Shrinkage Fields (image restoration) – Wikipedia
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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
.
Performance[edit]
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[edit]
- 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[edit]
See also[edit]
References[edit]
- ^
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.
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