Decomposition of Space-Variant Blur in Image Deconvolution

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 following 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 simultanously and used for reconstruction.  Space-variant optics blur estimated by a method propsoed 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


Duration: 2014-2015
Contact person: Filip Sroubek
Involved people: Jan Kamenicky, Yue M. Lu(Harvard University)