Image deblurring is the technique of removing blurring artifacts from an image that can come from object motion, camera shake or out-of-focus blur.
The blur in an image means a loss of relevant information, making deblurring an ill-posed challenging problem.
The image deblurring problem can be modelled as a convolution of the unknown Sharp image that we want to recover with an unknown point spread function K: Blurred = Sharp * K. When there is no information about the degradation, it is called blind image deconvolution.
Fig. 1 An example of image deblurring. Left, original image of moderate blurring level. Right, image deblurred with the BM3DDEB method .
Recovering sharp image details is complicated, as high frequency in an image can represent both detail and noise. A common technique is to formulate deblurring as image restoration from a blurry and noisy observation.
There are two consequent problems that can appear after deblurring: the image noise can be over-accentuated and ringing artifacts can appear near the edges. In the Fig 1. there is one example of a variational method  that incorporates a regularisation term to reduce ringing artifacts.
 A. Danielyan, V. Katkovnik and K. Egiazarian, "BM3D Frames and Variational Image Deblurring," in IEEE Transactions on Image Processing, vol. 21, no. 4, pp. 1715-1728, April 2012, doi: 10.1109/TIP.2011.2176954.