Elimination of k-space spikes in fMRI data

Xiaodong Zhang, Pierre-Francois Van De Moortele, Josef Pfeuffer, Xiaoping Hu*Center for Magnetic Resonance Research and Department of Radiology, University of Minnesota Medical School, Minneapolis, MN 55455, USA

Abstract

The subtle signal changes in functional magnetic resonance imaging (fMRI) can be easily overwhelmed by noise of various origins.Spikes in the collected fMRI raw data often arise from high-duty usage of the scanner hardware and can introduce significant noise in theimage and thereby in the image time series. Consequently, the spikes will corrupt the functional data and degrade the result of functionalmapping. In this work, a simple method based on processing the time course of the k-space data are introduced and implemented to removethe spikes in the acquired data. Application of the method to experimental data shows that the methods are robust and effective foreliminating of spike-related noise in fMRI time series. © 2001 Elsevier Science Inc. All rights reserved.

Keywords: fMRI; EPI; Spike noise removal; K-space

1. Introduction

Despite its routine use in studying brain function, func-tional magnetic resonance imaging (fMRI) based on theblood oxygenation level dependent or BOLD contrast is stilllimited by a number of factors. In particular, activationinduced signal changes are often small and may be over-whelmed by artifactual signal changes caused by gross bodymovements, physiological fluctuation, and system instabil-ities [1,2]. These artifacts have been known to degrade thefMRI data and hamper the detection of activation inducedBOLD response. A number of methods are available fortheir correction [1,3,4].

Recent advances in fMRI have moved it to the domain ofhigh spatial (�1 mm) and temporal resolutions (�100 ms),extending its utility in neuroscience. However, due to im-perfections in gradient coil, RF hardware, or other hardwarecomponents, noise spikes may appear in the acquired k-space data, especially when strong gradients are employedat a high duty cycle. The contribution of a single spike is asinusoid oscillation in the image domain. Spikes appearingrandomly in the k-space introduce complicated noises in the im-age domain, degrading the signal-to-noise ratio of the fMRI data.

In general, spikes appear randomly in the k-space. Fur-thermore, their occurrence in time is also random. A number

of these sporadic spikes in the k-space data for each imageadd a complicated pattern to the original image and theirrandom occurrence in time leads to detrimental spike-likefluctuations in the time series. While it is possible to reducethis kind of fluctuations with a low-pass filter or othermethods [5,6], filtering is insufficient for intense spikesbecause their energy spreads over a wide range of temporalfrequency. In addition, filtering may introduce unwantedsmoothing of the time course.

An algorithm for removing spikes in the k-space datawere recently introduced and applied to fMRI [7]. For eachimage, spikes are detected based on Hermitian symmetryand removed by replacing the corrupted k-space data withthe value predicted by Hermitian symmetry [8]. For anfMRI time series, the procedure is carried out image byimage. While this algorithm worked reasonably well, itcannot be applied to partial Fourier data and does not workrobustly near the center of the k-space where the spikeamplitude is comparable to the magnitude of the actualk-space signal.

In this note, we describe a method for removing spikes infMRI data based on the analysis of the k-space time series.Results on experimental data were obtained and demonstratedthat the method worked effectively and robustly for fMRI.

2. Methods

Examination of the EPI raw data reveals that spikesappear randomly in the k-space and time. In order to elim-

* Corresponding author. Tel.: �1-612-626-7411; fax: �1-612-626-2004.E-mail address: xiaoping@cmrr.umn.edu (X. Hu).Work supported by the National Institutes of Health (Grants

R01MH55346 and RR07809).

Magnetic Resonance Imaging 19 (2001) 1037–1041

0730-725X/01/$ – see front matter © 2001 Elsevier Science Inc. All rights reserved.PII: S0730-725X(01)00428-3

Fig. 1. Real and imaginary parts of the time course of a k-space point before (A, B) and after (A�, B�) correction by the present method.

Fig. 2. Average time course from an ROI in the background of the image before (A) and after the spike removal (B). The spikes in the image domain beforethe processing are much more frequent than those in the k-space. The effective of the spike removal is evident.

1038 X. Zhang et al / Magnetic Resonance Imaging 19 (2001) 1037–1041

inate the spikes from the measured data, two steps areneeded. The first is to locate the spikes, and the second is toreplace the spikes in the raw data with a reasonable approx-imation.

For an fMRI data set, hundreds of images of the sameslices are usually acquired consecutively. Because only asmall image-to-image variation is expected, the time courseof the k-space data should be relatively stable if only ran-dom noise is present. Based on this observation, spikedetection is achieved by examining the k-space time coursepoint-by-point. Examining the k-space time course is anatural approach as the spikes affect individual k-spacepoints at random times.

The spike removal procedure is applied as a slidingwindow operation on the time course of each k-space point.The detection operation is applied to the magnitude of thedata for simplicity. The first step in the detection process isthe estimation of the standard deviation of the thermal noisein the data, denoted as �, by calculating the std-deviation ofa high k-space data point. For each time point i, 10 timepoints preceding it are averaged to generate an estimate ofthe local mean, �i. The magnitude of the time point underconsideration, mi, is then compared with the mean. If �mi -�i� � (0.1 �i � �), point i is identified as a spike and itscomplex values are replaced by the average of 3 pointspreceding it. This procedure is repeated for the next time

point until all the time points are processed. Note that thesliding window approach ensures that spikes in the preced-ing time points are already removed before a given timepoint is processed.

The threshold, (0.1 �i � 3�), consists of two terms.The first, proportional to the local mean, is used toaccount for any possible fluctuations in the data thatarises from physiological noise or functional activation.The choice of 0.1 in the expression says that the changeabove 10% of the mean is classified as a spike. This levelis appropriate as most physiology related change in thek-space between the consecutive time points is under10%. The second term in the threshold is included toaccount for thermal noise.

The above algorithm is implemented in MATLAB 5.2(Mathworks, Inc, Boston, MA) and applied to a single-shotEPI data set obtained with a 7T human whole body MRIscanner (Varian, Palo Alto, CA). The MR imaging param-eters were, data matrix � 256 � 32, FOV � 23.0 cm(readout) � 2.88 cm (phase encoding), slice thickness � 3mm, TE � 20 msec, and TR � 0.5 sec. A number of intensespikes were seen in the raw data. The occurrence of thespikes was sporadic in the time series of 568 images. Allfunctional images were analyzed with Stimulate [9]. Forcomparison, the same data set was also processed with theHermitian symmetry based method [7].

Fig. 3. The plot of number of pixels passing threshold versus cross-correlation threshold. An increase in the number pixels passing the threshold is seen atall threshold levels.

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3. Results and discussion

The removal of spikes in the raw data was successfullyachieved in the k-space (Fig. 1). In order to illustrate theeffect of this removal, time courses of the image domainwere also examined. The time courses of an ROI in thebackground before and after the correction are shown in Fig.2. Evidently, the spike-removal process significantly re-duced the fluctuation in the background, where the spike-induced fluctuation was much higher than the backgroundnoise. It is interesting to see that spikes appear more fre-quently in the image time course because a spike in anyk-space point leads to a spike in the image. Because of thisfact, removing spikes in the k-space time course is advan-

tageous as the spikes are sparse in time for individualk-space data points.

Functional maps were obtained before and after the cor-rection. The plot of the number of active pixels vs. cross-correlation threshold is shown in Fig. 3. The functionalmaps with the thresholds equal to 0.25 are overlaid on thecorresponding anatomic image (Fig. 4). Evidently, spikeremoval improved the detection of activated pixels as can beseen from the increased number of activated pixels in Fig. 3.In the activation maps, there are only 147 pixels obtainedbefore the correction when the threshold is 0.25 (p � 10�6).After the correction of the two different spike-removalmethods, the resultant map contains 210 active pixels.Therefore, the time course spike removal approach showssubstantial improvement for fMRI. The number of activatedpixels detected after processing the Hermitian symmetrybased method [7] was 192, indicating that the presentmethod is slightly more robust.

Although a direct application of median filter may beeffective in removing the spikes, it will also alter the sta-tistics of the fMRI time course, making the assessment ofstatistical significance in activation detection difficult. Theapproach presented here alters the spike data alone andtherefore affects the time course data to a much less extent.

Also, it is interesting to note that carrying out the pro-cessing in the k-space is more appropriate for a number ofreasons. First, because the spikes appear in random loca-tions in the k-space, dealing with it directly in the k-space ismore robust. In the image domain, the effect of the spikesare spread out and mixed with other spikes, making thespikes more difficult to detect. In addition, it should benoted that the spike removal procedure described in thispaper is not a linear and shift-invariant procedure and can-not be equivalently implemented in the image space. Fur-thermore, unlike a filtering approach, the present approachdoes not introduce unnecessary temporal smoothing to thedata.

4. Conclusion

The algorithm for removing spikes in fMRI data set hasbeen described and demonstrated. The k-space time spikeremoval approach can be applied to fMRI data series andincreases the signal-to-fluctuation ratio of the fMRI signaland improve the detection of activated pixels. This methodis easy to implement and is expected to be useful particu-larly for functional imaging, particularly where the highduty cycle needed for rapid imaging may lead to spikes inthe data.

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Fig. 4. Activation maps (threshold: 0.25; p � 10�6) obtained without andwith spike removal overlaid on the anatomic image.

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