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.
The restored image formula_1 is predicted from a corrupted observation formula_2 after training on a set of sample images formula_3.
A shrinkage (mapping) function formula_4 is directly modeled as a linear combination of radial basis function kernels, where formula_5 is the shared precision parameter, formula_6 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 formula_7 where formula_8 denotes the discrete Fourier transform and formula_9 is the 2D convolution formula_10 with point spread function filter, formula_11 is an optical transfer function defined as the discrete Fourier transform of formula_12, and formula_13 is the complex conjugate of formula_11.
formula_15 is learned as formula_16 for each iteration formula_17 with the initial case formula_18, this forms a cascade of Gaussian conditional random fields (or cascade of shrinkage fields (CSF)). Loss-minimization is used to learn the model parameters formula_19.
The learning objective function is defined as formula_20, where formula_21 is a differentiable loss function which is greedily minimized using training data formula_22 and formula_23.
Performance.
Preliminary tests by the author suggest that RTF5 obtains slightly better denoising performance than formula_24, followed by formula_25, formula_26, formula_27, and BM3D.
BM3D denoising speed falls between that of formula_28 and formula_29, RTF being an order of magnitude slower.