Multivariate median filters and their extensions

Having been studied since long by statisticians, multivariate medianconcepts found their way into the image processing literature in thecourse of the last decades, being used to construct robust and efficientdenoising filters for multivariate images such as colour images but alsomatrix-valued images.Based on the similarities between image and geometric data as results ofthe sampling of continuous physical quantities, it can be expected that theunderstanding of multivariate median filters for images provides a startingpoint for the development of shape processing techniques.This paper presents an overview of multivariate median concepts relevantfor image and shape processing. It focusses on their mathematical principlesand discusses important properties especially in the context of imageprocessing.

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Multivariate Median Filters and Partial Differential Equations

Journal of Mathematical Imaging and Vision ◽

10.1007/s10851-016-0645-9 ◽

2016 ◽

Vol 56 (2) ◽

pp. 320-351 ◽

Cited By ~ 3

Author(s):

Martin Welk

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Partial Differential ◽

Median Filters ◽

Multivariate Median

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Feasibility of Total Variation Noise Reduction Algorithm According to Various MR-Based PET Images in a Simultaneous PET/MR System: A Phantom Study

Diagnostics ◽

10.3390/diagnostics11020319 ◽

2021 ◽

Vol 11 (2) ◽

pp. 319

Author(s):

Chan-Rok Park ◽

Seong-Hyeon Kang ◽

Young-Jin Lee

Keyword(s):

Image Quality ◽

Noise Reduction ◽

Total Variation ◽

Parallel Imaging ◽

Pulse Sequence ◽

Reduction Algorithm ◽

Median Filters ◽

Reduction Techniques ◽

Imaging Results ◽

Noise Reduction Algorithm

Recently, the total variation (TV) algorithm has been used for noise reduction distribution in degraded nuclear medicine images. To acquire positron emission tomography (PET) to correct the attenuation region in the PET/magnetic resonance (MR) system, the MR Dixon pulse sequence, which is based on controlled aliasing in parallel imaging, results from higher acceleration (CAIPI; MR-ACDixon-CAIPI) and generalized autocalibrating partially parallel acquisition (GRAPPA; MR-ACDixon-GRAPPA) algorithms are used. Therefore, this study aimed to evaluate the image performance of the TV noise reduction algorithm for PET/MR images using the Jaszczak phantom by injecting 18F radioisotopes with PET/MR, which is called mMR (Siemens, Germany), compared with conventional noise-reduction techniques such as Wiener and median filters. The contrast-to-noise (CNR) and coefficient of variation (COV) were used for quantitative analysis. Based on the results, PET images with the TV algorithm were improved by approximately 7.6% for CNR and decreased by approximately 20.0% for COV compared with conventional noise-reduction techniques. In particular, the image quality for the MR-ACDixon-CAIPI PET image was better than that of the MR-ACDixon-GRAPPA PET image. In conclusion, the TV noise-reduction algorithm is efficient for improving the PET image quality in PET/MR systems.

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