Superresolution with compound Markov random fields via the variational EM algorithm

Kanemura, Atsunori; Maeda, Shingo; Ishii, Shin

doi:10.1016/j.neunet.2008.12.005

Cited by 53 publications

(47 citation statements)

References 25 publications

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“…We have conducted extensive experiments with small images which permit the explicit inversion of (38) to verify the validity of this approximation, and we found out empirically that this approximation results in very close estimates and has a minor effect in the estimation process. Similar approximations have also been utilized in other Bayesian recovery methods [15], [16], [30].…”

Section: Estimation Of the Hyperparameter Distributionsmentioning

confidence: 97%

“…The independent Gaussian model in (3) is used in most of the existing super resolution methods [8], [9], [15]- [17], [28]. Some methods utilized -norm based observation models which take both acquisition and registration noise into account [5], [6].…”

Section: A Observation Modelmentioning

confidence: 99%

“…This approximating distribution is found by minimizing the Kullback-Leibler (KL) distance between and the posterior , given by (15) Generally, the only assumption made in variational Bayesian analysis is that the distribution can be factorized [35]- [37]. In this work, we use the following factorization (16) Unfortunately, we can not directly calculate the KL distance because of the TV image prior.…”

Section: Hyperpriors On the Hyperparametersmentioning

confidence: 99%

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Variational Bayesian Super Resolution

Babacan

Molina

Katsaggelos

2011

IEEE Trans. on Image Process.

233

193

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Abstract-In this paper, we address the super resolution (SR) problem from a set of degraded low resolution (LR) images to obtain a high resolution (HR) image. Accurate estimation of the sub-pixel motion between the LR images significantly affects the performance of the reconstructed HR image. In this paper, we propose novel super resolution methods where the HR image and the motion parameters are estimated simultaneously. Utilizing a Bayesian formulation, we model the unknown HR image, the acquisition process, the motion parameters and the unknown model parameters in a stochastic sense. Employing a variational Bayesian analysis, we develop two novel algorithms which jointly estimate the distributions of all unknowns. The proposed framework has the following advantages: 1) Through the incorporation of uncertainty of the estimates, the algorithms prevent the propagation of errors between the estimates of the various unknowns; 2) the algorithms are robust to errors in the estimation of the motion parameters; and 3) using a fully Bayesian formulation, the developed algorithms simultaneously estimate all algorithmic parameters along with the HR image and motion parameters, and therefore they are fully-automated and do not require parameter tuning. We also show that the proposed motion estimation method is a stochastic generalization of the classical Lucas-Kanade registration algorithm. Experimental results demonstrate that the proposed approaches are very effective and compare favorably to state-of-the-art SR algorithms.

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Section: Estimation Of the Hyperparameter Distributionsmentioning

confidence: 97%

Section: A Observation Modelmentioning

confidence: 99%

Section: Hyperpriors On the Hyperparametersmentioning

confidence: 99%

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Variational Bayesian Super Resolution

Babacan

Molina

Katsaggelos

2011

IEEE Trans. on Image Process.

233

193

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“…The limited accuracy inherent to HR registration from LR images is a shortcoming of this first approach. The second approach is to alternate between HR image registration and HR image estimation (see [5,[16][17][18][19][20][21][22][23][24][25]). …”

Section: Introductionmentioning

confidence: 99%

Bayesian combination of sparse and non-sparse priors in image super resolution

Villena¹,

Vega²,

Babacan³

et al. 2013

Digital Signal Processing

105

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In this paper the application of image prior combinations to the Bayesian Super Resolution (SR) image registration and reconstruction problem is studied. Two sparse image priors, a Total Variation (TV) prior and a prior based on the 1 norm of horizontal and vertical first order differences (f.o.d.), are combined with a non-sparse Simultaneous Auto Regressive (SAR) prior. Since, for a given observation model, each prior produces a different posterior distribution of the underlying High Resolution (HR) image, the use of variational approximation will produce as many posterior approximations as priors we want to combine. A unique approximation is obtained here by finding the distribution on the HR image given the observations that minimizes a linear convex combination of Kullback-Leibler (KL) divergences. We find this distribution in closed form. The estimated HR images are compared with the ones obtained by other SR reconstruction methods.

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“…The weakness of the Tikhonov prior is that it tends to destroy edges-an effect that degrades images. Therefore, the prior has captured the interest of many researchers to develop models that simultaneously suppress noise and preserve critical image features: Huber Markov random field (Huber-RMF) [27,28], edge-adaptive RMF [29,30], sparse directional [31,32], and total variation (TV) [33][34][35].…”

mentioning

confidence: 99%

A multi-frame super-resolution method based on the variable-exponent nonlinear diffusion regularizer

Maiseli

Elisha

Gao

2015

J Image Video Proc.

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In this work, the authors have proposed a multi-frame super-resolution method that is based on the diffusion-driven regularization functional. The new regularizer contains a variable exponent that adaptively regulates its diffusion mechanism depending upon the local image features. In smooth regions, the method favors linear isotropic diffusion, which removes noise more effectively and avoids unwanted artifacts (blocking and staircasing). Near edges and contours, diffusion adaptively and significantly diminishes, and since noise is hardly visible in these regions, an image becomes sharper and resolute-with noise being largely reduced in flat regions. Empirical results from both simulated and real experiments demonstrate that our method outperforms some of the state-of-the-art classical methods based on the total variation framework.

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Superresolution with compound Markov random fields via the variational EM algorithm

Cited by 53 publications

References 25 publications

Variational Bayesian Super Resolution

Variational Bayesian Super Resolution

Bayesian combination of sparse and non-sparse priors in image super resolution

A multi-frame super-resolution method based on the variable-exponent nonlinear diffusion regularizer

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