Noise based computation of decay control parameter in Nonlocal means filter for MRI restoration

The noise suppression and edge preservation offered by Nonlocal Means (NLM) filter depends on the selection of decay control parameter and radii of search and similarity windows. If the decay control parameter is too small then little noise will be removed, while if it is too high, the image becomes blurry. Empirical selection of the filter parameters are always subjective and may be far from optimal. The present study demonstrates an automated method to compute decay control parameter from the noise estimate and an objective method to identify the optimum values of operational parameters using modified Pratt's Figure of Merit (PFOM) on Magnetic Resonance (MR) images. The decay control parameter is computed as the product of standard deviation of the noise and an arbitrary constant, termed as coefficient of noise variance. The radii of search, similarity windows and coefficient of noise variance which offer maximum noise suppression with minimum edge degradation were identified on multiple MR images with different textural and noise content. It has been observed that regardless of the textural and noise content of the MR image, the optimum range of coefficient of noise variance lies between four and eight, typically at seven. For MR images, the minimum radii of similarity and search windows should be greater than three, beyond which the radii has no significant influence on the performance of NLM, provided the radius of search window should be sufficiently larger than radius of similarity window, typically four times. Since the radii of search, similarity windows and coefficient of noise variance is robust to textural and noise content of the MR image, the computed decay control parameter depends only on the standard deviation of the noise. Hence, the proposed NLM is fully noise adaptive. The experimental analysis was performed in Matlab®.