Real-time magnetic resonance Q-Ball imaging using Kalman filtering with Laplace-Beltrami regularization

Rachid Deriche; Jeff Calder

doi:10.1117/12.812263

27 March 2009 Real-time magnetic resonance Q-Ball imaging using Kalman filtering with Laplace-Beltrami regularization

Rachid Deriche, Jeff Calder

Proceedings Volume 7259, Medical Imaging 2009: Image Processing; 72591Z (2009) https://doi.org/10.1117/12.812263
Event: SPIE Medical Imaging, 2009, Lake Buena Vista (Orlando Area), Florida, United States

Abstract

Diffusion MRI has become an established research tool for the investigation of tissue structure and orientation from which has stemmed a number of variations, such as Diffusion Tensor Imaging (DTI) Diffusion Spectrum Imaging (DSI) and QBall Imaging (QBI). The acquisition and analysis of such data is very challenging due to its complexity. Recently, an exciting new Kalman filtering framework has been proposed for DTI and QBI reconstructions in real time during the repetition time (TR) of the acquisition sequence. In this article, we first revisit and thoroughly analyze this approach and show it is actually sub-optimal and not recursively minimizing the intended criterion due to the Laplace-Beltrami regularization term. Then, we propose a new approach that implements the QBI reconstruction algorithm in real-time using a fast and robust Laplace-Beltrami regularization without sacrificing the optimality of the Kalman filter. We demonstrate that our method solves the correct minimization problem at each iteration and recursively provides the optimal QBI solution. We validate with real QBI data that our proposed real-time method is equivalent in terms of QBI estimation accuracy to the standard off-line processing techniques and outperforms the existing solution. This opens new and interesting opportunities for real-time feedback for clinicians during an acquisition and also for researchers investigating into optimal diffusion orientation sets and, real-time fiber tracking and connectivity mapping.

Citation Download Citation

Rachid Deriche and Jeff Calder "Real-time magnetic resonance Q-Ball imaging using Kalman filtering with Laplace-Beltrami regularization", Proc. SPIE 7259, Medical Imaging 2009: Image Processing, 72591Z (27 March 2009); https://doi.org/10.1117/12.812263

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KEYWORDS

Filtering (signal processing)

Electronic filtering

Diffusion

Diffusion tensor imaging

Spherical lenses

Digital filtering

Signal to noise ratio

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