Image noise reduction based on block matching in wavelet frame domain
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Image noise reduction based on block matching in wavelet frame domain Nazeer Muhammad1 · Nargis Bibi2 · Muhammad Kamran3 · Yasir Bashir3 · Sangwoong Park4 · Kim Dai Gyoung4 Received: 17 May 2019 / Revised: 16 April 2020 / Accepted: 4 June 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper describes the shear wavelet frame transform (SWFT) with two sets of block matching for the application of image denoising. Using the SWFT, we can analyze anisotropic features, such as edges in images. To assign the directionality we use a shear matrix for the continuous wavelet transform. Block matching with 3-D collaborative filtering has been incorporated for hard thresholding of reference block. We deploy two sets of the search neighborhood blocks to avoid the artifacts while removing heavy noise. The proposed algorithm is evaluated on standard benchmark images and outperforms the recent state-of-the-art methods in terms of peak signal to noise ratio. Keywords Block mathcing · Edge enhancing · Image denoising · Shear wavelet frames · Minimum mean square error Kim Dai Gyoung
[email protected] Nazeer Muhammad [email protected] Nargis Bibi [email protected] Muhammad Kamran [email protected] Yasir Bashir [email protected] Sangwoong Park [email protected] 1
Department of IT and Computer Science (Software Engg), Pak-Austria Fachhochschule Institute of Applied Sciences and Technology, Mang Khanpur Road, Haripur, Pakistan
2
Department of Computer Science, Fatima Jinnah Women University, Rawalpindi, Pakistan
3
Department of Mathematics, COMSATS University Islamabad, Wah Campus, Pakistan
4
Department of Applied Mathematics, Hanyang University, Ansan, 426-791, South Korea
Multimedia Tools and Applications
1 Introduction An image is represented as a matrix of pixel values. Therefore, the direction of the image means the direction of pixels [7]. The Discrete Wavelet Transform (DWT) analyses the images by the horizontal, vertical, and diagonal directions for an image [11]. There have been several studies to compensate for the lack of various directions while performing the process of denoising [7, 16]. We will define the shear wavelet frame transform (SWFT) by using shear operator to give directionality for image analysis. To achieve the arbitrary direction we need to interpolate pixel values [7]. We designed SWFT to avoid interpolation which leads to severe artifacts in denoised images. Moreover, SWFT is used to supplement the limited directionality of the existing wavelet transform [7]. Several image representation have been proposed using curvelets [9] and contourlets [4, 20]. In particular, implementation of curvelets which is entirely done on Fourier domain with bandlimited directional filters are poorly localised in time. Therefore, this approach may not be able to analyse the significant region of interest of an image [11]. Contourless are adopted with elongated basis functions with less clear directional features which leads to severe a
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