Stochastic Deconvolution - Supplement

James Gregson, Felix Heide, Matthias B. Hullin, Mushfiqur Rouf and Wolfgang Heidrich
IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2013 (to appear)

Abstract

We present a novel stochastic algorithm for non-blind deconvolution based on point samples obtained from random walks. Unlike previous methods which must be tailored to specific regularization strategies, the new Stochastic Deconvolution method allows arbitrary priors to be introduced and tested with little effort. Stochastic Deconvolution is straightforward to implement, produces state-of-the-art results and directly leads to a natural boundary condition for image boundaries and saturated pixels. These claims are demonstrated on a number of captured and synthetic examples.

Per-Pixel PSFs:
Input blurry image and sampling of PSFs:
Please move your mouse over image to compare results

Deconvolution Results

Defocus Blur:
Input blurry image:

Deconvolution Results
Left: method of Levin et al., Right: Stochastic Deconvolution with Levin prior
Please move your mouse over image to compare results

Motion Blur, from Xu and Jia:
Input blurry image:

Deconvolution Results
Left: Xu and Jia., Right: Stochastic Deconvolution with Levin prior
Please move your mouse over image to compare results

Please note that for this example, we used a JPEG of the blurred image from the Xu and Jia 2010 project website as inputs to our method. Consequently some detail is irrevocably lost to compression and a slightly high regularizer weight is needed.

Motion Blur, from Raskar et al.:
Input blurry image:

Note that this image is scaled according to the process in Raskar et al.

Deconvolution Results
Left: Raskar et al., Right: Stochastic Deconvolution with Gamma-corrected prior
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Motion Blur, from Fergus et al.:
Input blurry image:

Deconvolution Results
Left: Fergus et al., Right: Stochastic Deconvolution with Gamma-corrected prior
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Convergence:
Here we present supplementary convergence results comparing Stochastic Deconvolution to the Primal-Dual method of Pock and Chambolle. Both codes used an anisotropic TV regularizer with weight of 0.001 compared to a unit-weight data-term. Images were generated by convolution with synthetic PSFs and corrupted by 1% sigma Gaussian noise. 500 iterations of the primal dual method and 300 iterations of Stochastic Deconvolution method were used. Final objective function values are summarised in the following table.

Image	Pock & Chambolle	Stochastic Deconvolution
bridge	31.256	31.229
dandelion	31.922	31.764
fruit	30.498	30.404
geese	33.226	33.342
meat	32.673	32.649

Note that in all cases, Stochastic Deconvolution achieves a final objective function within 0.5% of the Pock and Chambolle result. We attribute the minor discrepancy to the improved boundary handling in Stochastic Deconvolution, which is not implemented in the Pock and Chambolle method and in fact can't be implemented without switching to spatial convolution instead of FFT based convolution.

In all cases, the differences in image quality are negligible between the two methods except near the boundaries where the improved boundary handling reduces ringing, which is particularly evident in the 'bridge' and 'fruit' images.

Bridge input blurry image: