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Model-free denoising of multi b-value diffusion-weighted MR images using principal component analysis: simulations and in vivo results
Oliver Jacob Gurney-Champion1, David J Collins2, Andreas Wetscherek1, Mihaela Rata2, Remy Klaassen3, Hanneke W M van Laarhoven3, Kevin J Harrington1, Uwe Oelfke1, and Matthew R Orton2

1The Institute of Cancer Research and the Royal Marsden NHS Foundation Trust, London, United Kingdom, 2Cancer Research UK Cancer Imaging Centre, The Institute of Cancer Research and the Royal Marsden NHS Foundation Trust, London, United Kingdom, 3Cancer Center Amsterdam, Amsterdam UMC, University of Amsterdam, Amsterdam, Netherlands

Synopsis

We present a principal component analysis (PCA) toolkit for mode-free denoising of multi b-value diffusion-weighted images for clinical use. In simulations, PCA-denoising suppressed the random noise equally well (up to 55%) as synthetic MRI. Contrary to synthetic MRI (systematic error up to 29% of total signal intensity), PCA-denoising did not introduce any systematic errors (<2%). In volunteer and patient image data, PCA-denoising resulted in sharper and less noisy images than synthetic MRI, which resulted in sharper and clearer tumour boundaries. In conclusion, our PCA-denoising toolkit is promising for denoising b-value images for clinical use.

Introduction

Multi b-value diffusion-weighted MRI (DWI), such as intravoxel incoherent motion imaging, is often used for quantifying tissue properties relevant to lesion characterisation and treatment response monitoring1–6. However, for many clinical tasks, such as delineating tumours, images acquired at the highest b-value are preferred for their high tumour to background contrast. These high b-value images suffer from poor SNR3 and would benefit from denoising. One way of denoising these images is using synthetic MRI. In synthetic MRI, a diffusion model is fitted for each voxel and a denoised image at a given b-value is generated from the model fit. However, this approach is model-dependent and can cause systematic errors that obscure relevant lesions (Fig.1g). Here, we present a principal component analysis (PCA) approach that uses data sharing across all acquired b-values for model-free denoising.

Methods

PCA converts potentially correlated observations, into linearly uncorrelated orthogonal vectors, called principal components (PCs), and their corresponding weights7. The first PC is aligned with the axis of most variation, and each subsequent PC along the axis of largest remaining variation. For our implementation of PCA-denoising, signal intensities at different b-values and from repeated measures are treated as the observations. PCA then returns a set of dataset-specific PCs (equal to the number of b-values/repeats), and the weights per PC for each voxel required to reconstruct the original signal. As DWI-related signal-decay occurs similar throughout the images, whereas noise is random, diffusion-related effects are described by the initial PCs. Hence, DW-images were denoised model-free by using only the initial PCs and weights (Fig.1).

To achieve denoising, the informative PCs need to be separated from the PCs containing noise. First, we aimed at including >97% of the diffusion information into the reconstruction (Fig.2a,b). The mean of the absolute of the PC weights (the PC's power) was plotted per PC (Fig.2a). As later PCs only contain noise, the noise contribution from all PCs was estimated by fitting a 2nd order polynomial to the power of the highest 2/3 PCs (red curve) and subtracted from the power. The remaining curve, representing the informative signal, was integrated and normalized (Fig 2b, grey curve). The PCs up to which this curve reached 97% of all information were included.

After including 97% information, we assess the autocorrelation function of the remaining PCs. Signal decay as function of b-values is a smooth process and hence PCs with at least a positive autocorrelation function up to a delay of three were considered informative. Hence, after selecting 97% information, PCs up to the first PC that did not his constraint were included. Figs 2c,d show that for the simulated case, in which we know the resulting error (Fig 2e,f), our selection procedure resulted in minimizing the systematic error, with acceptable random error.

PCA-denoising was compared to several synthetic MRI approaches (mono-exponential, bi-exponential8, stretched-exponential9 and kurtosis10 models). Both approaches were compared in several simulated datasets (same four models; four SNR levels: 10, 20, 50 and 80), in which nine regions with distinct diffusion parameters were simulated and denoised11. This allowed for quantifying systematic and random errors. The performance of PCA-denoising and synthetic MRI was also compared in six healthy volunteers and three pancreatic cancer patients.

Results

In simulations, PCA-denoising reduced the random error substantial, by up to 55%, without adding any systematic error (<2%), as shown in Fig.3. Synthetic MRI had similar amount of reduction in random error (up to 53%), but this came at the expense of potentially introducing systematic errors (up to 29% of the signal intensity).

In vivo PCA-denoising resulted in sharper and less noisy images than synthetic MRI (Fig.4). This resulted in sharper and clearer tumour boundaries (Fig.5). Interestingly, contrary to synthetic MRI, PCA-denoising did not cause image blurring in the presence of motion.

Discussion

In contrast to literature12–15, we tailored PCA-denoising with the intention of improving image quality for diagnostic purposes, and evaluated its performance accordingly. PCA-denoising was able to denoise images as least as well as synthetic MRI, without assuming any model and without adding systematic error. Synthetic MRI added substantial systematic errors, particularly when the model was different from the model used for simulating the data. This reflects in vivo data for which the underlying model is unknown. Furthermore, in the presence of motion, PCA-denoising resulted in sharp images, suggesting PCA models some motion too.

Conclusion

PCA-denoising allows for model-free denoising of multi b-value DWI data. PCA-denoising reduces noise to a level similar to synthetic MRI, but without introducing systematic errors and without blurring the image in the presence of motion.

Acknowledgements

This work was supported by Cancer Research UK Programme Grants C33589/A19727 and C7224/A23275 and the Dutch Cancer Society (UVA2013-5932). CRUK and EPSRC support to the Cancer Imaging Centre at ICR and RMH in association with MRC and Department of Health C1060/A10334, C1060/A16464 and NHS funding to the National Institute for Health Research (NIHR) Biomedical Research Centre and the Clinical Research Facility in Imaging. This report represents independent research funded partially by the NIHR Biomedical Research Centre at the Royal Marsden NHS Foundation Trust and the Institute of Cancer Research. The views expressed in this publication are those of the author(s) and not necessarily those of the NHS, the National Institute for Health Research or the Department of Health.

References

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Figures

Figure 1: Panels a–c show a simplified example of PCA-denoising with only two b‑values. Panels d–g show synthetic MRI and PCA-denoising on data simulated using the stretched-exponential model, denoised with bi-exponential modelled synthetic MRI. This example was tailored such that the synthetic MRI produced a systematic error that obscured "cancer" on the high b-value image, whereas PCA-denoising did not. In panel g, the red and blue voxel represent data that were higher (red) or lower (blue) than the window level.

Figure 2: Panels a,b illustrate how the number of PCs taken along was chosen such that at least 97% of the information was included. Panels c-f show an example where for a stretched-exponential simulated dataset (SNR=20) an optimum of three PCs was selected. Panel c shows the last two retained PCs: 2nd (orange) and 3rd (green), and the first rejected PC: 4th (blue). Panel d shows the estimated autocorrelation. The blue arrow highlights the first PC with negative autocorrelation at delay 3. Panels e,f show, respectively, the random and systematic errors as a function of the number of PCs.

Figure 3: Random (left) and systematic (right) error fractions intensity from simulated noisy data (red) and denoised data using either PCA (green) or synthetic MRI (greys) in the highest b-values image (750 s/mm2). The errors were normalised to ground truth image signal. The root-mean-square of the random error (left column) and the maximum systematic error from the nine regions (right column) are shown.

Figure 4: PCA-denoising (3rd column), compared to the original data (1st column), averaging over repeated measures (2nd column) and bi-exponential synthetic MRI (4th column) in healthy volunteers. The highest b-value image from the series is shown, except for abdomen axial #2, which shows the second highest b-value (b=650 mm2/s). Arrows indicate structures that are less visible on synthetic MRI (Leg, abdomen axial blue, brain blue), have higher SNR (abdomen axial, abdomen coronal, brain 2) or are sharper (abdomen axial and abdomen coronal).

Figure 5: PCA-denoising (3rd column) compared to the original data (1st column), averaging over repeated measures (2nd column) and bi-exponential synthetic MRI (4th column) of pancreatic cancer patients. The axial acquisition and coronal reconstruction are shown of the highest b-value (b=600 s/mm2) are shown. The red arrows indicate the tumours. Compared to PCA-denoising, synthetic MRI blurred the image for all three examples (mainly visible in the coronal reconstruction), making accurate boundary detection more challenging.

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