Standard convolution as a model of radiometric degradation is in majority of cases inaccurate as the blur varies in space and we are thus required to work with a computationally demanding space-variant model. Space-variant degradation can be approximately decomposed to a combination of standard convolutions and point-wise multiplications. The space-variant degradation operator contains different filters in columns and rows as illustrated in the above figure.

Decomposition can be carried out row-wise or column-wise. We propose a computationally efficient space-variant deconvolution algorithm that belongs to a category of alternating direction methods of multipliers, which consists of four update steps with closed-form solutions.  Depending on the used decomposition, two variations of the algorithm exist with distinct properties. You can download the code here.

Examples on real data: 

Video frame from a traffic camera (Courtesy of Lukáš Maršík from CAMEA)	cropped region used for deconvolution
space-invariant deconvolution	space-variant deconvolution
JPEG image captured with a DSLR camera. A raw image was captured simultaneously and used for reconstruction.	Space-variant optics blur estimated by a method proposed by Radka Tezaur et al. "A system for estimating optics blur psfs from test chart images," EI 2015, vol. 9404.
cropped region of the JPEG image	space-variant reconstruction of the RAW image using blurs above

Publications:

• Šroubek Filip, Kamenicky, J.; Lu, Y.: Decomposition of Space-Variant Blur in Image Deconvolution, Signal Processing Letters, IEEE (2016) doi: 10.1109/LSP.2016.2519764