IEEE Trans Image Process - A general framework for regularized, similarity-based image restoration.

Tópicos

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Resumo

Any image can be represented as a function defined on a weighted graph, in which the underlying structure of the image is encoded in kernel similarity and associated Laplacian matrices. In this paper, we develop an iterative graph-based framework for image restoration based on a new definition of the normalized graph Laplacian. We propose a cost function, which consists of a new data fidelity term and regularization term derived from the specific definition of the normalized graph Laplacian. The normalizing coefficients used in the definition of the Laplacian and associated regularization term are obtained using fast symmetry preserving matrix balancing. This results in some desired spectral properties for the normalized Laplacian such as being symmetric, positive semidefinite, and returning zero vector when applied to a constant image. Our algorithm comprises of outer and inner iterations, where in each outer iteration, the similarity weights are recomputed using the previous estimate and the updated objective function is minimized using inner conjugate gradient iterations. This procedure improves the performance of the algorithm for image deblurring, where we do not have access to a good initial estimate of the underlying image. In addition, the specific form of the cost function allows us to render the spectral analysis for the solutions of the corresponding linear equations. In addition, the proposed approach is general in the sense that we have shown its effectiveness for different restoration problems, including deblurring, denoising, and sharpening. Experimental results verify the effectiveness of the proposed algorithm on both synthetic and real examples.

Resumo Limpo

imag can repres function defin weight graph under structur imag encod kernel similar associ laplacian matric paper develop iter graphbas framework imag restor base new definit normal graph laplacian propos cost function consist new data fidel term regular term deriv specif definit normal graph laplacian normal coeffici use definit laplacian associ regular term obtain use fast symmetri preserv matrix balanc result desir spectral properti normal laplacian symmetr posit semidefinit return zero vector appli constant imag algorithm compris outer inner iter outer iter similar weight recomput use previous estim updat object function minim use inner conjug gradient iter procedur improv perform algorithm imag deblur access good initi estim under imag addit specif form cost function allow us render spectral analysi solut correspond linear equat addit propos approach general sens shown effect differ restor problem includ deblur denois sharpen experiment result verifi effect propos algorithm synthet real exampl

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