A customized nonlocal restoration schemes with adaptive strength of smoothening for magnetic resonance images

Abstract Background Nonlocal Means (NLM) filter is a nonlinear filter exclusively suitable for images comprising redundant patterns at spatially distinct locations, like Magnetic Resonance (MR) images. However, its performance heavily depends on the selection of one of its arbitrary operational parameters termed as smoothening strength (ξ). Improper selection of ξ may lead to over-blurring or partial denoising. Objectives An image adaptive algorithm, to determine the optimum value of ξ, meant for customizing the NLM for MR images is proposed. Methods In the proposed scheme for initializing ξ, its value is increased in proportion to the standard deviation of noise σ ^ n , according to a linear model ξ=β σ ^ n . The optimum value of the arbitrary parameter β is identified through an iterative search, using a composite metric termed as Optimum Denoising Index (ODI), which objectively accounts for the noise suppression and edge preservation capability of the filter, as target function. Assuming the noise to be Gaussian distributed with zero mean, its standard deviation is computed using a ‘difference of Laplacian’ kernel. Results The techniques available in literature for the selection of β are (i) Coupe’s model with β derived out of minimum error sense, (ii) simple linear model ξ=βσ with empirically decided value β = 10 and global optimum of β modified locally in proportion to either (iii) local noise statistics or (iv) edge strength. ODI exhibited by the above techniques and the proposed iterative search are 0.3145 ± 0.0347, 0.2509 ± 0.0149, 0.1210 ± 0.0143, 0.1790 ± 0.0511 and 0.3678 ± 0.0022, respectively. Peak Signal to Noise Ratio (PSNR) between the denoised and the noise-free ground truth images exhibited by Kuwahara Filter, Total Variation (TV) Filter, Anisotropic Diffusion (AD) Filter, Bilateral Filter, SUSAN Filter and the proposed NLM Filter are 21.8739 ± 4.7310, 20.9596 ± 5.0518, 22.1553 ± 5.3369, 22.2142 ± 5.1275, 28.5628 ± 0.02 and 28.9967 ± 0.13, on 30 standard images. Conclusion The iterative search is superior to methods available in literature with regard to the sharpness of the true morphological edges and smoothness of the homogenous regions in the denoised image. The proposed scheme of NLM is found to be superior to Kuwahara, TV, AD, Bilateral and SUSAN Filters.