Image Restoration via the Integration of Optimal Control Techniques and the Hamilton–Jacobi–Bellman Equation

Dragos-Patru Covei ()
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Dragos-Patru Covei: Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana, No. 6, District 1, 010374 Bucharest, Romania

Mathematics, 2025, vol. 13, issue 19, 1-28

Abstract: In this paper, we propose a novel image restoration framework that integrates optimal control techniques with the Hamilton–Jacobi–Bellman (HJB) equation. Motivated by models from production planning, our method restores degraded images by balancing an intervention cost against a state-dependent penalty that quantifies the loss of critical image information. Under the assumption of radial symmetry, the HJB equation is reduced to an ordinary differential equation and solved via a shooting method, from which the optimal feedback control is derived. Numerical experiments, supported by extensive parameter tuning and quality metrics such as PSNR and SSIM, demonstrate that the proposed framework achieves significant improvement in image quality. The results not only validate the theoretical model but also suggest promising directions for future research in adaptive and hybrid image restoration techniques.

Keywords: image restoration; numerical experiments (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:19:p:3137-:d:1762483

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