Adaptive Regularization Parameters and Norm Selection for Sparse Gradient Based Image Restoration

Anisotropic partial differential equation (PDE)-based image restoration schemes employ a local edge indicator function typically based on gradients. In this paper, an alternative pixel-wise adaptive diffusion scheme is proposed. It uses a spatial function giving better edge information to the diffusion process. It avoids the over-locality problem of gradient-based schemes and preserves discontinuities coherently. The scheme satisfies scale space axioms for a multiscale diffusion scheme; and it uses a well-posed regularized total variation (TV) scheme along with Perona-Malik type functions. Median-based weight function is used to handle the impulse noise case. Numerical results show promise of such an adaptive approach on real noisy images.

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Image restoration using L1-norm regularization and a gradient-based neural network with discontinuous activation functions

2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence) ◽

10.1109/ijcnn.2008.4634149 ◽

2008 ◽

Author(s):

Leonardo V. Ferreira ◽

Eugenius Kaszkurewicz ◽

Amit Bhaya

Keyword(s):

Neural Network ◽

Image Restoration ◽

Activation Functions ◽

Discontinuous Activation ◽

Gradient Based ◽

Discontinuous Activation Functions

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Simultaneous multichannel image restoration and estimation of the regularization parameters

IEEE Transactions on Image Processing ◽

10.1109/83.568936 ◽

1997 ◽

Vol 6 (5) ◽

pp. 774-778 ◽

Cited By ~ 27

Author(s):

Moon Gi Kang ◽

A.K. Katsaggelos

Keyword(s):

Image Restoration ◽

Regularization Parameters

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An Adaptive Variational PDE Based Image Restoration Model Using Hopfield Neural Network

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.48-49.174 ◽

2011 ◽

Vol 48-49 ◽

pp. 174-178

Author(s):

Wei Sun ◽

Sheng Nan Liu

Keyword(s):

Neural Network ◽

Image Restoration ◽

Regularization Parameter ◽

Signal To Noise Ratio ◽

Hopfield Neural Network ◽

Adaptive Regularization ◽

Proposed Model ◽

Degraded Image ◽

Restoration Problem ◽

Restoration Model

An adaptive variational partial differential equation (PDE) based aproach for restoration of gray level images degraded by a known shift-invariant blur function and additive noise is presented. The restoration problem of a degraded image is solved by minimizing this model, and this minimizing problem is realized by using Hopfield neural network. In the proposed image restoration model, an adaptive regularization parameter is developed instead of the constant regularization parameter used in previous PDE model. The value of the adaptive regularization parameter changes according to different regions of the image to remove noises and preserve edge better. Several computer simulation results show that the image restoration results of the proposed model both look better and have better SNR (Signal to Noise Ratio) than the previous variational PDE based model.

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Gradient-based bandwidth selection for estimating average derivatives

Economics Letters ◽

10.1016/j.econlet.2015.12.005 ◽

2016 ◽

Vol 140 ◽

pp. 19-22

Author(s):

Cong Li ◽

Yanfei Wang

Keyword(s):

Bandwidth Selection ◽

Gradient Based ◽

Selection For

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Pruning from Adaptive Regularization

Neural Computation ◽

10.1162/neco.1994.6.6.1223 ◽

1994 ◽

Vol 6 (6) ◽

pp. 1223-1232 ◽

Cited By ~ 37

Author(s):

Lars Kai Hansen ◽

Carl Edward Rasmussen

Keyword(s):

Bayesian Methods ◽

Random Variable ◽

Bayesian Regularization ◽

Generalization Error ◽

Weight Decay ◽

Adaptive Regularization ◽

Regularization Parameters ◽

Noise Limit ◽

The Mean

Inspired by the recent upsurge of interest in Bayesian methods we consider adaptive regularization. A generalization based scheme for adaptation of regularization parameters is introduced and compared to Bayesian regularization. We show that pruning arises naturally within both adaptive regularization schemes. As model example we have chosen the simplest possible: estimating the mean of a random variable with known variance. Marked similarities are found between the two methods in that they both involve a “noise limit,” below which they regularize with infinite weight decay, i.e., they prune. However, pruning is not always beneficial. We show explicitly that both methods in some cases may increase the generalization error. This corresponds to situations where the underlying assumptions of the regularizer are poorly matched to the environment.

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