Rician noise reduction is an essential issue in magnetic resonance imaging (MRI). Recently, learning-based methods have achieved great success in dealing with image restoration problems, which provide fast inference and good performance. One limitation of these methods, however, is that the training procedure is usually noise-level dependent, i.e. the trained models are bound to a specific noise level and lack the ability to automatically adapt to different noise levels. In this study, the authors propose a variational model for Rician noise removal by integrating a noise adaption function into the field of experts image prior, which can adapt to different noise levels. Instead of directly solving the energy minimisation problem, the authors unroll the gradient descent step of the energy functional for several iterations, the time-dependent parameters of which can be learned through a supervised training process. The authors call this methodology as the noise adaptive trainable non-linear reaction–diffusion model. The proposed methodology is robustness against noise level changing and noise distributions. Experimental results over $T 1$ -, $T 2$ - and PD-weighted MRI data set demonstrate that the proposed model can achieve superior performance compared with other methods in terms of both the peak signal-to-noise ratio and the structural similarity index.

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Adaptive trainable non-linear reaction diffusion for Rician noise removal

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