Noise and Signal Estimation in Magnitude MRI and Rician Distributed Images: A LMMSE Approach

• Published in: IEEE transactions on image processing 2008-08, Vol.17 (8), p.1383-1398
• Main Authors: Aja-Fernandez, S., Alberola-Lopez, C., Westin, C.-F.
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Biological and medical sciences; Brain - anatomy & histology; Closed-form solution; Computerized, statistical medical data processing and models in biomedicine; Data Interpretation, Statistical; Detection, estimation, filtering, equalization, prediction; Estimation; Estimators; Exact sciences and technology; Filtering; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Information, signal and communications theory; Least-Squares Analysis; Linear minimum mean square error (LMMSE) estimator; Magnetic noise; Magnetic resonance; Magnetic resonance imaging; Magnetic Resonance Imaging - methods; Magnetic separation; Mathematical models; Mean square error methods; Medical management aid. Diagnosis aid; Medical sciences; Miscellaneous; Models, Statistical; MRI filtering; Noise; noise estimation; Reproducibility of Results; Rician channels; Rician noise; Samples; Sensitivity and Specificity; Signal and communications theory; Signal processing; Signal, noise; Statistical analysis; Statistical distributions; Statistical methods; Statistics; Telecommunications and information theory
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2008.925382

A new method for noise filtering in images that follow a Rician model-with particular attention to magnetic resonance imaging-is proposed. To that end, we have derived a (novel) closed-form solution of the linear minimum mean square error (LMMSE) estimator for this distribution. Additionally, a set of methods that automatically estimate the noise power are developed. These methods use information of the sample distribution of local statistics of the image, such as the local variance, the local mean, and the local mean square value. Accordingly, the dynamic estimation of noise leads to a recursive version of the LMMSE, which shows a good performance in both noise cleaning and feature preservation. This paper also includes the derivation of the probability density function of several local sample statistics for the Rayleigh and Rician model, upon which the estimators are built.