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Iterative Estimation Algorithms Using Conjugate Function Lower Bound and Minorization-Maximization with Applications in Image Denoising
2008
EURASIP Journal on Advances in Signal Processing
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In this paper, we study iterative algorithms based on the conjugate function lower bound (CFLB) and minorization-maximization (MM) for a class of objective functions. ...
Optimizations based on variational lower bound and minorization-maximization have been widely used in machine learning research, signal processing, and statistics. ...
This is because for a convex and differentiable function its conjugate function lower bound [41] is the same as the minorizing function used in the MM algorithm. ...
doi:10.1155/2008/429128
fatcat:iccnlzbqenbdvh734tqdskjpii
Edge-Preserving Image Denoising via Group Coordinate Descent on the GPU
2015
IEEE Transactions on Image Processing
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Image denoising is a fundamental operation in image processing, and its applications range from the direct (photographic enhancement) to the technical (as a subproblem in image reconstruction algorithms ...
Results from a large 2D image denoising problem and a 3D medical imaging denoising problem demonstrate that the proposed algorithms converge rapidly in terms of both iteration and run-time. ...
A practical alternative to running an arbitrarily large number of inner minorize-majorize iterations is to track the cost function value (n) j ⇣ x j ⇣ (m) j ⌘⌘ and terminate the minorize-maximize algorithm ...
doi:10.1109/tip.2015.2400813
pmid:25675454
pmcid:PMC4339499
fatcat:hoqtrrwabnd4pmflaylwrwvxb4
Bayesian Blind Deconvolution From Differently Exposed Image Pairs
2010
IEEE Transactions on Image Processing
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Using shorter exposure times results in sharper images but with a very high level of noise. ...
In this paper, we address the problem of utilizing two such images in order to obtain an estimate of the original scene and present a novel blind deconvolution algorithm for solving it. ...
Using and in the inequality (27) , it can be seen that the functional is a lower bound of the image prior , that is (29) The quadratic form of the bounding functional renders the analytical derivation ...
doi:10.1109/tip.2010.2052263
pmid:20529746
fatcat:x73bnaqaejdv3m63irtqh45jkq
Bayesian blind deconvolution from differently exposed image pairs
2009
2009 16th IEEE International Conference on Image Processing (ICIP)
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Using shorter exposure times results in sharper images but with a very high level of noise. ...
In this paper, we address the problem of utilizing two such images in order to obtain an estimate of the original scene and present a novel blind deconvolution algorithm for solving it. ...
Using and in the inequality (27) , it can be seen that the functional is a lower bound of the image prior , that is (29) The quadratic form of the bounding functional renders the analytical derivation ...
doi:10.1109/icip.2009.5414104
dblp:conf/icip/BabacanWMK09
fatcat:dcp7ildli5f6th4j7w3jriflwy
An algorithm for improving Non-Local Means operators via low-rank approximation
[article]
2014
arXiv
pre-print
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The method is efficiently implemented based on Chebyshev polynomials and is demonstrated on the application of natural images denoising. ...
For this application, we provide a comprehensive comparison of our method with leading denoising methods. ...
However, most results assume that the approximated function is analytic, and so not applicable in our case. In this section we use the following notation. ...
arXiv:1412.2067v1
fatcat:hndgqssaxvdltc3dlpdvregcji
Deep Learning for Uplink Spectral Efficiency in Cell-Free Massive MIMO Systems
2021
Journal of Advances in Information Technology
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2021 pre-print arXiv:2110.04968v1 fatcat:p7heymxzvjgy3laiejazfopile
Experimental results showed that, compared to the conventional iterative optimization algorithm, the proposed DNN has excessively lower computational complexity with the trade-off of approximately only ...
1% loss in the sum rate and the fairness performance. ...
Meanwhile, the sigmoid and the tanh functions are nonlinear and bounded. ...
doi:10.12720/jait.12.2.119-127
fatcat:yaoi375zh5ebzpw6uutwrn6xru
What makes a good model of natural images?
2007
2007 IEEE Conference on Computer Vision and Pattern Recognition
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In this paper we present (1) tractable lower and upper bounds on the partition function of models based on filter outputs and (2) efficient learning algorithms that do not require any sampling. ...
Many low-level vision algorithms assume a prior probability over images, and there has been great interest in trying to learn this prior from examples. ...
Acknowledgements Funding for this research was provided by NGA NEGI-1582-04-0004, Shell Research, ONR-MURI Grant N00014-06-1-0734, the AMN Foundation and Israeli Science Foundation. ...
doi:10.1109/cvpr.2007.383092
dblp:conf/cvpr/WeissF07
fatcat:v7byx3y4s5afzfcplnlueeua2a
The Maximum Entropy on the Mean Method for Image Deblurring
[article]
2020
arXiv
pre-print
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Using techniques from convex analysis and probability theory, we show that the method is computationally feasible and amenable to very large blurs. ...
Our method is based upon the idea of maximum entropy on the mean wherein we work at the level of the probability density function of the image whose expectation is our estimate of the ground truth. ...
We thank Yakov Vaisbourd for proposing the use of FISTA in Section 6.1. We would also like to thank the anonymous referees for their many comments which significantly improved the paper. ...
arXiv:2002.10434v4
fatcat:i6cvogrbmnb2dfpp6k2xup33s4
Efficient Variational Bayesian Approximation Method Based on Subspace Optimization
2015
IEEE Transactions on Image Processing
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We highlight the efficiency of our new VBA method and its application to image processing by considering an ill-posed linear inverse problem using a total variation prior. ...
The proposed method is based on the adaptation of subspace optimization methods in Hilbert spaces to the function space involved, in order to solve this optimization problem in an iterative way. ...
This difficulty has been solved by adopting Minorization-Maximization (MM) techniques [34] , in which maximizing the negative free energy is substituted by maximizing a tractable lower bound. ...
doi:10.1109/tip.2014.2383321
pmid:25532179
fatcat:e63q5zewnrfi3f5ugy7lfwahrq
Denoising Two-Photon Calcium Imaging Data
2011
PLoS ONE
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The application of our approach to in vivo imaging data recorded in the ferret primary visual cortex demonstrates that our method yields substantially denoised signal estimates. ...
We provide an efficient cyclic descent algorithm to compute approximate maximum likelihood parameter estimates by combing a weighted least-squares procedure with the Burg algorithm. ...
However, the expectation-maximization estimation algorithm used in that method has high computational complexity. ...
doi:10.1371/journal.pone.0020490
pmid:21687727
pmcid:PMC3110192
fatcat:2ldqsq5rvzgpdjeusj5c3uqliu
Modular proximal optimization for multidimensional total-variation regularization
[article]
2017
arXiv
pre-print
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We study TV regularization, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for ℓ_p-norm TV. ...
To underscore our claims and permit easy reproducibility, we provide all the reviewed and our new TV solvers in an easy to use multi-threaded C++, Matlab and Python library. ...
Tibshirani for bringing [45] to our attention, and S. Jegelka for alerting us to the importance of weighted total-variation problems. ...
arXiv:1411.0589v3
fatcat:skttuobi3nbbvdsyomhiedq5wy
The MM Alternative to EM
2010
Statistical Science
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2011 pre-print arXiv:1104.2203v1 fatcat:plewsisz3zcgfjoxspfxwyzaby
In minimization, MM stands for majorize--minimize; in maximization, it stands for minorize--maximize. This two-step process always drives the objective function in the right direction. ...
Our applications to random graph models, discriminant analysis and image restoration showcase this ability. ...
ACKNOWLEDGMENT Research supported in part by USPHS Grants GM53275 and MH59490 to KL. ...
doi:10.1214/08-sts264
fatcat:4xy5iujwxzdyxmrqbx2qwexzti
Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging
[article]
2023
arXiv
pre-print
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2023 pre-print arXiv:2311.08972v1 fatcat:ndf5isczoncv5kz6xr3ihsm2ya
We also survey a number of provably convergent plug-and-play algorithms (based on gradient-step deep denoisers), which are among the most important and widely applied unsupervised approaches for imaging ...
In this chapter, we review theoretically principled unsupervised learning schemes for solving imaging inverse problems, with a particular focus on methods rooted in optimal transport and convex analysis ...
In Figure 12 , we present
Plug-and-play methods and data-driven regularization Denoising is the simplest and arguably the most well-studied inverse problem in imaging, with numerous algorithms being ...
arXiv:2311.08972v2
fatcat:6s2dc73eu5e77gqawp5p6xupz4
Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization
2007
Applied and Computational Harmonic Analysis
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A thorough numerical comparison of the denoising application is presented, using the basis pursuit denoising (BPDN) objective function, which leads all of the above algorithms to an iterated shrinkage ...
Despite being frequently deployed in many applications, the RLS problem is often hard to solve using standard iterative methods. In a recent work [M. ...
This conclusion will be verified in the image-denoising experiments to follow.
Image denoising The RLS problem can be used to remove noise from images as well. ...
doi:10.1016/j.acha.2007.02.002
fatcat:ldhnvr7irzd5fl445qaozonzwq
Low-Complexity Blind Parameter Estimation in Wireless Systems with Noisy Sparse Signals
[article]
2023
arXiv
pre-print
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We also provide three application examples that deviate from the BCG prior in millimeter-wave multi-antenna and cell-free wireless systems for which we develop nonparametric denoising algorithms that improve ...
channel-estimation accuracy with a performance comparable to denoisers that assume perfect knowledge of the system parameters. ...
In Section V, we apply our estimators and algorithms to three distinct applications in wireless systems. ...
arXiv:2302.14089v1
fatcat:56yprkcmxrdnxkifklyktahqvy
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