deblurring

Deblurring is the process of removing blur from an image to recover a sharper version of the scene. It is a common task in image processing, photography, astronomy, microscopy, and surveillance, where blur degrades detail and interpretability.

Blur is typically modeled as a convolution with a point spread function (PSF) plus noise: g = k * f + n, where g is the observed image, f is the latent sharp image, k is the PSF, and n represents noise. If the PSF is known, the problem is non-blind deblurring; if it is unknown, the task becomes blind deconvolution, which also estimates the blur kernel. Blur can originate from camera motion, defocus, atmospheric turbulence, or sensor integration.

Classical non-blind methods rely on deconvolution with regularization. The Wiener filter performs a frequency-domain deconvolution with noise weighting but can amplify noise and ringing artifacts. Iterative methods such as Richardson-Lucy assume Poisson noise. Regularization techniques, including total variation, promote edge preservation while reducing noise, helping to stabilize the inversion of the blur.

Blind deblurring estimates both the latent image and the blur kernel, typically through iterative, priors-based optimization. Approaches use sparsity, edge-preserving priors, or non-local similarities. Blind methods are more challenging and prone to artifacts if the blur model is inaccurate or the noise is high.

Recent advances include deep learning approaches that learn mappings from blurred to sharp images or jointly estimate blur. While they can achieve impressive results on representative data, they may generalize poorly to unseen blur types. Evaluation often uses metrics such as PSNR and SSIM to quantify restoration quality.