Abstract
Image denoising is a fundamental problem in both image processing and computer vision with numerous applications. It can be formulated as an inverse problem. Variational methods are commonly used to solve noise removal problems. The Total Variation (TV) regularization has evolved from an image denoising method for images corrupted with multiplicative noise into a more general technique for inverse problems such as denoising, deblurring, blind deconvolution, and inpainting, which also encompasses the Impulse, Poisson, Speckle, and mixed noise models. Multiplicative noise removal based on TV regularization has been widely researched in image science. In multiplicative noise problems, original image is multiplied by a noise rather than added to the original image. This article proposes a novel meshless collocation technique for the solution of a model having multiplicative noise. This technique includes TV and local collocation along with Multiquadric Radial Basis Function (MQ-RBF) for the solution of associated Euler-Lagrange equation for restoring multiplicative noise from digital images. Numerical examples demonstrate that the proposed algorithm is able to preserve small image details while the noise in the homogeneous regions is removed sufficiently. As a consequence, our method yields better denoised results than those of the current state of the art methods with respect to the Peak-Signal to Noise Ratio (PSNR) values.
Highlights
Image denoising is a research topic that has been studied by researchers from last many decades
This section is dedicated to an examination of some numerically computed examples to show the execution of proposed strategy M2 over methods M1 on two types of multiplicative noises, to be specific multiplicative noise (Gamma distribution, mean 1and variance L1) and speckle noise (Gamma distribution, mean 1 and variance L2)
A new meshless collocation technique that is Multiquadric Radial Basis Function (MQ-Radial Basis Function (RBF)) combined with Total Variation (TV) regularization is proposed for multiplicative noise removal model
Summary
Image denoising is a research topic that has been studied by researchers from last many decades. Image noise removal problem is of two types, one is additive noise removal and the second one is the multiplicative noise removal problem. Multiplicative model noise removal is more challenging as compared to additive noise removal, we focus on models for removing multiplicative noise, which can be stated as: g = zn (1). Where g: Ω⊂R2→R is the given noisy image, having multiplicative noise n and z is the original image. Multiplicative denoising is one of the most important and challenging task. Various methods have been utilized for the numerical solution of Partial Differential Equations (PDEs) connected with models having multiplicative noise, for example, see [5,6,7,8,9]
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