Denoising of MR Spectroscopic Imaging Data Using Statistical Selection of Principal Components (SSPC)
Abas Abdoli1, Radka Stoyanova2, and Andrew A. Maudsley1

1Radiology, University of Miami, Miami, FL, United States, 2Radiation Oncology, University of Miami, Miami, FL, United States

Synopsis

In this study we evaluate a new principal components analysis (PCA) based denoising method for volumetric MRSI data that employs a statistical test for the selection of the significant noise-free principle components (PCs).

Purpose

The technical challenges in acquiring MR imaging data from low concentration metabolites compromise the spatial resolution and signal to noise ratio (SNR) of the measurement, which can decrease the value for clinical applications. While increased SNR can be achieved by signal averaging, this is frequently impractical for clinical studies due to the increased scan times and susceptibility to movement artifacts. An alternative approach to improving SNR is to reduce the noise in the data as part of the reconstruction procedure. Several different methods have been proposed for MRSI denoising (1-4). Singular Value Decomposition (SVD) and PCA provide a representation of complex data in a lower dimensional space that is defined by the significant PCs (5,6). The total number of PCs is usually much larger than the number of independent variations in the dataset. Therefore, by recalculating the data using only the significant PCs while ignoring the higher noise-related will effectively reduce the noise in the data. However, the selection of the optimal rank for approximation of the noise-free signal is one of the main challenges of the PCA denoising methods. In this study a spatial-spectral low-rank method was developed for denoising of volumetric 1H MRSI data of the brain that was combined with a new approach for selection of the significant signal-related PCs obtained from PCA.

Materials and Methods

The proposed statistical selection of PC (SSPC) method determines the significant signal related PCs in the spatial-spectral MRSI data. The technique is based on examining each PC and comparing the variance in regions of frequencies with known metabolites vs the variance in the ‘noise’ regions. For this purpose, Levene’s test (7) was performed to assess the equality of variances between these two regions. Levene’s test is a popular variance equality test that can handle the non-normality of data. After performing Levene’s test, a judicious threshold was applied on the significant difference (p-value) calculated by the test to retain the significant PCs and construct the noiseless data. Therefore, SSPC may select PCs which are not consecutive, i.e. PCi+1 may be included of the data reconstruction while PCi is excluded. To evaluate the performance of the SSPC method, a simulated dataset was generated to resemble the volumes and metabolites in a hypothetical brain in vivo MRSI of a patient with brain tumor. Spectra were simulated to represent a lipid ring, a metabolite region, two regions having only a water signal, and a small region representing a brain lesion/tumor. Gaussian noise with relative standard deviation of 0.5 was added in the time-domain. Volumetric MRSI data of one normal subject and one brain tumor subject were obtained at 3T with 8-channel detection. Sequence details have been provided elsewhere (8,9). All data were processed using the MIDAS software (10). Processing for data used for the denoising tests did not have any spectral smoothing applied. For comparison to standard processing methods, data were also processed using Gaussian apodization of the time data, for a relatively small 2 Hz line-broadening and a value more typically used (for 3 T) with 5 Hz line-broadening.

Results

Fig. 1a.iii and Fig. 1b.iii show that the SSPC denoising reconstructed the signals without loss of information and with improved SNR. Note that the reconstructed “tumor” spectrum, Fig. 1b.iii, is noisier than that from the “normal” region. The tumor spectra are associated with a relatively small volume and thus they contribute a small fraction of the total variance. As the PCs are ordered by the amount of variation they explain, the first few PCs are dominated by the signal from the “normal” volumes. It can be observed that for the same number of PCs the SSPC denoising (Fig. 2e) performed better than the conventional PCA denoising with no PC filtration (Fig. 2d) in terms of CRB and SNRArea (using NAA). The improvements in metabolite peak area images were more prominent for the lower concentration metabolite, GlxArea, compared to the higher concentration metabolite, CRArea. Gaussian apodization resulted in increased LW. A visual evaluation of spectra in Fig. 3a.iii and Fig. 3c.iv indicates the SSPC performed better than the conventional PCA denoising.

Discussion

The proposed SSPC denoising significantly improved the SNR and fitting accuracy without significantly compromising metabolite information. Using both simulated and in vivo MRSI data it was shown that the SSPC denoising resulted in higher SNRArea and lower CRBs values comparted to the conventional PCA denoising with the same number of PCs, and that the relative performance varied spatially in a manner that depended on the number of spectra with similar spectral patterns.

Acknowledgements

This work was supported by NIH grants R01EB016064 and R01CA172210. The authors thank Dr. M. Goryawala for assistance with data collection.

References

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Figures

Figure 1. Example spectra from simulation studies; a) voxel 1, and b) voxel 2 from ellipsoidal object. Spectra in rows are as follow: (i) simulated data, (ii) simulated after addition of random noise, and (iii) denoised data using SSPC

Figure 2. Images of denoising results for the mid-axial slice; a) acquired data, b) Gaussian apodization (2 Hz), c) Gaussian apodization (5 Hz), d) conventional PCA denoising using the first 65 PCs, e) SSPC denoising with threshold of 1E-10 (the algorithm found 65 PCs for this threshold).

Figure 3. Example spectra from the denoising of in vivo MRSI study of a patient with brain tumor; a) voxel 1 in the normal appearing white matter region in the opposite side of the tumor, and b) voxel 2 in the tumor region. The row (i) shows the noisy data, (ii) Gaussian denoising, (iii) PCA denoising using the first 119 PCs, SSPC denoising with threshold of 1E-5 (the algorithm found 119 PCs for this threshold), and (v) SSPC denoising with threshold of 1E-10.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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