Abstract
The Digital Total Variation (DTV) scheme is a digitized energy regularization scheme used for image denoising. This technique takes advantage of being applied to arbitrarily located data points and also has the edge detective property. This article aims to introduce a novel meshless scheme using DTV filtering and Radial Basis Functions (RBFs) to solve the associated equation with the DTV model numerically which results in the image denoising to remove additive noise from image information. This meshless algorithm based on local collocation and Multiquadric Radial Basis Function. These appearances allow this algorithm not only to remove the additive noise from images but also to resolve the discontinuities sharply. It is also noticed that the proposed meshless scheme is simple, fast, computationally effective, requires simply post-processing, and can be easily implemented mathematically. Experimental results confirm that the peak signal-to-noise ratio, the structural similarity, signal-to-noise ratio, the visual effect, and the computational performance of this new meshless scheme are improved compared with state-of-the-art denoising schemes. Furthermore, the proposed scheme can be applied to colour images as well.
Highlights
Image denoising is one of the most powerful aspects of image processing and computer vision
Various filter-based approaches have been introduced based on these IN detectors, for instance, adaptive center-weighted median filter [19], progressive switching median filter [20], adaptive weighted median filter (AWMF) [21], noise adaptive fuzzy switching median filter (NAFSMF) [22], modified decision- based unsymmetrical trimmed median filter (MDBUTMF) [23], and morphological mean filter (MMF) [24]
PROPOSED MESHLESS SCHEME M2 In this new subsection, we introduce the meshless scheme by applying the BRF collocation scheme for the numerical solution of Digital Total Variation (DTV) filter-based restoration equation (12) and to get resultant image z from the given noisy image z0 selected in model (9)
Summary
Image denoising is one of the most powerful aspects of image processing and computer vision. The classical numerical schemes unsuccessful to solve the PDE equation for the smooth solution, which produces staircase effects, textures, and degrading the fine details during the image denoising process. Some numerical schemes have been produced for the numerical solutions of DTV based nonlinear equation for smooth solutions i.e. to remove the noise and restore the accuracy of the given image information, for instance, see [25], [27]–[29], [31]. Kansa method is a domain type strategy, which has numerous features like the finite element approach for the approximation of the solution of the nonlinear equation This proposed scheme will be helpful in image denoising and edge preservation and be helpful in the minimization of staircase effect, preservation of textures, and fine details during the restoration process. In the foregoing equation (4), the first term is the regularization term, while the second term is the data fidelity term, where γ and α are called the fitting and regularization parameters, respectively
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