Differential and Integral Equations

A gradient constraint variational approach to image reconstruction

Oana Carja

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In this paper we propose a variational model for image restoration based on the minimization of a convex functional with a gradient constraint. This approach has a smoothing effect on the degraded image, as it does not allow rapid changes in the image content. We also consider the evolutionary model of the resulting nonlinear differential equation. Furthermore, we discuss the dual problem associated with the model and propose a numerical algorithm for approximating its solution.

Article information

Differential Integral Equations, Volume 22, Number 3/4 (2009), 285-301.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49K20: Problems involving partial differential equations 49N15: Duality theory 46N10: Applications in optimization, convex analysis, mathematical programming, economics


Carja, Oana. A gradient constraint variational approach to image reconstruction. Differential Integral Equations 22 (2009), no. 3/4, 285--301. https://projecteuclid.org/euclid.die/1356019775

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