IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 27, NO. 2, FEBRUARY 2018 649 Edge Probability and Pixel Relativity-Based Speckle Reducing Anisotropic Diffusion Deepak Mishra , Santanu Chaudhury, Mukul Sarkar, Arvinder Singh Soin, and Vivek Sharma Abstract—Anisotropic diffusion filters are one of the best choices for speckle reduction in the ultrasound images. These filters control the diffusion flux flow using local image statistics and provide the desired speckle suppression. However, inefficient use of edge characteristics results in either oversmooth image or an image containing misinterpreted spurious edges. As a result, the diagnostic quality of the images becomes a concern. To alleviate such problems, a novel anisotropic diffusion-based speckle reducing filter is proposed in this paper. A probability density function of the edges along with pixel relativity informa- tion is used to control the diffusion flux flow. The probability density function helps in removing the spurious edges and the pixel relativity reduces the oversmoothing effects. Furthermore, the filtering is performed in superpixel domain to reduce the execution time, wherein a minimum of 15% of the total number of image pixels can be used. For performance evaluation, 31 frames of three synthetic images and 40 real ultrasound images are used. In most of the experiments, the proposed filter shows a better performance as compared to the state-of-the-art filters in terms of the speckle region’s signal-to-noise ratio and mean square error. It also shows a comparative performance for figure of merit and structural similarity measure index. Furthermore, in the subjective evaluation, performed by the expert radiologists, the proposed filter’s outputs are preferred for the improved contrast and sharpness of the object boundaries. Hence, the proposed filtering framework is suitable to reduce the unwanted speckle and improve the quality of the ultrasound images. Index Terms— Ultrasound image, speckle, anisotropic diffu- sion, edge probability, pixel relativity. I. I NTRODUCTION S PECKLE adversely affects the quality and contrast of the ultrasound (US) images [1], [2]. Though some researchers have used it for tissue characterization, a major section treats it Manuscript received February 15, 2017; revised August 11, 2017; accepted September 26, 2017. Date of publication October 12, 2017; date of current version November 14, 2017. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Oleg V. Michailovich. (Corresponding author: Deepak Mishra.) D. Mishra and M. Sarkar are with the Electrical Engineering Depart- ment, IIT Delhi, New Delhi 110016, India (e-mail: deemishra21@gmail.com; msarkar@ee.iitd.ac.in). S. Chaudhury is with the Electrical Engineering Department, IIT Delhi, New Delhi 110016, India, and also with the Central Electronics Engineering Research Institute, Pilani 333031, India (e-mail: santanuc@ee.iitd.ac.in). A. S. Soin and V. Sharma are with the Medanta Hospital, Gurgaon 122018, India (e-mail: absoin@gmail.com; vivax08@hotmail.com). This paper has supplementary downloadable material available at http://ieeexplore.ieee.org., provided by the author. The material includes a document containing the expressions of the evaluation metrics used in this work. The file size is 0.0777 MB. Contact deemishra21@gmail.com for further questions about this work. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIP.2017.2762590 as an unwanted noise [3]–[5]. The primary reason behind this perspective is that the interpretation of speckle contaminated US images always requires a high level of expertise and experience. A rather technical reason is that the speckle is generated from unwanted echoes of US waves. Since these echoes are produced from the randomly situated scatterers, the speckle can be considered a random phenomenon. Unlike the thermal noise, speckle is known to have mul- tiplicative nature [4]. In terms of statistics, it is modeled using Rayleigh distribution for a high density of scatterers. For smaller scatterer density, it is considered to be partially developed and modeled using K distribution [6]. Some other popular choices of distributions are Nakagami, Gamma, and Rician distributions [7]. These theoretical models have helped in the development of the filters to reduce speckle from US images. However, diagnostic quality of the filtered outputs has always been a concern. For example, in liver US images, speckle pattern over the parenchyma region provides infor- mation about the echogenicity of the liver, which helps in the diagnosis of diseases like fatty liver. Therefore, speckle removal from parenchyma region may result in an incorrect diagnosis. On the other hand, in heart images, speckle present over the blood chambers obstruct the visibility of septum wall boundaries and ventricle valves, therefore should be removed. Hence, the reduction of speckle from the entire image, which is the case with most of the existing filters, is not desirable from the point of view of diagnostic requirements. Thus, being a characteristic attribute, the speckle should be preserved over the tissue regions and at the same time, it should be selectively removed from the regions of low clinical significance to improve the image quality. Most of the existing filters do not have the ability to perform selective filtering. The traditional filters are local statistics based spatially adaptive filters which preclude filtering near the edges to preserve object boundaries. The Lee filter [8] and Kuan filter [9] are two well known traditional filters. The idea of local statistics based filtering has been incorpo- rated in anisotropic diffusion framework by Yu and Acton [10]. Their filter is named as speckle reducing anisotropic dif- fusion (SRAD). A better filter known as detail preserving anisotropic diffusion (DPAD) has been reported in [11]. Fundamentally, the anisotropic diffusion filters detect the edges and avoid filtering across them to preserve the object boundaries. These filters use diffusion coefficient which attains low values, close to zero, near the edges and high values in the homogeneous regions. As a result, the homogeneous regions are filtered and the edges are preserved. Further improvements 1057-7149 © 2017 IEEE. 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