beelddeblurring

Beelddeblurring (image deblurring) is the process of reversing blur in digital images to recover the original scene. Blur can arise from camera motion, out-of-focus optics, atmospheric turbulence, or motion in the scene. The mathematical model commonly used is I = K * J + N, where I is the observed image, J is the latent sharp image, K is the point spread function (PSF) describing the blur, * denotes convolution, and N is noise. Deblurring aims to estimate J (and sometimes K) from I. When K is known, the problem is non-blind deconvolution; when K is unknown it is blind deconvolution.

Classic approaches include inverse filtering and Wiener filtering, which assume a known PSF and statistical properties of noise, but tend to amplify noise. Regularized deconvolution adds constraints such as total variation (TV) or L2 norms to promote plausible solutions. Iterative algorithms like Richardson–Lucy deconvolution iteratively maximize likelihood under Poisson noise assumptions. More robust non-blind methods use sparsity or priors in transform domains (wavelets, gradients).

Blind deconvolution jointly estimates J and K, but is highly ill-posed and susceptible to artifacts. Modern methods often combine variational formulations with priors or optimization schemes, and increasingly use data-driven approaches. Deep learning methods train neural networks to map blurred images to sharp ones, sometimes with synthetic blur models or paired data.

Applications span photography, surveillance, astronomy, microscopy, and medical imaging. Evaluation typically uses metrics such as PSNR and SSIM, and qualitative assessment. Limitations include residual artifacts, natural image statistics mismatch, and computational cost. The field continues to evolve with hybrid model-based and learning-based techniques.