Efficient bias correction for magnetic resonance image denoising

Magnetic resonance imaging (MRI) is a popular radiology technique that is used for visualizing detailed internal structure of the body. Observed MRI images are generated by the inverse Fourier transformation from received frequency signals of a magnetic resonance scanner system. Previous research has demonstrated that random noise involved in the observed MRI images can be described adequately by the so-called Rician noise model. Under that model, the observed image intensity at a given pixel is a nonlinear function of the true image intensity and of two independent zero-mean random variables with the same normal distribution. Because of such a complicated noise structure in the observed MRI images, denoised images by conventional denoising methods are usually biased, and the bias could reduce image contrast and negatively affect subsequent image analysis. Therefore, it is important to address the bias issue properly. To this end, several bias-correction procedures have been proposed in the literature. In this paper, we study the Rician noise model and the corresponding bias-correction problem systematically and propose a new and more effective bias-correction formula based on the regression analysis and Monte Carlo simulation. Numerical studies show that our proposed method works well in various applications.