Original contributionA simple and fast adaptive nonlocal multispectral filtering algorithm for efficient noise reduction in magnetic resonance imaging
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)| i ∈ I, 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 bywhere 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.
References (33)
- et al.
Evidence of demyelination in mild cognitive impairment and dementia using a direct and specific magnetic resonance imaging measure of myelin content
Alzheimers Dement
(2018) - et al.
Improved determination of the myelin water fraction in human brain using magnetic resonance imaging through Bayesian analysis of mcDESPOT
NeuroImage
(2016) - et al.
Rapid simultaneous high-resolution mapping of myelin water fraction and relaxation times in human brain using BMC-mcDESPOT
NeuroImage
(2017) - et al.
Clinical high-resolution mapping of the proteoglycan-bound water fraction in articular cartilage of the human knee joint
Magn Reson Imaging
(2017) - et al.
A new non-local maximum likelihood estimation method for Rician noise reduction in magnetic resonance images using the Kolmogorov-Smirnov test
Signal Process
(2014) - et al.
Noise estimation in single- and multiple-coil magnetic resonance data based on statistical models
Magn Reson Imaging
(2009) - et al.
Rapid B1 field mapping at 3T using the 180 degrees signal null method with extended flip angle
Magn Reson Imaging
(2018) - et al.
The use of power images to perform quantitative-analysis on low Snr Mr-images
Magn Reson Imaging
(1993) - et al.
A nonparametric method for automatic correction of intensity nonuniformity in MRI data
IEEE Trans Med Imaging
(1998) - et al.
Analysis of mcDESPOT- and CPMG-derived parameter estimates for two-component nonexchanging systems
Magn Reson Med
(2016)
Use of the NESMA filter to improve myelin water fraction mapping with brain MRI
J Neuroimaging
Spatially adaptive unsupervised multispectral nonlocal filtering for improved cerebral blood flow mapping using arterial spin labeling magnetic resonance imaging
J Neurosci Methods
Enhanced Quality of Myelin Water Fraction Mapping From GRASE Imaging Data of Human Brain Using a New Nonlocal Estimation of multi-Spectral Magnitudes (NESMA) Filter
Predicting early symptomatic osteoarthritis in the human knee using machine learning classification of magnetic resonance images from the osteoarthritis initiative
J Orthop Res
A non-local algorithm for image denoising
Proc CVPR IEEE
A nonlocal maximum likelihood estimation method for Rician noise reduction in MR images
IEEE Trans Med Imaging
Cited by (5)
An adaptive optimum weighted mean filter and bilateral filter for noise removal in cardiac MRI images
2023, Measurement: SensorsStructural networks of healthy infants built from dMRI images smoothed with multi-volume nonlocal estimation
2023, Multimedia Tools and ApplicationsAn aeromagnetic denoising-decomposition-3D inversion approach for mineral exploration
2023, Frontiers in Earth Science
- 1
Equal contribution.