Blind Image Deblurring via the Weighted Schatten p -norm Minimization Prior
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Blind Image Deblurring via the Weighted Schatten p‑norm Minimization Prior Zhenhua Xu1 · Huasong Chen2 · Zhenhua Li1 Received: 18 November 2019 / Revised: 12 May 2020 / Accepted: 15 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we propose a new image blind deblurring model, based on a novel low-rank prior. As the low-rank prior, we employ the weighted Schatten p-norm minimization (WSNM), which can represent both the sparsity and self-similarity of the image structure more accurately. In addition, the L0-regularized gradient prior is introduced into our model, to extract significant edges quickly and effectively. Moreover, the WSNM prior can effectively eliminate harmful details and maintain dominant edges, to generate sharper intermediate images, which is beneficial for blur kernel estimation. To optimize the model, an efficient optimization algorithm is developed by combining the half-quadratic splitting strategy with the generalized soft-thresholding algorithm. Extensive experiments have demonstrated the validity of the WSNM prior. Our flexible low-rank prior enables the proposed algorithm to achieve excellent results in various special scenarios, such as the deblurring of text, face, saturated, and noise-containing images. In addition, our method can be extended naturally to non-uniform deblurring. Quantitative and qualitative experimental evaluations indicate that the proposed algorithm is robust and performs favorably against state-of-the-art algorithms. Keywords Image deblurring · Low-rank prior · L0-regularized gradient · Weighted Schatten p-norm
* Zhenhua Xu [email protected] * Zhenhua Li [email protected] Huasong Chen [email protected] 1
School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
2
Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an 223001, China
Vol.:(0123456789)
Circuits, Systems, and Signal Processing
1 Introduction Blind image deblurring has become an important research topic in the field of image processing and computer vision. It is a challenging and interesting problem and has been applied widely in various fields, including biomedicine, aerospace, and public safety. A common type of blurring is motion blurring, which is caused by the motion of an object relative to the camera during the exposure time. When the motion blurring is uniform and spatially invariant, the relationship between the latent sharp image L and the observed blurred image B can be established by using the following model:
B = L ∗ k + n,
(1)
where *, k , and n represent the convolution operator, blur kernel, and additive noise, respectively. According to (1), we need to restore both L and k , with the blurred image B as the only input. This problem is challenging and ill-posed because there are an infinite number of different solution sets ( L , k ), each of which can correspond to the same B . In addition, the effect of noise makes blind image restoration more difficult. Theref
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