Single Image Blind Deblurring Based on Salient Edge-Structures and Elastic-Net Regularization
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Single Image Blind Deblurring Based on Salient Edge-Structures and Elastic-Net Regularization XiaoYuan Yu1 · Wei Xie1 Received: 14 February 2019 / Accepted: 4 February 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In single image blind deblurring, the blur kernel and latent image are estimated from a single observed blurry image. The associated mathematical problem is ill-posed, and an acceptable solution is difficult to obtain without additional priors or heuristics. Inspired by the nonlocal self-similarity in image denoising problem, we introduce elastic-net regularization as a rank prior to improve the estimation of the intermediate image. Furthermore, it is well known that salient edge-structures can provide reliable information for kernel estimation. Therefore, we propose a new blind image deblurring method by combining the salient edge-structures and the elastic-net regularization. The salient edge-structures are selected from the intermediate image and used to guide the estimation of the blur kernel. Then, we employ the elastic-net regularization and edge-structures to further estimate intermediate latent image, by retaining the dominant edge and removing slight texture, for a better kernel estimation. Finally, quantitative and qualitative evaluations are conducted by comparing the results with those obtained by state-of-the-art methods. We conclude that the proposed method performs favorably when considering both synthetic and real blurry images. Keywords Single image blind deblurring · Salient edge-structures · Elastic-net regularization · Kernel and latent image estimation
1 Introduction
b = k ⊗ f + n,
Single image blind deblurring is a classical and significant image issue and has attracted much attention in the computer vision community within the last decade. With the development of smartphones or handheld cameras, blurriness of photography is inevitable because the object and the camera sometimes move relative to one another during exposure. Unfortunately, it is difficult to obtain the same image in the same scene. Therefore, it is necessary to restore the blurry image to a discernible high-quality image with high resolution. Assuming that the blurriness of image is uniform and spatially invariant, the image-blur model is represented as follows:
where b ∈ R n 1 ×n 2 denotes the blurry image, f ∈ R n 1 ×n 2 denotes the sharp latent image, and n ∈ R n 1 ×n 2 is additive white Gaussian noise whose elements follow the distribu tion N 0, σ 2 . ⊗ denotes convolution operator incorporating boundary condition, and k ∈ R kh×kw denotes the blur convolutional kernel. The purpose of blind image deblurring is how to estimate the latent image f from single blurry image b with unknown kernel k. The related mathematical problem is ill-posed because different pairs of f and k can produce the same b. Therefore, we need additional priors or some heuristics to constrain the solution of image blind deblurring problem. In the past decade, researchers had focused on the establish
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