voxel). Unlike local kernel methods such as boxcar or Gaussian averaging, nonlocal (NL) filtering algorithms permit the inclusion of non-neighboring voxels in the intensity estimation of an index voxel [[7], [8], [9]]. Rather than using spatial proximity as a criterion for inclusion in the intensity estimate, NL filters use the similarity of signal intensities between voxels [[7], [8], [9], [10]]. This increases the number of similar voxels available while not forcing inclusion of dissimilar ones, leading to improved denoising and feature preservation.

MRI studies often involve acquiring multispectral (MS) images, e.g. images obtained at different echo times (TEs), repetition times (TRs), flip angles, or diffusion b-values [[9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]]. These image sets provide varying contrast that reflect the evolution of the MR signal for different tissues with respect to the varied acquisition parameter. While noise may make two dissimilar tissues appear similar within a given image, the overall evolution of intensity across MS images improves discrimination between different tissue types leading to improved filtering [[9], [10], [11]].

We have recently introduced a new MS nonlocal maximum likelihood (MS-NLML) filter [9] and demonstrated its superior performance as compared to current advanced filters in terms of noise reduction and feature preservation. This filter restores the amplitude of an index voxel using a maximum likelihood estimation (MLE) based on R pre-selected voxels with similar MS signal patterns. However, the MS-NLML filter is relatively complex to implement and requires lengthy processing times, especially for large datasets, due to the MLE calculation. Here, we introduce a new filter, termed nonlocal estimation of multispectral magnitudes (NESMA), which replaces the MLE with a mean estimate of R similar voxels; this greatly simplifies implementation and accelerates processing time. Note that the MS-NLML and NESMA filters are similar in that they are both non-local estimates of index voxel intensity based on incorporating data from voxels deemed similar to the index voxel. However, in practical terms, they are very different, due to the use of simple averaging in NESMA as opposed to maximum likelihood estimation in MS-NLML.

The number of similar voxels used in nonlocal MLE filters, including in our previous MS-NLML filter, is conventionally set to a fixed value, R, throughout the image (8, 9, 20). In many instances this includes too many or too few voxels, depending upon the local structure of the image. For example, if there are relatively few voxels similar to the index voxel, as is the case for heterogeneous regions and near object edges, fixing R may force inclusion of dissimilar voxels and cause blurring. In contrast, if R is too small for an index voxel in which there are many similar voxels, as in homogenous regions, the denoising process will be suboptimal. Previous implementations of adaptive filtering have used different approaches to overcome this limitation. Rajan et al. introduced a method to compare the MLE of local noise variance, based on a progressively increasing number of NL voxels, to the noise variance estimated from the image background. The optimal value of R for each index voxel was then defined as the value yielding the closest match [21]. The same authors proposed a method to replace the Euclidean distance with a Kolgomorov-Smirnov test to evaluate the difference between the neighborhoods surrounding the index voxel, i, and a candidate voxel, j, to determine if the difference was Gaussian-distributed [22]. However, these approaches involve a complex definition of voxel similarity or lengthy processing times. Here we introduce two new, easy-to-implement, adaptive methods that permit spatial variation of R. We term these methods semi-adaptive (SA) and fully-adaptive (FA).

The plan of the paper is as follows. First, we describe and detail the implementation of the MS-NLML and NESMA filters. We then outline the two new adaptive methods for determining R. Finally, we present the results and discuss the filtering performance of the MS-NLML and NESMA filters. Analyses were performed on both synthetic and in vivo datasets.

Section snippets

Theory

We assume that the data consists of a multispectral set of registered images S defined on a discrete grid I, given by S = {Sk(i)| iI, Sk(i) ∈ ℝK}, where K is the total number of images in the spectral dimension. Each measured signal intensity Sk(i) and true intensity Ak(i) for index voxel i and spectral image k follows a Rician-distributed conditional probability density function P(Sk(i)|Ak(i), σ) given byPSkAk,σ=Skσ2expSk2+Ak22σ2·I0SkAkσ2,where Sk represents the measured signal intensity

Simulation datasets

Synthetic multislice T2-weighted (T2W) brain datasets were obtained from BrainWeb, [29] from which a T2 map was generated. Representative T2 values for white matter, gray matter, and cerebrospinal fluid were chosen as 60 ms, 85 ms, and 180 ms, respectively. T2W brain images were then generated with twenty values of TE ranging uniformly from 10 ms to 200 ms. Rician-distributed noise was incorporated into the noise-free images to create datasets with SNR values of 10 or 20 [30]. SNR was defined

Results

Fig. 1 shows a comparison of the filtering performance of the NA, SA, and FA NESMA and MS-NLML filters on a synthetic T2W dataset generated with SNR = 20. NA-NESMA and NA-MS-NLML filtered images showed comparable levels of noise reduction and have nearly identical MSE values, 0.027 and 0.029, respectively, and identical SSIM values (0.95) (Table 1). However, the zoomed-in images in Fig. 1 show that noise reduction for both filters is not optimal in white matter regions. While noise reduction

Discussion

We present a new nonlocal multispectral filter, NESMA, which greatly simplifies implementation and reduces computational time as compared with MLE-based filters, including the MS-NLML filter. We show that filtering quality is retained with respect to noise reduction and feature preservation. Furthermore, we propose two simple approaches for spatially varying the number of similar voxels, R, used in denoising. Our analyses of synthetic and in vivo data show that the SA method provides an

Conclusion

We have introduced a new fast multispectral nonlocal filter, NESMA, and two adaptive variants, for filtering magnitude MR images. In addition to its robust filtering performance, NESMA is straightforward to implement and requires minimal user-defined parameters. These features render it suitable for routine clinical use and analysis of large datasets.

Acknowledgment

This work was supported by the Intramural Research Program of the NIH, National Institute on Aging.

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