• Mariusz Nieniewski Faculty of Mathematics and Informatics University of Lodz, ul. Banacha 22, 90-238 Lodz, Poland
  • Paweł Zajączkowski Faculty of Mathematics and Informatics University of Lodz, ul. Banacha 22, 90-238 Lodz, Poland



forward-backward diffusion, multivariate kurtosis, nonlinear coherent diffusion, speckle filtering, ultrasound images


Comparison of the quality of despeckled US medical images is complicated because there is no image of a human body that would be free of speckles and could serve as a reference. A number of various image metrics are currently used for comparison of filtering methods; however, they do not satisfactorily represent the visual quality of images and medical expert’s satisfaction with images. This paper proposes an innovative use of relative multivariate kurtosis for the evaluation of the most important edges in an image. Multivariate kurtosis allows one to introduce an order among the filtered images and can be used as one of the metrics for image quality evaluation. At present there is no method which would jointly consider individual metrics. Furthermore, these metrics are typically defined by comparing the noisy original and filtered images, which is incorrect since the noisy original cannot serve as a golden standard. In contrast to this, the proposed kurtosis is the absolute measure, which is calculated independently of any reference image and it agrees with the medical expert’s satisfaction to a large extent. The paper presents a numerical procedure for calculating kurtosis and describes results of such calculations for a computer-generated noisy image, images of a general purpose phantom and a cyst phantom, as well as real-life images of thyroid and carotid artery obtained with SonixTouch ultrasound machine. 16 different methods of image despeckling are compared via kurtosis. The paper shows that visually more satisfactory despeckling results are associated with higher kurtosis, and to a certain degree kurtosis can be used as a single metric for evaluation of image quality. 

Author Biographies

Mariusz Nieniewski, Faculty of Mathematics and Informatics University of Lodz, ul. Banacha 22, 90-238 Lodz, Poland

Prof. of the Faculty of Mathematics and Informatics, University of Lodz.

Paweł Zajączkowski, Faculty of Mathematics and Informatics University of Lodz, ul. Banacha 22, 90-238 Lodz, Poland

Assistant Lecturer of the Faculty of Mathematics and Informatics, University of Lodz.


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How to Cite

Nieniewski, M., & Zajączkowski, P. (2017). COMPARISON OF ULTRASOUND IMAGE FILTERING METHODS BY MEANS OF MULTIVARIABLE KURTOSIS. Image Analysis and Stereology, 36(2), 79–94.



Original Research Paper