A mixed model with multi-fidelity terms and nonlocal low rank regularization for natural image noise removal
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A mixed model with multi-fidelity terms and nonlocal low rank regularization for natural image noise removal Yuepeng Li1,2 · Chun Li1,2 Received: 1 January 2020 / Revised: 3 July 2020 / Accepted: 6 August 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Reconstructing an original image from its corrupted observation is an important and fundamental problem in many image processing applications. Generally, the L1 -norm or L2 -norm combined with a regularization term (the total variation (TV), total generalized variation (TGV) or nuclear norm) is used to fit the impulse noise and Gaussian noise, respectively. However, these methods can only be used to remove a single type of noise from images, and traditional regularization terms often have difficulties in capturing some important prior knowledge of images, such as nonlocal self-similarity, low rank and sparsity. To overcome the above issues, we propose a mixed noise removal model with L1 -L2 fidelity terms and a popular nonlocal low-rank regularization term, which has been shown to have more effective image denoising performance than traditional regularization methods. To solve this model, the split Bregman iteration method (SBIM) is adopted to decompose the difficult minimization optimization problem into four simple subproblems. Extensive experiments on natural images demonstrate that the effectiveness of the proposed method is better than that of other state-of-the-art methods. Keywords Mixed denoising model · Inverse problem · Alternative minimization · Image processing
1 Introduction Reconstructing a true image from its poor-quality observation is one of the most important issues in image processing applications [5, 37, 38, 41]. Generally, we encounter two types of noise during the image acquisition process: impulse noise (IN) and additive white Gaussian noise (AWGN). IN is generally produced due to transmission errors and damaged pixels in camera sensors, and AWGN is generally produced during the image acquisition itself [4]. Yuepeng Li
[email protected] 1
Computer Network Information Center, Chinese Academy of Sciences, Beijing, 100190 China
2
University of Chinese Academy of Sciences, Beijing, 100049 China
Multimedia Tools and Applications
Many methods have been developed for removing either AWGN or IN. However, a mixture of IN and AWGN is normally encountered in real-life applications, which makes image denoising a challenging problem. Formally, the aim of the denoising problem is to solve the inverse problem Au = f
(1)
Here, A is an identity operator or blurring operator, and f is the known data (observed image) from the sensors, which may be of poor quality. u : Ω ⊂ R d → R denotes the unknown object (uncorrupted image). Assume that u is an instance of a random variable U itself, and the corrupted image follows the conditional probability density p(f ; u) = p(f |U = u) = p(f |u). Given f , we can obtain the posteriori probability density for u based on the Bayesian formula |u)p(u) . p(u|f ) = p(fp(f ) To reso
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