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. Author manuscript; available in PMC: 2021 Jul 1.
Published in final edited form as: Magn Reson Imaging. 2020 Apr 22;70:108–114. doi: 10.1016/j.mri.2020.04.013

Effects of Apodization Smoothing and Denoising on Spectral Fitting

Mohammed Goryawala 1, Molly Sullivan 2, Andrew A Maudsley 1
PMCID: PMC7311312  NIHMSID: NIHMS1591922  PMID: 32333950

Abstract

Purpose:

Visual review of individual spectra in magnetic resonance spectroscopic imaging (MRSI) data benefits from the application of spectral smoothing; however, if this processing step is applied prior to spectral analysis this can impact the accuracy of the quantitation. This study aims to analyze the effect of spectral denoising and apodization smoothing on the quantitation of whole-brain MRSI data obtained at short TE.

Methods:

Short-TE MRSI data obtained at 3T were analyzed with no spectral smoothing, following (i) Gaussian apodization with values of 1, 2, 4, 6, and 8 Hz, and (ii) denoising using principal component analysis (dnPCA) with 3 different values for the number of retained principal components. The mean lobar white matter estimates for four metabolites, signal-to-noise ratio (SNR), spectral linewidth, and confidence intervals were compared to data reconstructed using no smoothing. Additionally, a voxel-wise comparison for N-acetylaspartate quantitation with different smoothing schemes was performed.

Results:

Significant pairwise differences were seen for all Gaussian smoothing methods as compared to no smoothing (p<0.001) in linewidth and metabolite estimates, whereas dnPCA methods showing no statistically significant differences in these measures. Confidence intervals decreased, and SNR increased with increasing levels of apodization smoothing or dnPCA denoising.

Conclusion:

Mild Gaussian apodization (≤ 2 Hz at 3T) can be applied with minimal (1%) errors in quantitation; however, smoothing values greater than that can significantly affect metabolite quantification. In contrast, mild to moderate dnPCA based denoising provides quantitative results that are consistent with the analysis of unsmoothed data and this method is recommended for spectral denoising.

Keywords: MRSI, spectral fitting, denoising, smoothing, metabolite quantification, PCA

1. INTRODUCTION

Automated spectral analysis methods are established and essential tools for quantitation of in vivo MR spectroscopy, with the primary methods using iterative parametric modeling approaches that incorporate prior knowledge and constraints on model parameters.[1–5] These methods aim to determine the optimal parameters for a spectral model function that minimizes the difference between the data and the noise-free model function, with the assumption of Gaussian white noise in the data in order to obtain a bias-free estimate. The spectral model can be conveniently described in the time domain, however, for in vivo MRS measurements the signal model must also account for variable baselines and signal components from lipids and unsuppressed water that can more conveniently be modeled in the frequency-domain. [6] For this reason, the Fourier transform to the frequency-domain is typically done prior to spectral analysis or incorporated into the analysis algorithm.

Historically, spectral filtering by apodization with a weighting function matched to the decay envelope of the spectral lineshape has been used to maximize the spectral signal-to-noise (SNR) ratio and the application of this preprocessing step has the potential to improve quantitation accuracy through the reduction of noise while also improving the visual review. [7] However, apodization smoothing is known to increase the spectral linewidth and it has been widely assumed that such methods should not be applied prior to applying a parametric fitting procedure. Bartha et al.[8] have shown that spectral smoothing using a Lorentzian function decreased the precision of the quantitation for spectra obtained at 1.5T for TE=20 ms, although with minimal effect on the NAA quantitation and differing trends for the other metabolites. That study also showed that the standard deviation for repeated measures decreased with increasing filter strength, indicating improved reproducibility of the spectral fitting following smoothing. These results indicate that there is a tradeoff between the effects of the increased SNR and increased spectral overlap that results from the apodization, which will be dependent on the complexity of the spectral model.

Magnetic resonance spectroscopic imaging (MRSI) data can contain several thousand spectra, making automated spectral fitting methods essential for creating maps of individual metabolite distributions. Spectral smoothing, which is most easily implemented as an apodization in the time domain prior to Fourier transformation, also benefits a visual review of individual spectra that is often required for clinical applications. However, the effects of this spectral smoothing must be considered on automated spectral analysis methods in MRSI quantification.

The availability of multiple voxels in MRSI data that exhibit common spectral features presents a unique opportunity for applying signal denoising methods, for example using wavelet shrinkage,[9] low-rank image reconstruction,[10] or singular value decomposition (SVD).[11–13] Such methods aim to separate common signal features from noise and have the advantage over apodization smoothing methods in that the spectral lineshape is not affected. However, the determination of the appropriate thresholds that separate the noise from the signal can be problematic, leading to possible loss of spatial resolution or the elimination of spectral features that are present in only a small fraction of the voxels.[11, 14] While denoising methods have been demonstrated to improve SNR for MRSI data, the impact of this operation on a parametric spectral analysis procedure has not been evaluated.

The aim of this study is to analyze the impact of denoising and apodization smoothing on automated spectral analysis of whole-brain MRSI data obtained at short TE by studying the impact on spectral quality using linewidth and signal-to-noise of the resultant spectra and certainty of spectral fitting using confidence intervals. Overall, the study has the objective of determining if spectral smoothing can be used to improve visualization of spectra from MRSI datasets without significantly impacting spectral quantitation using either SVD based denoising and apodization smoothing.

2. METHODS

2.1. Study Population

Data were obtained from an existing database for 11 normal control subjects, 6 females, and 5 males, with a mean age of 40 ± 12.7 years. Subjects completed a self-reporting questionnaire to indicate the absence of neurological or psychological disease or injury and all MRIs were confirmed to be without any structural abnormalities via visual inspection. Informed consent was acquired from each subject, and the protocol was approved by the human subjects’ research review board.

2.2. Imaging Protocol

MRI and MRSI data were acquired at 3T (Siemens Medical Solutions, Erlangen, Germany). T1-weighted imaging was carried out using a 3D Magnetization Prepared Rapid Acquisition Gradient Echo (MPRAGE) sequence with 1.0 mm isotropic or 0.9 × 0.9 × 0.7 mm3 resolution; TR/TE/TI=2300/2.41/930 ms; FA, 9°; NEX, 1; image matrix, 256 × 256 or 320 × 216 with 192 slices acquired. Whole-brain MRSI was acquired using echo-planar acquisition with spin-echo excitation; TR/TE = 1551/17.6 ms; non-selective lipid inversion-nulling with TI = 198 ms; a FOV of 280 × 280 × 180 mm3; matrix size of 50×50 with 18 slices; echo train length of 1000 points; bandwidth of 2500 Hz; and a nominal voxel volume of 0.313 cc and acquisition time of 15 min [15]. A water reference MRSI dataset was obtained using an acquisition interleaved with the metabolite signal acquisition.

2.3. MRSI Processing

MRSI data were processed using the MIDAS package (http://mrir.med.miami.edu/).[16, 17] This included B0 and phase correction using the water reference data prior to any further processing in the frequency domain. The relative gray- and white-matter tissue and cerebrospinal fluid (CSF) contents in each SI voxel were estimated by downsampling the tissue segmentation maps, which were obtained using FSL/FAST algorithm,[18] using the spatial response function of the MRSI acquisition. Additional processing included generating masks for brain and lipid regions, k-space extrapolation to reduce the contribution of extracranial lipid into the brain,[19] linear registration between the T1-weighted MR and MRSI, and signal intensity normalization following the creation of individual metabolite maps. The spectral datasets were interpolated to 64×64×32 points and spatial smoothing was applied after B0 correction, resulting in an effective voxel volume of 1.55 ml.

To estimate the effects of noise reduction on the metabolite quantification the MRSI data were analyzed following i) application of a Gaussian apodization smoothing and ii) a PCA based denoising method.[11] Gaussian smoothing (SM) was applied after spatial reconstruction by multiplication of the complex time-domain data with a function defined as, exp(−0.6πG(n/((N – 1).sw))2), with G = 0 (no smoothing), 1, 2, 4, 6, and 8 Hz, and where N is the number of spectral points in the time domain, n is the data point running from n to N-1, and sw is the sweep width in Hz.[20]. The PCA denoising (dnPCA) was performed with 3 levels of noise reduction controlled by a statistical choice of the number of principal components (PCs).[11] The number of PCs selected, L, was based on a p-value threshold for Levene’s test of 10−5 (dnPCA5), 10−7 (dnPCA7), or 10−10 (dnPCA10), and with the number of PCs being retained decreasing (i.e. resulting in increasing SNR) as the threshold for the Levene’s test is decreased [11]. A previous study reported that the 10−10 level provided a factor of 2.9 improvement in SNR relative to the original spectrum though with some indication of a loss of information for small metabolite resonances and that a value of 10−5 offered a conservative approach that provided approximately a factor of 2.5 increase in SNR [11]. The processing resulted in a total of nine processing variants (6 Gaussian and 3 dnPCA) for each of the 11 datasets.

Following denoising, automated spectral analysis was carried out for N-acetylaspartate (NAA), creatine and phosphocreatine (Cr), choline, glycerophosphocholine, and phosphocholine (Cho), myo-inositol (mI), lactate and glutamate and glutamine.[4] This used an iterative procedure that combined a time-domain definition of the spectral model with a frequency-domain wavelet smoothing method for characterization of the more slowly varying baseline signal components.[4, 5] The spectral and baseline fitting models were kept consistent across all datasets. The resultant signal-normalized metabolite maps were then spatially registered to a reference MRI defined in MNI space with an associated lobar brain atlas.[16] Additional maps were generated for the fitted spectral linewidth, the confidence intervals for each parameter,[21] and SNR, which was estimated as the ratio of the area under the NAA peak (1.9 and 2.1 ppm) to the standard deviation of the noise signal estimated between 0 and 1.2 ppm.[22] The estimation of the variances of the fitted parameters using the Cramer-Rao lower bounds was not used since this depends on a measure of the noise, which is not constant over the set of conditions studied, while confidence intervals are independent of the noise.[21] This technique of calculating confidence interval is similar in nature to that proposed by Draper and Smith [23], but is more tolerant of inexact model specification generally encountered in MRSI quantification.

2.4. Comparative Analysis

Three comparative analyses were performed to characterize the effects of apodization methods. Two “lobar” analyses were performed using mean values from left/right frontal and left/right parietal white matter to evaluate 1) metabolite concentrations differences NAA, Cr, Cho, and mI and 2) SNR, linewidth and confidence interval differences in each lobe. The third analysis, used a voxel-to-voxel based comparison in left and right combined parietal white matter to evaluate only metabolite concentration differences. Lobar metabolite concentrations and quality parameters were compared using repeated-measures analysis of variance (ANOVA) to data reconstructed using no smoothing. [24] Sidak’s multiple comparison test [25, 26] was used for pairwise comparisons whereby data constructed using different apodization levels and dnPCA thresholds are compared to data that reconstructed using no spectral smoothing. Before performing any comparisons, quality criteria were applied to limit the analysis to spectra with a linewidth of <12 Hz and a CSF fraction <20%. Voxels were also limited to the white matter using partial volume fraction of >80%.

To reduce the effects of correlation among neighboring voxels in the voxel-to-voxel based comparison only every fourth voxel in each dimension was analyzed. Prior to statistical comparison of voxel-to-voxel based data, spectral quality criteria were applied to select only voxels that had a linewidth of <12 Hz, a white matter partial volume fraction of >80%. and a confidence interval for the NAA quantification of <30% in all spectrally fitted results. Spectral quality criteria were independently applied to data reconstructed using different smoothing levels and only common voxels retrained after the quality checking were included in the analysis.

3. RESULTS

3.1. Qualitative Results

In Figure 1A are shown representative spectra from a single voxel from the location indicated in the structural T1 image shown in Figure 1B with metabolite maps for NAA using the different smoothing and denoising schemes shown in Figure 1C. As anticipated, larger smoothing levels result in spectra with decreased high-frequency noise and loss of spectral detail, chiefly evident for myo-inositol located at 3.5 ppm and in the range of 2.3 to 2.8 ppm that contains multiplet resonances for glutamate, glutamine, and NAA, whereas the dnPCA based smoothing methods maintain these spectral patterns. The NAA maps (Figure 1C) indicate that differences in the spectral processing do not result in major changes, although hyperintensities in the left frontal region (image right shown in square boxes) that likely result from increased lipid extracranial contamination and fitting baseline errors are more widespread with larger smoothing levels, possibly due to increased difficulty for the fitting algorithm to distinguish between broad features of the metabolite peaks and the baseline signals.

Figure 1:

Figure 1:

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Representative single-voxel spectra (A) and NAA maps (C) from reconstructions using dnPCA (dnPCA5, dnPCA7, dnPCA10) and different smoothing levels using Gaussian spectral smoothing (SM) with G = 0, 1, 2, 4, 6, and 8. Square box shows locations where significant differences are seen with different smoothing levels. The structural T1 image (B) shows the location of the selected voxel and the slice in the figure.

3.2. Regional Analysis

In Figure 2A are shown the mean linewidths taken from the frontal and parietal regions obtained using the different smoothing techniques and in Figure 2B are shown the percent differences obtained using these smoothing levels as compared to data reconstructed without any smoothing. Mean linewidths and other parameters for regional analysis are derived from 5300 ± 491 voxels, 4831 ± 506 voxels, 2848 ± 67 voxels, and 2783 ± 45 voxels in the right frontal, left frontal, right parietal, and left parietal lobes respectively. The numbers represent the mean ± standard deviation in the number of voxels with the standard deviation in these measurements showing the range in the number of voxels retained using the different smoothing levels.

Figure 2:

Figure 2:

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(A) Regional mean linewidth measures in the right frontal (RF), left frontal (LF), right parietal (RP), and left parietal (LP) lobes calculated from reconstructions using dnPCA (dnPCA5, dnPCA7, dnPCA10) and different smoothing levels using Gaussian apodization (SM) with G = 0, 1, 2, 4, 6, and 8 Hz. Bars indicate the ±Standard Deviation in the measurement. Asterisks denote statistically significant paired differences from reconstruction using no smoothing. (B) Percentage differences in mean linewidth between specific smoothing method and reconstruction using no smoothing (G = 0).

Significant pairwise differences were seen for all Gaussian smoothing methods as compared to no smoothing (p<0.001). dnPCA methods show no significant differences in linewidth as compared to data reconstructed without any smoothing in any lobar regions except in left parietal lobe for dnPCA10 (p<0.01). Results show the expected increase of linewidth with increased spectral smoothing, with a strong linear correlation observed between linewidth and the level of smoothing applied (for all lobar regions R2 > 0.99). Further, the variance in the linewidth across the regions reduced with increased spectral smoothing (R2 > 0.98 for all lobar regions).

In Figures 3A, 3C and 3E are shown mean lobar concentrations for NAA, Cho, and mI, respectively, calculated for the different processing methods and in Figures 3B, 3D, and 3F are shown the corresponding percent differences in concentration from data reconstructed using no smoothing. Results for Cr were comparable to those obtained for NAA showing similar pattern of changes in metabolite concentrations with different smoothing levels and hence to reduce redundancy Cr results are not shown in the manuscript. Results show significant differences in metabolite concentrations with apodization smoothing applied as compared to reconstructions using no smoothing. Moreover, a linear relationship can be observed between the percentage difference in NAA and Cho concentration and Gaussian smoothing applied to the data (R2 > 0.98 for all studied regions). On the other hand, dnPCA methods show no statistically significant differences in NAA and Cho concentrations as compared to unsmoothed data across all studied regions, with the exception for dnPCA10 that showed significant differences in the frontal lobes (RF: p=0.029; LF: p=0.018). NAA estimates showed a trend to higher metabolite concentrations with dnPCA denoising (Figure 3B), whereas Cho showed a trend to lower metabolite concentrations (Figure 3D). Measurements for mI showed no significant differences between different smoothing techniques and unsmoothed data with large variability, as can be seen from the large standard deviations in Figure 3E.

Figure 3:

Figure 3:

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Regional mean concentration of N-acetylaspartate (A), choline (C), and myo-Inositol (E) in the right frontal (RF), left frontal (LF), right parietal (RP), and left parietal (LP) lobes calculated from reconstructions using dnPCA (dnPCA5, dnPCA7, dnPCA10) and different smoothing levels using Gaussian spectral smoothing (SM) with G = 0, 1, 2, 4, 6, and 8. IU denotes institutional units and bars indicate the ±Standard Deviation in the measurement. Asterisks denote statistically significant paired differences from reconstruction using no smoothing. Percentage differences in mean NAA (B), choline (D), and myo-Inositol (F) concentrations between specific smoothing method and reconstruction using no smoothing (SM0).

In Figure 4A are shown the confidence interval estimates for NAA. These decreased for increased levels of apodization smoothing or dnPCA denoising. All dnPCA based methods showed significant differences from unsmoothed data (p < 0.001). For Gaussian apodization, a strong linear correlation was observed between confidence intervals and the level of smoothing applied (for all lobar regions R2 > 0.97), as shown in Figure 4B.

Figure 4:

Figure 4:

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(A) Regional confidence limit measures for NAA estimation in the right frontal (RF), left frontal (LF), right parietal (RP), and left parietal (LP) lobes calculated from reconstructions using dnPCA (dnPCA5, dnPCA7, dnPCA10) and different smoothing levels using Gaussian spectral smoothing (SM) with G = 0,1, 2, 4, 6, and 8. Bars indicate the ±Standard Deviation in the measurement. Asterisks denote statistically significant paired differences from reconstruction using no smoothing. (B) Relationship between confidence limit and the Gaussian smoothing factor (G) showing a strong linear correlation (RF: R2 = 0.978; LF: R2 = 0.971; RP: R2 = 0.969; LF: R2 = 0.972).

Lobar SNR measurements showed a significant increase in SNR using dnPCA methods (p-values < 0.001) as compared to reconstructions using no smoothing. Denoising based on PCA methods showed a 17.1% (dnPCA5), 29.6% (dnPCA7), and 44.7% (dnPCA10) improvement in SNR over reconstructions without smoothing. Moreover, reconstructions using all levels of Gaussian smoothing also showed increased SNR (6.1%, 17.8%, 42.6%, 67.2%, and 49.3% for G = 1, 2, 4, 6, and 8, respectively) as compared to data reconstructed without any smoothing (p values < 0.001).

3.3. Voxel-based Analysis

The voxel-based analysis compared NAA concentrations in 92 matched voxels for the different smoothing methods across the parietal white matter regions that passed quality criteria. ANOVA results show a significant (p < 0.05) difference in voxel NAA values obtained by applying different smoothing techniques. In Figure 5A are shown the mean parietal white matter NAA concentration using the different smoothing methods with differences from unsmoothed data shown in Figure 5B. Pairwise comparisons show that dnPCA methods show a significant increase in NAA quantification as compared to unsmoothed data (p < 0.001). Moreover, all Gaussian smoothing levels except G = 1 Hz (p = 0.417) show a significant increase in the quantification of NAA as compared to unsmoothed data (p < 0.001). For the voxel-based analysis Cho, Cr, and mI showed similar results to NAA and to reduce redundancy only results for NAA are discussed in detail in the manuscript.

Figure 5:

Figure 5:

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(A) Mean concentration of N-acetylaspartate in voxel-based analysis in the parietal white matter from reconstructions using dnPCA (dnPCA5, dnPCA7, dnPCA10) and different smoothing levels using Gaussian spectral smoothing (SM) with G = 0, 1, 2, 4, 6, and 8. IU denotes institutional units. Bars indicate the ±Standard Deviation in the measurement. Asterisks denote statistically significant paired differences from reconstruction using no smoothing. (B) Percentage differences in mean NAA concentrations between specific smoothing method and reconstruction using no smoothing (SM0).

4. DISCUSSION

This study evaluated the effects of spectral smoothing on quantification of whole-brain MRSI data using two different techniques, Gaussian apodization and denoising using principal component analysis. Results indicate that dnPCA based spectral smoothing had little effect on spectral linewidth and spectral quantification, while also providing improved confidence in the accuracy of the spectral fitting (i.e. lower confidence intervals). Gaussian smoothing based techniques show increased concentrations with increased levels of smoothing, along with improved confidence in the accuracy of the spectral fitting. Both noise reduction methods were found to improve visualization of spectra. As practical guidelines, light Gaussian apodization value with a filter of 2 Hz was found to have minimal impact (1.1 Hz) on spectral linewidths and the accuracy of the fitting, while providing a visible reduction of noise and reduced confidence intervals by a mean value of 15.2%. Similarly, dnPCA with conservative noise reduction levels, e.g. a value of p = 10−5 or 10−7 for the method used in this study, was similarly found to improve visualization without affecting the quantitation accuracy while reducing confidence intervals by an average of 9.8% and 16.1% for dnPCA5 and dnPCA7, respectively. These levels of denoising are also anticipated to have minimal impact on loss of information.[11]

Linewidth measurements indicated that all levels of Gaussian apodization result in an increase in linewidth in a linear fashion. This is expected behavior and results in quantification errors due to broadening of peaks and affecting the fitting of the closely overlapping peaks such as those of Cr and Cho. In comparison, small levels of smoothing using PCA denoising reveal no statistical difference in linewidth, which has also been demonstrated in earlier reports.[10, 11, 14] The alteration of NAA quantitation seen with apodization smoothing differs from that reported by Bartha et al.,[8] where minimal impact was seen. A possible reason for this is that the spectral models used differ, with each resonance having independent lineshape terms in the model used by Bartha et al., whereas a common lineshape is used for all resonance in the spectral model used for this study, which is considered to be more robust for analysis of the lower SNR spectra typically acquired using MRSI.[4]

Gaussian smoothing resulted in significant improvement in the mean SNR for NAA as compared to unsmoothed data, which is expected as increased smoothing reduces noise.[7] The dnPCA methods also result in a significant increase in SNR without significantly compromising metabolite information, provided that a sufficient number of PCs are retained. Comparing the two methods of apodization, results show that dnPCA5 method provides a comparable improvement in SNR as apodization with a Gaussian smoothing of G = 2 (17.1% for dnPCA5 vs 17.8% for G=2). Larger smoothing using dnPCA10 results in greater SNR improvement (similar to Gaussian apodization using G = 4) but shows significant differences in Cho estimates which can be due to the linewidth broadening seen with dnPCA10.

The voxel-based analysis showed that any amount of smoothing applied to the data, irrespective of the method used, resulted in statistically significant alterations in the estimated NAA concentrations. Differences at the voxel level may affect studies using MRSI that aim to employ voxel-wise differences between groups of subjects. In such cases, it is recommended to either employ none or very little smoothing. As such, the application under consideration drives the choice of the smoothing method and the level of smoothing. Mild Gaussian apodization (≤ 2 Hz at 3T) which shows an error of about 1% in NAA quantification may provide a compromise in terms of fitting performance and visual reads.

Limitations of this study include that the effects of fitting baseline signals were not considered for the different methods. Baseline variations seen due to different noise levels obtained using different apodization methods may result in variations in metabolite estimation. Optimization of fitting parameters for baseline variations may improve quantification results but as seen from the small confidence intervals their impact may not be substantial. For consistency in results, the baseline fitting model and the lipid extraction parameters were kept consistent across all datasets and pairwise analysis or repeated-measures ANOVA was used to compare methods among the same subject data. Finally, the spectral fitting models for metabolite fitting were not altered across subjects and smoothing schemes and optimization of the model for better spectral fitting under different smoothing schemes may be advantageous.

In conclusion, this study has shown that Gaussian apodization significantly affects metabolite quantification, although very mild levels of smoothing (≤ 2 Hz at 3T) has minimal impact on metabolite quantitation (approximately 1% error) but provides some benefit for the reproducibility of the fitting (approximately 15.2% reduction in confidence intervals) and aids in visualization. The dnPCA based methods also affected metabolite quantitation, as compared to unsmoothed data, with approximately 2% error for moderate levels of denoising, but with no impact on spectral linewidth and a significant improvement in measurement reliability showing an average reduction of 9.8% and 16.1% for dnPCA5 and dnPCA7 in confidence intervals, respectively. For applications that aim to explore small changes in metabolite concentrations, dnPCA methods may be beneficial.

Highlights.

  • Analyze spectral denoising and apodization smoothing on the quantitation of MRSI

  • Gaussian apodization and denoising using principal component analysis (dnPCA)

  • Mild Gaussian apodization can be applied with minimal errors in quantitation

  • dnPCA based denoising methods produce more consistent results

ACKNOWLEDGMENTS

Grant Support: This work was supported by National Institute of Health (NIH) grants R01CA172210, R01EB016064

Footnotes

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Declarations of interest: none

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