Image Recovery via Nonlocal Operators

By Yifei Lou, Xiaoqun Zhang, Stanley J. Osher, Andrea L. Bertozzi. Journal of Scientific Computing, 2010

371 citations recorded by the source corpus.

This paper considers two nonlocal regularizations for image recovery, which exploit the spatial interactions in images. We get superior results using preprocessed data as input for the weighted functionals. Applications discussed include image deconvolution and tomographic reconstruction. The numerical results show our method outperforms some previous ones.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/57ff6d7860bf420b15594a9f74937f47e5495051

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In Computational Mechanics

In Computer Vision and Pattern Recognition

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Citations in the corpus

A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations (2015, background): “Anomalous diffusion phenomena are ubiquitous in nature [29, 35]; among the several applications of these nonlocal models let us mention image processing [8, 22, 24, 32], finance [11, 13], electromagnetic fluids [34], peridynamics [42] and porous media flow [2, 14].”
From Local Kernel to Nonlocal Multiple-Model Image Denoising (2009, methodology): “3): [64],[40],[39],[73],[74],[28],[106],[107].”
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction (2010, methodology): “Note that the weight function was computed in the whole searching window in [33], while here only 10 best and 4 nearest neighbors are used for each pixel.”
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints (2012, background): “The operator L and its generalizations arise in many applications such as image analyses [19, 32, 33, 39], machine learning [47], nonlocal Dirichlet forms [5, Sec.”
Image Denoising Methods. A New Nonlocal Principle (2010, background): “Several articles on deblurring have followed this variational line [49], [66], [43] (for image segmentation), [9] (in fluorescence microscopy), [99], (again for nonlocal deconvolution), and [55] (for deconvolution and tomographic reconstruction).”
Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems (2013, methodology): “Among those applications we have image analyses [14, 24, 25, 32], machine learning [36], nonlocal Dirichlet forms [6], kinetic equations [8, 31], phase transitions [11, 23], and nonlocal heat conduction [12].”
Traces for fractional Sobolev spaces with variable exponents (2017, background): “From an applied point of view we recall that non-local energies with constant exponents (we quote here [9, 10]) and also local equations with variable exponents (see [2]) where used in image processing.”
Recovering missing pixels for Landsat ETM + SLC-off imagery using multi-temporal regression analysis and a regularization method (2013, positive): “Several studies (Lou et al., 2010; Peyré et al., 2008) have shown that using the constraint of a non-local regularization method can effectively improve the detailed texture of the processing results.”