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.
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.