Confidence-based anisotropic filtering of magnetic resonance images

Wiener filter restoration, followed by a difference operator, is used to estimate the standard deviation of the noise based on the additive noise assumption. Simulation studies show that a 5 × 5 Wiener filter gives an estimate of noise within a 5% error margin. A careful examination of the conductance map in the brain MR image reveals that a wide band of zero conductance region is seen around blurred boundaries. To blend these regions without allowing a generous blurring, a small constant can be added to the conductance function. A better approach will be incorporating the second derivative information into the conductance function. As edges are defined at the zero-crossings of the second derivative response, the strength of the second derivative response can be used as a measure of distance to a boundary. Unfortunately, in the discrete domain, edges generally fall off pixel locations. Thus, second derivative strength would not be a quite reliable measure, unless interpolation and subsampling are employed.