2025/05/12 by Dragoş-Pătru Covei, Covei, Dragos-Patru · 3 citations
Computer Science · #Advanced Image Processing Techniques #Analysis of PDEs (math.AP) #FOS: Mathematics #Image Enhancement Techniques #Image and Signal Denoising Methods
paper · pdf · doi:10.48550/arxiv.2505.07699
openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.