A Non Local Means Method Using Fuzzy Similarity Criteria for Restoration of Ultrasound Images Kamran Binaee and Reza P. R. Hasanzadeh DSP Research Laboratory, Department of Electrical Engineering, University of Guilan, Rasht, Iran kamranbinaee@msc.guilan.ac.ir, hasanzadehpak@guilan.ac.ir Abstract—Conventional Non-Local Means (NLM) as one of the most powerful denoising filters especially for reduction of additive Gaussian noise is not successful in the case of Ultrasound (US) Images noise suppression. In the presence of additive Gaussian noise model, the NLM filter uses Euclidean distance similarity criterion to find similar patches and therefore it is not appropriate for US images which have noise with multiplicative and signal dependant nature. The more successful version of NLM filter for US images which is known as Optimized Bayesian NLM (OBNLM) is developed based on Pearson Distance similarity criterion to measure and find the similar patches. In this paper, we tried to improve the performance of NLM filter using appropriate fuzzy similarity criteria. The proposed filters are evaluated in objective and subjective manners with both synthetic phantom and real clinical US images. It is shown that the proposed methods have better ability for noise reduction comparing with the other state-of-art de-speckling filters. Key Words: fuzzy similarity measure, multiplicative noise, non- local means filter, Speckle noise. I. INTRODUCTION Image restoration as one of the most important fields of image processing has a critical role in medical imaging and diagnosis [1-3]. Dealing with several noise models, researchers have proposed various denoising algorithms in the literature [1-2]. Non-Local Means (NLM) is one of the state-of-art methods for image restoration which has an outstanding performance in case of additive Gaussian noise model [3]. This filter and its properties will be reviewed briefly in section II. On the other hand, in Ultrasound Images (US), noise and degradation function usually have multiplicative and signal dependent nature which in these cases the performance of NLM filter is degraded significantly [4-6]. Coupe et al. [4] proposed a modification for NLM in case of signal dependant noise using Bayesian framework, which is known as Optimized Bayesian Non Local Means (OBNLM) filter [4]. The main advantage of this method is using Pearson distance instead of Euclidean distance, which was derived by assuming the appropriate model of noise [4]. Regarding the performance of these alternative methods shown in section III, although the amount of noise reduction is increased but it seems to be possible to improve the denoising ability using heuristic and knowledge-based fuzzy similarity measures. In section IV of this work some well known fuzzy similarity measures used in image processing applications are introduced and compared [7-9]. As shown in section V, synthetic phantom US images with appropriate model of noise are used to evaluate and find the best setup of fuzzy similarity criteria and then the proposed methods are compared with several recently developed de-speckling filters namely; NLM, OBNLM and also Speckle Reducing Anisotropic Diffusion (SRAD) filter which adapts a Diffusion method to US images using edge-sensitive operators [5]. Several experiments on real clinical US images are included in section VI respectively. II. NON LOCAL MEANS FILTER The key idea of the NLM filter is to consider the data redundancy among the “patches” of a noisy image, and restore the noise free pixel using weighted average of non local pixels [3]. ∑ = j j j i i x u x x w x u NL ) ( ) , ( )) ( ( (1) As shown in (1) and also in Fig.1 NL(u(x i )) is the restored intensity of the noisy pixel u(x i ) where w(x i ,x j ) is the weight assigned to the noisy value u(x j ). This weight evaluates the similarity between two neighbourhoods N i and N j centered on pixels x i and x j called “patches” or “similarity window”. The original non local means filter considers the pixel intensities of the whole image in the weighted average, while for practical and computational reasons this is restricted to a neighbourhood called “search window”. Figure 1. Determining the weights for image patches in NLM method 978-1-4577-1535-8/11/$26.00 ©2011 IEEE