Technical noteBilateral filtering of magnetic resonance phase images☆
Introduction
The brain's cortical areas, which comprise the outer few millimeters of the brain, are of great interest. Examples are images of the cortical surface, which can be important for surgical planning [1], [2] by providing landmarks [3], [4] and recent advances in functional magnetic resonance imaging (MRI), which demonstrate layer-specific brain activation [5]. Magnetic resonance phase imaging at high spatial resolution and very high field strength provides anatomical images where the substructure of the cortex is resolved [6].
Magnetic resonance phase images [7] have two distinct features that must be dealt with: phase wraps and background field inhomogeneities. Phase wraps occur because MRI maps phase information into the range [−π, π). Since the underlying information may belong to a range beyond [−π, π), the phase images must be unwrapped before further data processing [8]. Moreover, phase contrast contains large contributions from background field inhomogeneities. These contributions have low spatial frequencies compared with the structures of interest and can be removed by high-pass filtering [9]. High-pass filtering is performed by subtracting a low-pass-filtered phase image from the original phase image. While high-pass filtering leads to improved contrast within the brain, it also leads to a poor visualization at the brain's surface [10]. The reason for this is that the low-pass filter blurs the image across boundaries between areas with different signal intensity. The brain's surface is such an area where, in the phase image, the transition between the brain and the noise outside the brain has high spatial frequency. Blurring at the brain's surface is therefore a typical feature of phase images (e.g., Figs. and 1 and 2 in the work of He and Yablonskiy [11] or Fig. 4 in the work of Rowe and Haacke [12]).
Here we propose to perform high-pass filtering of the unwrapped phase images using a bilateral filter [13], instead of a Gaussian filter. The bilateral filter [13] is a nonlinear method used to smooth images while preserving contrast at boundaries. A bilateral filter weights a pixel's neighborhood according spatial distance as well as to similarity in intensity.
Section snippets
Theory
Bilateral filtering is a nonlinear technique introduced by Tomasi and Manduchi [13]. Conventional low-pass filtering computes a weighted average of voxel values in the vicinity of a voxel of interest, in which the average decreases with distance away from the center voxel, usually according to a Gaussian function [14]. Typically, images vary slowly over space, so pixels close to each other are likely to have similar values. The noise values are less correlated than the signal, so the noise is
Data acquisition
Data from two healthy volunteers with no history of neurological or psychiatric diseases was acquired. Informed, written consent was obtained before imaging. Images were acquired on a 3-T system (Philips Achieva) using an eight-channel head coil. Susceptibility-weighted imaging [16], [17] data were acquired using a three-dimensional gradient-echo sequence with the imaging plane parallel to the line connecting the anterior and posterior commissures. Imaging parameters were as follows: echo time
Single echo data
A raw phase image (Fig. 2A), the same image after unwrapping (B), the unwrapped phase image after Gaussian filtering with σd=1.7 mm (D) and after bilateral filtering with σd=1.7 mm and σr=0.5 rad (C) are shown in Fig. 2. Gaussian filtering was performed using bilateral filter in the Gaussian limit by setting σr=1000 rad. Both filters had a kernel size of 9×9 mm. Contrast and windowing settings are identical for all images in Fig. 2. Gaussian filtering leads to surface artifacts in the frontal
Discussion
We have shown that high-pass bilateral filtering with appropriate parameters improves the quality of phase images at the boundary of the brain, compared with Gaussian high-pass filtering. Previous methods employing Gaussian high-pass filtering suffered from artifacts at the boundaries of the brain. These artifacts are reduced with bilateral filtering.
The robustness of the method is due to the reproducible contrast obtained with phase images and due to the large difference between phase contrast
Conclusion
Bilateral filtering is a fast and noniterative robust method for high-pass filtering of magnetic resonance phase images that is easy to implement. The filter behaves like a spatial Gaussian filter in areas with similar pixel values, but it reduces artifacts at boundaries between areas with very different pixel values, such as the surface of the brain.
We would like to direct the reader to very recent work by Ng et al. [19].
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Cited by (10)
Foundations of MRI phase imaging and processing for Quantitative Susceptibility Mapping (QSM)
2016, Zeitschrift fur Medizinische PhysikCitation Excerpt :Heuristic approaches rely on the observation that in most parts of the brain the background field is spatially more slowly varying than the internal field. Established heuristic techniques to suppress background contributions are, e.g., high-pass filtering [63,68,121,125,132,161] and polynomial fitting [36,47,149,177]. Several authors have successfully applied these techniques for QSM in small regions of the brain [149,161].
Quantitative susceptibility mapping: Current status and future directions
2015, Magnetic Resonance ImagingMaximum AmbiGuity distance for phase imaging in detection of traumatic cerebral microbleeds: An improvement over current imaging practice
2020, American Journal of NeuroradiologyAn Automatic Parameter Decision System of Bilateral Filtering with GPU-Based Acceleration for Brain MR Images
2019, Journal of Digital Imaging
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Part of this work was presented at the 17th Scientific Meeting of the International Society of Magnetic Resonance in Medicine, 18–24 April, Honolulu, HI.