A Tutorial on MM Algorithms

Hunter, David R.; Lange, Kenneth

doi:10.1198/0003130042836

Cited by 1,481 publications

(1,151 citation statements)

References 24 publications

Supporting

Mentioning

1,149

Contrasting

Unclassified

Order By: Relevance

“…As a more accurate alternative to the primal-dual algorithm, one could use a majorization-minimization (MM) approach (Hunter and Lange 2004), in a similar manner as proposed by Candes et al (Candes et al 2008). In the MM approach one defines an upper bound functional ψ(u|u t ) given the current estimate u t at time t. This upper bound must satisfy the following properties…”

Section: A Majorization-minimization Approachmentioning

confidence: 99%

A Logarithmic Image Prior for Blind Deconvolution

Perrone

Favaro

2015

Int J Comput Vis

View full text Add to dashboard Cite

Blind Deconvolution consists in the estimation of a sharp image and a blur kernel from an observed blurry image. Because the blur model admits several solutions it is necessary to devise an image prior that favors the true blur kernel and sharp image. Many successful image priors enforce the sparsity of the sharp image gradients. Ideally the L 0 "norm" is the best choice for promoting sparsity, but because it is computationally intractable, some methods have used a logarithmic approximation. In this work we also study a logarithmic image prior. We show empirically how well the prior suits the blind deconvolution problem. Our analysis confirms experimentally the hypothesis that a prior should not necessarily model natural image statistics to correctly estimate the blur kernel. Furthermore, we show that a simple Maximum a Posteriori (MAP) formulation is enough to achieve state of the art results. To minimize such formulation we devise two iterative minimization algorithms that cope with the non-convexity of the logarithmic prior: one obtained via the primaldual approach and one via majorization-minimization.

show abstract

Section: A Majorization-minimization Approachmentioning

confidence: 99%

A Logarithmic Image Prior for Blind Deconvolution

Perrone

Favaro

2015

Int J Comput Vis

View full text Add to dashboard Cite

show abstract

“…The majorization-minimization (MM) algorithm (also known as auxiliary functionbased optimization) (Leeuw and Heiser, 1977;Hunter and Lange, 2004) is a generalization of the EM algorithm. When constructing an MM algorithm for a given minimization problem, the main issue is to design an auxiliary function called a majorizer that is guaranteed to never go below the cost function.…”

Section: Algorithmmentioning

confidence: 99%

Gaussian Model Based Multichannel Separation

Ozerov

Kameoka²

2018

Audio Source Separation and Speech Enhancement

View full text Add to dashboard Cite

“…techniques [34], in which maximizing the negative free energy is substituted by maximizing a tractable lower bound. To get such a lower bound of the negative free energy, a lower bound of the approximate TV prior is firstly constructed by introducing positive auxiliary variables λ = [λ 1 , .…”

Section: Application Of Variational Bayesian Approximation Methodsmentioning

confidence: 99%

“…To tackle this problem, Minorization-Maximization (MM) techniques [34] are employed here to get a conjugate variant, as done by Babacan et al in [22].…”

Section: Hyperpriorsmentioning

confidence: 99%

Efficient Variational Bayesian Approximation Method Based on Subspace Optimization

Zheng

Fraysse

Rodet

2015

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

Variational Bayesian approximations have been widely used in fully Bayesian inference for approximating an intractable posterior distribution by a separable one. Nevertheless, the classical variational Bayesian approximation (VBA) method suffers from slow convergence to the approximate solution when tackling large-dimensional problems. To address this problem, we propose in this paper an improved VBA method. Actually, variational Bayesian issue can be seen as a convex functional optimization problem.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. The aim is to determine an optimal direction at each iteration in order to get a more efficient method. 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. Comparisons with state of the art variational Bayesian methods through a numerical example show the notable improved computation time.

show abstract

A Tutorial on MM Algorithms

Cited by 1,481 publications

References 24 publications

A Logarithmic Image Prior for Blind Deconvolution

A Logarithmic Image Prior for Blind Deconvolution

Gaussian Model Based Multichannel Separation

Efficient Variational Bayesian Approximation Method Based on Subspace Optimization

Contact Info

Product

Resources

About