Shrinkage Fields (image restoration)

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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.


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 .


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.


  • 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


See also[edit]


  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.