### 0143

Denoising of Z-spectra for stable CEST MRI using principal component analysis
Johannes Breitling1,2,3, Anagha Deshmane4, Steffen Goerke1, Kai Herz4, Mark E. Ladd1,2,5, Klaus Scheffler4,6, Peter Bachert1,2, and Moritz Zaiss4

1Division of Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany, 2Faculty of Physics and Astronomy, University of Heidelberg, Heidelberg, Germany, 3Max Max Planck Institute for Nuclear Physics, Heidelberg, Germany, 4High-field Magnetic Resonance Center, Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 5Faculty of Medicine, University of Heidelberg, Heidelberg, Germany, 6Department of Biomedical Magnetic Resonance, Eberhard-Karls University Tübingen, Tübingen, Germany

### Synopsis

Chemical exchange saturation transfer (CEST) MRI allows for the indirect detection of low-concentration biomolecules by their saturation transfer to the abundant water pool. However, reliable quantification of CEST effects remains challenging and requires a high image signal-to-noise ratio. In this study, we show that principle component analysis can provide a denoising capability which is comparable or better than 6-fold averaging. Principle component analysis allows identifying similarities across all noisy Z-spectra, and thus, extracting the relevant information. The resulting denoised Z-spectra provide a more stable basis for quantification of selective CEST effects, without requiring additional measurements.

### Introduction

Chemical exchange saturation transfer (CEST) MRI allows for the indirect detection of low-concentration biomolecules by their saturation transfer to the abundant water pool. However, quantification of inherently small CEST effects remains challenging and requires high image signal-to-noise ratio (SNR) to achieve reliable results. For optimized saturation parameters and image readout, higher SNR can only be achieved by averaging, resulting in prolonged measurement times. In this study, principle component analysis (PCA) was utilized to identify similarities across all Z-spectra, extract the relevant information i.e. principal components (PCs) and reduce the dimensionality to improve the SNR without averaging.1,2

### Methods

The proposed denoising algorithm (Fig. 1) is applied after motion correction using a rigid-registration-algorithm in MITK3, normalization, correction of B0-inhomogeneities, and segmentation of brain tissues (cerebrospinal fluid, gray matter, and white matter). CEST data, consisting of images of size ${u}\times{v}\times{w}$ for the $n$ saturation frequency offsets, is reshaped into a Casorati matrix $\textbf{C}$ of size ${m}\times{n}$ , with ${m}\leq{u}\cdot{v}\cdot{w}$ being the number of brain voxels. Each row of $\textbf{C}$ represents the Z-spectrum of one voxel and each column represents a complete segmented image for one saturation frequency offset. PCA is performed by eigendecomposition of the covariance matrix

$$\mathrm{cov}(\textbf{C})=\frac{1}{n-1}\widetilde{\textbf{C}}^\textbf{T}\widetilde{\textbf{C}}$$

$$\quad=\bf\Phi^\textbf{T}\Lambda\Phi$$

with $\widetilde{\textbf{C}}$ being the column-wise mean-centered Casorati matrix, ${\bf\Phi}=({\bf\varphi}_1{\bf\varphi}_2\ldots{\bf\varphi}_n)$ being the ${n}\times{n}$ orthonormal eigenvector matrix and ${\bf\Lambda}=\mathrm{diag}(\lambda_1,\lambda_2,\ldots,\lambda_n)$ being the associated diagonal eigenvalue matrix with $\lambda_1\geq\lambda_2\geq\cdots\geq\lambda_n$ . The variance i.e. information content of a signal will concentrate in the first few PCs, whereas the noise is spread evenly over the dataset. Therefore preserving the first few PCs will remove noise from the data set. The optimal number of components can be determined by an empirical indicator function applied to the eigenvalues.4

$$k=\underset{i}{\mathrm{argmin}}\left[\frac{\sum_{l=i+1}^{l=n}\lambda_l}{m(n-i)^5}\right]^\frac{1}{2}$$

Projection of $\widetilde{\textbf{C}}$ onto the reduced set of the first $k$ eigenvectors ${\bf\Phi}_{(k)}$

$$\widetilde{\textbf{C}}_{(k)}=\widetilde{\textbf{C}}{\bf\Phi}_{(k)}{{\bf\Phi}_{(k)}}^\textbf{T}$$

and addition of the mean Z-spectrum results in the denoised Casorati matrix. Denoised Z-spectra are reformatted into a final denoised image series with dimensions ${u}\times{v}\times{w}\times{n}$.

In vivo 3D-CEST-MRI (1.7×1.7×3 mm3, 12 slices) was performed on a 7T whole-body scanner (Siemens Healthineers, Germany) using the snapshot-CEST approach5. Pre-saturation by 140 Gaussian-shaped pulses (tp = 15 ms, duty cycle = 60%, tsat = 3.5 s) was applied at 54 unevenly distributed offsets for two different mean B1 = 0.6 and 0.9 µT. Each Z-spectrum was acquired six times to enable comparison with high-SNR data obtained by averaging. Conventional, averaged and denoised Z-spectra were fitted pixel-wise with a Lorentzian 5-pool fit model. Lorentzian difference images were calculated according to $\mathrm{MTR_{LD}}=Z_{ref}-Z$ and corrected for B1-inhomogeneities6.

### Results

Considerable noise is observed in the unprocessed Z-spectra (Fig. 2 left). Averaging 6 measurements reduces the noise significantly, allowing reliable identification of CEST resonances (Fig. 2 middle). The same resonances are also revealed by application of the denoising algorithm, indicating the correct choice for the number of components (Fig. 2 right). The smoother overall appearance of the denoised vs. averaged Z-spectra suggests the algorithm is equivalent or better than averaging. This result is also apparent in the APT and rNOE MTRLD contrasts calculated from denoised Z-spectra, which exhibit comparable or better image quality than those from averaged spectra (Fig. 3).

### Discussion

PCA was previously shown to be a powerful denoising technique in HyperCEST, with the optimal number of components deduced from the composition of the investigated phantom.2 For conventional CEST experiments, the number of relevant components is not straightforward to determine, as the number of contributions, their dependencies on physiological parameters and pathological alterations thereof are unknown. If too few components are preserved, resonances would be missing or deformed; too many components would diminish the denoising performance. In this study, the optimal number is determined using a data-driven approach4, the functionality of which was verified by the similarity of averaged and denoised Z-spectra. Prior segmentation and correction for B0 inhomogeneities ensured only relevant i.e. meaningful voxels with the same spectral position were included. PCA generally requires a sound statistical basis (i.e. a large number of voxels) to determine the PCs whereas the denoising performance itself depends on the number of preserved components. Therefore the denoising approach will benefit from 3D imaging, especially whole-brain imaging, and from a large number of acquired offsets.

### Conclusion

PCA denoising of Z-spectra results in contrasts which are comparable or even superior to those achieved by averaging. With this technique at hand, small CEST effects can be reliably quantified without the need for additional measurements. This might allow clinical application of CEST MRI at low field strengths as well as with fast imaging sequences by compensating for the expected SNR deterioration.

### Acknowledgements

Max Planck Society (support to JB, MZ, AD); German Research Foundation (DFG, grant ZA 814/2-1, support to MZ); European Union Horizon 2020 research and innovation programme (Grant Agreement No. 667510, support to MZ, AD).

### References

1. Hotelling, H. Analysis of a Complex of Statistical Variables into Principal Components. Journal of Educational Psychology 1933;24:417-441,498-520.
2. Döpfert J, Witte C, Kunth M, and Schröder L. Sensitivity enhancement of (Hyper-)CEST image series by exploiting redundancies in the spectral domain. Contrast Media Mol. Imaging 2014;9:100-107.
3. Nolden M, Zelzer S, Seitel A, et al. The Medical Imaging Interaction Toolkit: challenges and advances. Int J CARS 2013; 8(4):607-620.
4. Malinowski ER. Determination of the number of factors and the experimental error in a data matrix. Anal. Chem. 1977;49:612-617.
5. Zaiss M, Ehses P, and Scheffler K. Snapshot-CEST: Optimizing spiral-centric-reordered gradient echo acquisition for fast and robust 3D CEST MRI at 9.4 T. NMR Biomed 2018;31:e3879.
6. Windschuh J, Zaiss M, Meissner JE, et al. Correction of B1-inhomogeneities for relaxation-compensated CEST imaging at 7 T. NMR Biomed 2015;28:529-537.

### Figures

Fig. 1: Illustration of the PCA denoising algorithm (Z-spectrum of an exemplary voxel in red): The normalized and B0 corrected CEST data set is reformatted into a Casorati Matrix with voxels outside the brain segment being omitted. Principal component analysis using the covariance matrix yields the mean Z-spectrum, eigenvalues and eigenvectors (blue). The optimal number of components k for denoising is determined by an empirical indicator function applied to the eigenvalues. Projection onto the first k eigenvectors results in denoised Z-spectra, which are reformatted back into an image series in the final step.

Fig. 2: Z-spectra of exemplary voxels in grey matter (GM, red lines), white matter (WM, blue lines) and cerebrospinal fluid (CSF, green lines). Averaging of 6 measurements (middle) yields the expected increase in quality compared to the single measurement (left). Application of the PCA algorithm to the single measurement results in denoised Z-spectra (right) exhibiting the same resonances as the averaged Z-spectra, and with an even smoother appearance

Fig. 3: MTRLD images for APT (top) and rNOE (bottom) of a healthy volunteer. As expected averaging 6 measurements results in less noisy contrasts (middle) compared to the single measurement (left). By applying the denoising algorithm, an image quality (right) at least on par with the 6 averaged measurements can be achieved.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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