Abstract
Image denoising is one of the fundamental problems in image processing. Digital images are often contaminated by noise due to the image acquisition process under poor conditions. In this paper, we propose an effective approach to remove mixed Poisson-Gaussian noise in digital images. Particularly, we propose to use a spatially adaptive total variation regularization term in order to enhance the ability of edge preservation. We also propose an instance of the alternating direction algorithm to solve the proposed denoising model as an optimization problem. The experiments on popular natural images demonstrate that our approach achieves superior accuracy than other recent state-of-the-art techniques.
Highlights
Image degradation is the result of defects of the imaging system and noise coming from the formation, transmission and recording processes
To better improve the edge-preserving removal of Poisson noise, the authors in [Zhou, 2012 ] proposed an adaptive model of (3) described as follows (M1): We propose to use a spatially adaptive total variation regularization term in order to enhance the ability of edge preservation
Where u, u∗ are the original image, the reconstructed or noisy image ; Imax is the maximum intensity of the original image; M and N are the number of image pixels in rows and columns; μu, μu∗ - means of images; σu, σu∗ - standard deviations of images; σu,u∗ - covariance of two images u and u∗; c1 = (K1L)2, c2 = (K2L)2, L is the dynamic range of the pixel values (255 for 8-bit grayscale images), and K1 1, K2 1 are small constants
Summary
Image degradation is the result of defects of the imaging system and noise coming from the formation, transmission and recording processes. Let Ω ⊂ R2 be a bounded open set, and let u(x) : Ω → R be a true image describing a real scene, and let f (x) be the observed image of the same scene ( x = (x1, x2) ∈ Ω), which is a degraded image of u. Image restoration is often formulated as the problem of reconstructing a true image u with the size of (M × N ) corrupted by random noise η, from an observed image f. The sought-for image u is a solution of the corresponding inverse problem [Pham, 2015; Pham, 2018]. One of successful edge preserving image denoising models is the wellknown ROF model [Rudin, 1992]. The ROF model is defined by the following unconstrained discrete minimization problem: min u u λ TV + 2 u−f (1)
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