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.

The restored image

is predicted from a corrupted observation

after training on a set of sample images

A shrinkage (mapping) function

π

π

γ 2

μ

is directly modeled as a linear combination of radial basis function kernels, where

is the shared precision parameter,

μ

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

λ

π

λ

denotes the discrete Fourier transform and

with point spread function filter,

is an optical transfer function defined as the discrete Fourier transform of

is the complex conjugate of

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

π

The learning objective function is defined as

is a differentiable loss function which is greedily minimized using training data

Preliminary tests by the author suggest that RTF5[1] obtains slightly better denoising performance than

BM3D denoising speed falls between that of

, RTF being an order of magnitude slower.