# De-noising of Contrast-Enhanced MRI Sequences by an Ensemble of Expert Deep Neural Networks

## Abstract

Dynamic contrast-enhanced MRI (DCE-MRI) is an imaging protocol where MRI scans are acquired repetitively throughout the injection of a contrast agent. The analysis of dynamic scans is widely used for the detection and quantification of blood brain barrier (BBB) permeability. Extraction of the pharmacokinetic (PK) parameters from the DCE-MRI washout curves allows quantitative assessment of the BBB functionality. Nevertheless, curve fitting required for the analysis of DCE-MRI data is error-prone as the dynamic scans are subject to non-white, spatially-dependent and anisotropic noise that does not fit standard noise models. The two existing approaches i.e. curve smoothing and image de-noising can either produce smooth curves but cannot guaranty fidelity to the PK model or cannot accommodate the high variability in noise statistics in time and space.

We present a novel framework based on Deep Neural Networks (DNNs) to address the DCE-MRI de-noising challenges. The key idea is based on an ensembling of expert DNNs, where each is trained for different noise characteristics and curve prototypes to solve an inverse problem on a specific subset of the input space. The most likely reconstruction is then chosen using a classifier DNN. As ground-truth (clean) signals for training are not available, a model for generating realistic training sets with complex nonlinear dynamics is presented. The proposed approach has been applied to DCE-MRI scans of stroke and brain tumor patients and is shown to favorably compare to state-of-the-art de-noising methods, without degrading the contrast of the original images.

## Notes

### Acknowledgments

This study was supported by the European Union’s Seventh Framework Program (FP7/2007–2013; grant agreement 602102, EPITARGET; A.F.), the Israel Science Foundation (A.F.) and the Binational Israel-USA Foundation (BSF; A.F.).

### References

- 1.Abbott, N.J., Friedman, A.: Overview and introduction: the blood-brain barrier in health and disease. Epilepsia
**53**(s6), 1–6 (2012)CrossRefGoogle Scholar - 2.Bridle, J.S.: Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. In: Soulié, F.F., Hérault, J. (eds.) Neurocomputing. NATO ASI Series, vol. 68, pp. 227–236. Springer, Heidelberg (1990)CrossRefGoogle Scholar
- 3.Brix, G., Semmler, W., Port, R., Schad, L.R., Layer, G., Lorenz, W.J.: Pharmacokinetic parameters in CNS Gd-DTPA enhanced MR imaging. J. Comput. Assist. Tomogr.
**15**(4), 621–628 (1991)CrossRefGoogle Scholar - 4.Buades, A., Coll, B., Morel, J.M.: A non-local algorithm for image denoising. In: Computer Vision and Pattern Recognition, CVPR, vol. 2, pp. 60–65 (2005)Google Scholar
- 5.Dahl, G.E., Sainath, T.N., Hinton, G.E.: Improving deep neural networks for LVCSR using rectified linear units and dropout. In: ICASSP, pp. 8609–8613. IEEE (2013)Google Scholar
- 6.Gal, Y., et al.: Denoising of dynamic contrast-enhanced MR images using dynamic nonlocal means. IEEE Trans. Med. Imaging
**29**(2), 302–310 (2010)CrossRefGoogle Scholar - 7.Golkov, V., et al.: q-space deep learning for twelve-fold shorter and model-freediffusion MRI scans. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9349, pp. 37–44. Springer, Heidelberg (2015)Google Scholar
- 8.Hinton, G.E., Salakhutdinov, R.R.: Reducing the dimensionality of data with neural networks. Science
**313**(5786), 504–507 (2006)MathSciNetCrossRefMATHGoogle Scholar - 9.Hinton, G., et al.: Deep neural networks for acoustic modeling in speech recognition: the shared views of four research groups. IEEE Sig. Process. Mag.
**29**(6), 82–97 (2012)CrossRefGoogle Scholar - 10.Hinton, G.E.: Training products of experts by minimizing contrastive divergence. Neural Comput.
**14**(8), 1771–1800 (2002)CrossRefMATHGoogle Scholar - 11.Hinton, G.E., Osindero, S., Teh, Y.W.: A fast learning algorithm for deep belief nets. Neural Comput.
**18**(7), 1527–1554 (2006)MathSciNetCrossRefMATHGoogle Scholar - 12.Kimmel, R., Malladi, R., Sochen, N.: Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images. Int. J. Comput. Vis.
**39**(2), 111–129 (2000)CrossRefMATHGoogle Scholar - 13.Martel, A.L.: A fast method of generating pharmacokinetic maps from dynamic contrast-enhanced images of the breast. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4191, pp. 101–108. Springer, Heidelberg (2006)CrossRefGoogle Scholar
- 14.Murase, K.: Efficient method for calculating kinetic parameters using T1-weighted dynamic contrast-enhanced magnetic resonance imaging. Magn. Reson. Med.
**51**(4), 858–862 (2004)CrossRefGoogle Scholar - 15.Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by error propagation. Technical report, DTIC Document (1985)Google Scholar
- 16.Schmid, V.J., et al.: A bayesian hierarchical model for the analysis of a longitudinal dynamic contrast-enhanced MRI oncology study. Magn. Reson. Med.
**61**(1), 163–174 (2009)CrossRefGoogle Scholar - 17.Sourbron, S.P., Buckley, D.L.: Classic models for dynamic contrast-enhanced MRI. NMR Biomed.
**26**(8), 1004–1027 (2013)CrossRefGoogle Scholar - 18.Tofts, P.: Quantitative MRI of the Brain: Measuring Changes Caused by Disease. Wiley, Hoboken (2005)Google Scholar
- 19.Tofts, P.S.: Modeling tracer kinetics in dynamic Gd-DTPA MR imaging. J. Magn. Reson. Imaging
**7**(1), 91–101 (1997)CrossRefGoogle Scholar - 20.Tofts, P.S., et al.: Estimating kinetic parameters from dynamic contrast-enhanced T1-weighted MRI of a diffusable tracer: standardized quantities and symbols. J. Magn. Reson. Imaging
**10**(3), 223–232 (1999)CrossRefGoogle Scholar - 21.Veksler, R., Shelef, I., Friedman, A.: Blood-brain barrier imaging in human neuropathologies. Arch. Med. Res.
**45**(8), 646–652 (2014)CrossRefGoogle Scholar - 22.Vincent, P., et al.: Stacked denoising autoencoders: learning useful representations in a deep network with a local denoising criterion. J. Mach. Learn. Res.
**11**, 3371–3408 (2010)MathSciNetMATHGoogle Scholar