Introduction

Principal Component Analysis (PCA) is a non-parametric technique originally designed to reduce the dimensionality of a given dataset, while retaining the essence of the data^1,2. It extracts a new set of variables, called Principal Components (PCs) which are ordered based on the variability of the original data each component explains, i.e. their associated eigenvalues.
PCA has been successfully used for denoising purposes in multi-acquisition MRI, usually reconstructing the original dataset selecting the signal-related components and rejecting noise-related components. For example, in³, three eigenvalues-based methods are presented (Malinowski, Nelson and Median criteria) and thereafter investigated for their applicability to denoising of in vivo Chemical Exchange Saturation Transfer (CEST) MRI data⁴.
Other methods exist^5,6 but many rely on the eigenvalues associated with the extracted principal components for the selection of the signal-related components. However, such methods risk discarding anatomical structures and pathological information hidden in the noise of the extracted components, especially if those areas are small, as eigenvalues measures blindly the variance of components regardless if it is noise or relevant clinical information.
A Z-Spectrum for a given voxel in the CEST data can be expressed as:
$$\mathbf{Z_i}=\overline{z_{i}}+\sum_j\alpha_{ ij}\mathbf{v_j}$$
where $$$\overline{z_{i}}$$$ is the mean value of the Z-Spectrum, $$$\mathbf{v_j}$$$ is a principal component and $$$\alpha_{ ij}$$$ is the coefficient of $$$\mathbf{v_j}$$$ of voxel $$$i$$$.
Collecting all coefficients $$$\omega_{ij}$$$ of a component $$$j$$$ in the same order of the Z-Spectra in the CEST acquisitions, we obtain the PC related image (or volume) of the $$$j^{th}$$$ component (see Figure1).

Methods

Technical Solution:
Our proposed method, called Component Analysis based on Standard-deviation Attenuation (CASA) criterion is based on the decrease of the variance of a PC related image after a smoothing filter is applied on it, as detailed in the following steps (see Figure2):
1) PCA is performed to obtain the PC related images. The standard deviation of the voxels of the full image or within a segmented region (for example excluding background voxels) is computed for each of the $$$N$$$ PC related images to form the vector $$$\sigma^a=[\sigma^a_{1},\sigma^a_{2},\sigma^a_{3},…\sigma^a_{N}]$$$. Then a Gaussian smoothing filter of a factor $$$\Sigma$$$ is applied to each component and standard deviation is recomputed on the smoothed PC related images to obtain $$$\sigma^b=[\sigma^b_{1},\sigma^b_{2},\sigma^b_{3},…\sigma^b_{N}]$$$, where $$$\sigma^a_{i}>\sigma^b_{i}$$$. The rate of decrease of standard deviation is then computed, for each component, as $$$\sigma^r =(\sigma^a -\sigma^b) / \sigma^a$$$, where $$$0<\sigma^r_{i}<1$$$, $$$\forall i$$$. Components whose $$$\sigma^r_{i}$$$ rate is on the plateau of the curve are rejected (see Figure2).
2) Before the signal reconstruction a smoothing filter or denoising method can be applied on the retained PCs (PC related images). The strength of the applied filter is proportional to the amount of information that the $$$i^{th}$$$ component carries expressed in $$$\sigma^r_{i}$$$, as $$$w^r_{i}=(\sigma^r_{i}-\sigma^r_{1})/(\sigma^r_{plateau}-\sigma^r_{1})$$$ (see Figure2). This allows to optimize the filtering method based on the amount of noise and information present in each component.
3) The retained component coefficients are projected back in the original space and used for the denoised data reconstruction.
Carrying out only the first and third step, we call the method “CASA basic”, and “CASA advanced” when all three steps are applied.

Patient data acquisition and postprocessing:
Imaging clinical data on a glioma patient were acquired on a 3T whole-body MRI system (MAGNETOM Prisma; Siemens Healthcare, Erlangen, Germany) with a 64-channel Head/Neck coil. A 3D snapshot-GRE CEST protocol⁷ (MPI03) was used to acquire WASAB1⁸ and Amide Proton Transfer weighted⁴ (APTw) data with parameter details listed in Figure3. Data were motion corrected with SimpleElastix⁹. Olea Sphere 3.0 (Olea Medical, La Ciotat, France) was used to compute B0/rB1 map from WASAB1 and correct the APTw-Z-Spectra.

Synthesized data:
A simulated brain phantom was generated starting from the clinical APTw dataset with its same 3D resolution. The Z-Spectra were fitted with the Bloch-McConnel equations modified to include the exchange terms with a five pools model^10,11, using MATLAB (parameters in Figure3). The phantom (ground truth) Z-Spectrum volumes were computed at 25 equally-spaced offsets from -6ppm to 6ppm (step=0.5ppm).
The phantom was corrupted by several percentage levels of Rician noise (0.25%,0.5%,1%,3% of the maximum intensity for each Z-Spectra) in frequency domain. The phantom data were PCA denoised using both CASA methods, Malinowski, Nelson and Median selection criteria. MTRasym¹² (at 3.5ppm) maps were computed on the ground truth and on various denoised data. These maps were used for comparison.

Results

Data quality analysis using Peak signal-to-noise ratio (PSNR), Structural Similarity Index (SSIM), Correlation and Mean Square Error (MSE) have been used to evaluate the goodness of the various denoising methods.
The results in Figure4 shows that for all noise levels "advanced CASA" metric leads to the best results (highest PSNR/SSIM/Correlation and Lowest MSE). Figure5 shows the MTRasym maps of ground truth, data corrupted by various noise levels, and after PCA denoising with "advanced CASA" criterion.

Discussion and Conclusion

A new PCA denoising methodology has been proposed for multi-acquisition MRI data, optimized to preserve anatomical structures and pathological information. The advanced version of the proposed method led to the best results between the different evaluated PCA denoising methods on CEST APTw multi-volume acquisitions. An additional investigation should be performed to compare the advanced CASA method with other PCA denoising methods in the literature^5,6.

Acknowledgements

The research leading to these results has received funding from AIRC MFAG 2017 ‐ ID. 20153 project – P.I. Longo Dario Livio.
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 667510 and the Department of Health’s NIHR-funded Biomedical Research Centre at University College London. SB and LM are supported by the National Institute of Health Research Biomedical Research Council, UCL Hospitals NHS Trust.