Stefano Casagranda^{1}, Christos Papageorgakis^{1}, Feriel Romdhane^{2}, Eleni Firippi^{1}, Timothé Boutelier^{1}, Laura Mancini^{3,4}, Moritz Zaiss^{5}, Sotirios Bisdas^{3,4}, and Dario Livio Longo^{2}

^{1}Department of Research & Innovation, Olea Medical, La Ciotat, France, ^{2}Institute of Biostructures and Bioimaging (IBB), National Research Council of Italy (CNR), Torino, Italy, ^{3}Lysholm Department of Neuroradiology,, University College of London Hospitals NHS Foundation Trust, London, United Kingdom, ^{4}Institute of Neurology UCL, London, United Kingdom, ^{5}Department of Neuroradiology, University Clinic Erlangen, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), Erlangen, Germany

This work provides a new denoising methodology for multi-acquisition magnetic resonance images (MRI) based on principal components analysis (PCA). We are proposing a new principal component selection criterion that identifies spatial information in the extracted component coefficients, leading to a better preservation of anatomical structures and pathological information. In addition, our adaptive filtering step allows us to further denoise the MRI data, rejecting persistent spatial noise from the extracted component coefficients. In our investigations the proposed method outperformed the eigenvalue based selection criteria on Amide Proton Transfer weighted CEST data.

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, in

Other methods exist

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).

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.

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 protocol

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. MTRasym

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.

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.

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**Figure1**: A) Example of extracted PC related images of a glioma patient. PC_{1} until PC_{3} clearly contain spatial information while PC_{28} and PC_{29} contain only noise. PC_{9} and PC_{10} however, contain both noise and spatial information. B) PC related image that has been discarded by an eigenvalue-based method (left), although it contains brain tumor related information in agreement with the contrast-enhanced T1-weighted map (right).

**Figure2**: Step1: on the PC_{3} related volume is applied a Gaussian filter and the standard deviation is measured on the image before and after smoothing. In this way $$$\sigma_r3$$$ is calculated. The components with $$$\sigma_r$$$ on the convergence point (purple points on the plateau) are discarded assuming that contain only noise.

Step2: The retained PC related volumes are spatially denoised with a gaussian filter of strength A multiplied by their weights. For example PC_{3} related volume is smoothed with strength $$$A \cdot w^r_3$$$. $$$A=0.5$$$ was used for this study.

**Figure4**:** **Quantitative analysis of the performance of the PCA denoising methods on MTRAsym maps of different SNR levels: A) Peak signal-to-noise ratio (PSNR), B) Structural Similarity Index (SSIM), C) Correlation, D) Mean Square Error (MSE).

DOI: https://doi.org/10.58530/2022/2080