Deblurring

Deblurring is the process of removing blurring artifacts from images. Deblurring recovers a sharp image S from a blurred image B, where S is convolved with K (the blur kernel) to generate B. Mathematically, this can be represented as ${\displaystyle B=S*K}$ (where * represents convolution).

Deblurring an image using Wiener deconvolution

While this process is sometimes known as unblurring, deblurring is the correct technical word.

The blur K is typically modeled as point spread function and is convolved with a hypothetical sharp image S to get B, where both the S (which is to be recovered) and the point spread function K are unknown. This is an example of an inverse problem. In almost all cases, there is insufficient information in the blurred image to uniquely determine a plausible original image, making it an ill-posed problem. In addition the blurred image contains additional noise which complicates the task of determining the original image. This is generally solved by the use of a regularization term to attempt to eliminate implausible solutions. This problem is analogous to echo removal in the signal processing ___domain. Nevertheless, when coherent beam is used for imaging, the point spread function can be modeled mathematically.^[1] By proper deconvolution of the point spread function K and the blurred image B, the blurred image B can be deblurred (unblur) and the sharp image S can be recovered.

See also

• Denoising
• Super-resolution
• Blind deconvolution
• Modulation transfer function

References

1. Ahi, Kiarash (26 May 2016). Anwar, Mehdi F; Crowe, Thomas W; Manzur, Tariq (eds.). "Modeling of terahertz images based on x-ray images: a novel approach for verification of terahertz images and identification of objects with fine details beyond terahertz resolution". Proc. SPIE 9856, Terahertz Physics, Devices, and Systems X: Advanced Applications in Industry and Defense, 985610. Terahertz Physics, Devices, and Systems X: Advanced Applications in Industry and Defense. 9856: 985610. Bibcode:2016SPIE.9856E..10A. doi:10.1117/12.2228685. S2CID 124315172. Retrieved 26 May 2016.