Abstract
As a powerful statistical image modeling technique, sparse representation has been successfully applied in various image restoration applications. Most traditional methods depend on ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm optimization and patch-based sparse representation models. However, these methods have two limits: high computational complexity and the lack of the relationship among patches. To solve the above problems, we choose the group-based sparse representation models to simplify the computing process and realize the nonlocal self-similarity of images by designing the adaptive dictionary. Meanwhile, we utilize Ipnorm minimization to solve nonconvex optimization problems based on the weighted Schatten p-norm minimization, which can make the optimization model more flexible. Experimental results on image inpainting show that the proposed method has a better performance than many current state-of-the-art schemes, which are based on the pixel, patch, and group respectively, in both peak signal-to-noise ratio and visual perception.
Highlights
Restoring a clean image from its degraded image has been widely studied by various methods [1]–[7] in recent years
Inspired by the Weighted Schatten p-norm Minimization (WSNM) [16] and Group-based Sparse Representation (GSR) [3], we propose the group-based sparse representation based on p-norm minimization (LPGSR)
EXPERIMENT RESULTS extensive experimental results are conducted to verify the performance of the proposed LPGSR for image restoration applications, where we focus on the aspect of image inpainting
Summary
Restoring a clean image from its degraded image has been widely studied by various methods [1]–[7] in recent years. In some image restoration problems [8], the observed image Y can be mathematically modeled by: Y = HX + N. We aim to restore the underlying image X. For different choices of H, Equation (1) becomes different image processing problems [3], [9], [10]. When H is a binary diagonal matrix, Equation (1) becomes an image inpainting problem [11]. We focus on image inpainting, aiming for estimating suitable pixel information to fill areas of lost pixels in colorful images
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