Shrinkage Fields (image restoration)

Shrinkage fields is a random field-based machine learning technique that aims to perform high quality image restoration (denoising and deblurring) using low computational overhead.

Method

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The restored image   is predicted from a corrupted observation   after training on a set of sample images  .

A shrinkage (mapping) function   is directly modeled as a linear combination of radial basis function kernels, where   is the shared precision parameter,   denotes the (equidistant) kernel positions, and M is the number of Gaussian kernels.

Because the shrinkage function is directly modeled, the optimization procedure is reduced to a single quadratic minimization per iteration, denoted as the prediction of a shrinkage field   where   denotes the discrete Fourier transform and   is the 2D convolution   with point spread function filter,   is an optical transfer function defined as the discrete Fourier transform of  , and   is the complex conjugate of  .

  is learned as   for each iteration   with the initial case  , this forms a cascade of Gaussian conditional random fields (or cascade of shrinkage fields (CSF)). Loss-minimization is used to learn the model parameters  .

The learning objective function is defined as  , where   is a differentiable loss function which is greedily minimized using training data   and  .

Performance

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Preliminary tests by the author suggest that RTF5[1] obtains slightly better denoising performance than  , followed by  ,  ,  , and BM3D.

BM3D denoising speed falls between that of   and  , RTF being an order of magnitude slower.

Advantages

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  • Results are comparable to those obtained by BM3D (reference in state of the art denoising since its inception in 2007)
  • Minimal runtime compared to other high-performance methods (potentially applicable within embedded devices)
  • Parallelizable (e.g.: possible GPU implementation)
  • Predictability:   runtime where   is the number of pixels
  • Fast training even with CPU

Implementations

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See also

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References

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  1. ^ Jancsary, Jeremy; Nowozin, Sebastian; Sharp, Toby; Rother, Carsten (10 April 2012). Regression Tree Fields – An Efficient, Non-parametric Approach to Image Labeling Problems. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). Providence, RI, USA: IEEE Computer Society. doi:10.1109/CVPR.2012.6247950.