Noise and signal estimation in magnitude MRI and Rician distributed images: a LMMSE approach.
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.
Aja-Fernandez
Santiago
S
LPI, ETSI Telecomunicacion, Universidad de Valladolid, Valladolid, Spain.
Alberola-Lopez
Carlos
C
Westin
Carl-Fredrik
CF
D000465:Algorithms; D016477:Artifacts; D001921:Brain / Q000033:anatomy & histology*; D003627:Data Interpretation, Statistical; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016018:Least-Squares Analysis; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015233:Models, Statistical; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity