Image deblurring is a challenging problem in image processing, which aims to reconstruct an original high-quality image from its blurred measurement caused by various factors, for example, imperfect focusing caused by the imaging system or different depths of scene appearing commonly in our daily photos. Recently, sparse representation whose basic idea is to code an image patch as a linear combination of a few atoms chosen out from an over-complete dictionary has shown uplifting results in image deblurring. Based on this and another heart-stirring property called nonlocal self-similarity, some researchers have developed nonlocal sparse regularization models to unify the local sparsity and the nonlocal self-similarity into a variational framework for image deblurring. In such models, the similarity evaluation for searching similar image patches is indispensable and influential in deblurring performance. Though the traditional Euclidean distance is generally a choice as a similarity metric, its application might give rise to inferior performance since it fails to capture the intrinsic structure of image patches. Consequently, in this article, based on structural similarity index and principal component analysis, we propose the nonlocal sparse regularization-based image deblurring with novel similarity criteria called structural similarity distance and principal component analysis-subspace Euclidean distance to improve the accuracy of deblurring. The structural similarity index is commonly used for assessing perceptual image quality, and principal component analysis is pervasively used in pattern recognition and dimensionality reduction. In our comprehensive experiments, the nonlocal sparse regularization-based image deblurring with our novel similarity criteria has achieved higher peak signal-to-noise and favorable consistency with subjective vision perception compared with state-of-the-art deblurring algorithms.
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