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ADMM in imaging inverse problems: some history and recent advances

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Post-edited
Authors : Figueiredo, Mário (Author of the conference)
CIRM (Publisher )

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Alternating Direction Method of Multipliers imaging inverse problem convex regularization image deconvolution and inpainting blind deconvolution image segmentation plug and play models patch-based denoising Gaussian mixture models hyperspectral fusion questions of the audience
Abstract : The alternating direction method of multipliers (ADMM) is an optimization tool of choice for several imaging inverse problems, namely due its flexibility, modularity, and efficiency. In this talk, I will begin by reviewing our earlier work on using ADMM to deal with classical problems such as deconvolution, inpainting, compressive imaging, and how we have exploited its flexibility to deal with different noise models, including Gaussian, Poissonian, and multiplicative, and with several types of regularizers (TV, frame-based analysis, synthesis, or combinations thereof). I will then describe more recent work on using ADMM for other problems, namely blind deconvolution and image segmentation, as well as very recent work where ADMM is used with plug-in learned denoisers to achieve state-of-the-art results in class-specific image deconvolution. Finally, on the theoretical front, I will describe very recent work on tackling the infamous problem of how to adjust the penalty parameter of ADMM.

MSC Codes :
65J22 - Inverse problems (numerical methods in abstract spaces)
 65K10 - Optimization and variational techniques
 65T60 - Wavelets (numerical methods)
 94A08 - Image processing (compression, reconstruction, etc.)
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 10/11/16
    Conference Date : 03/11/16
    Subseries : Research talks
    arXiv category : Computer Science ; Optimization and Control
    Mathematical Area(s) : Computer Science ; Analysis and its Applications
    Format : MP4 (.mp4) - HD
    Video Time : 00:50:44
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2016-11-03_Figueiredo.mp4
Information on the Event

Event Title : SIGMA (Signal-Image-Geometry-Modelling-Approximation) / SIGMA (Signal-Image-Géométrie-Modélisation-Approximation)
Event Organizers : Beckermann, Bernhard ; Chazal, Frédéric ; Lyche, Tom ; Mazure, Marie-Laurence ; Peyré, Gabriel
Dates : 31/10/16 - 04/11/16
Event Year : 2016
Event URL : http://conferences.cirm-math.fr/1506.html

Citation Data

DOI : 10.24350/CIRM.V.19080303
Cite this video as: Figueiredo, Mário (2016). ADMM in imaging inverse problems: some history and recent advances. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19080303
URI : http://dx.doi.org/10.24350/CIRM.V.19080303

See Also

Bibliography

  • Afonso, M., Bioucas-Dias, J., & Figueiredo, M. (2011). An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Transactions on Image Processing, 20, 681-695 - http://dx.doi.org/10.1109/TIP.2010.2076294

  • Almeida, M., & Figueiredo, M. (2013). Deconvolving images with unknown boundaries using the alternating direction method of multipliers. IEEE Transactions on Image Processing, 22(8), 3084-3096 - http://dx.doi.org/10.1109/TIP.2013.2258354

  • Almeida, M., & Figueiredo, M. (2013). Blind image deblurring with unknown boundaries using the alternating direction method of multipliers. IEEE International Conference on Image Processing, 586-590 - http://dx.doi.org/10.1109/ICIP.2013.6738121

  • Bioucas-Dias, J., & Figueiredo, M. (2010). Multiplicative noise removal using variable splitting and constrained optimization. IEEE Transactions on Image Processing, 19, 1720-1730 - http://dx.doi.org/10.1109/TIP.2010.2045029

  • Figueiredo, M., & Bioucas-Dias, J. (2016). Bayesian image segmentation using hidden fields: supervised, unsupervised, and semi-supervised formulations. Proceedings of EUSIPCO 2016, 24th European Signal Processing Conference - http://www.eurasip.org/Proceedings/Eusipco/Eusipco2016/papers/1570256362.pdf

  • Figueiredo, M., & Bioucas-Dias, J. (2012). Algorithms for imaging inverse problems under sparsity regularization. IEEE International Workshop on Cognitive Information Processing, 1-6 - http://dx.doi.org/10.1109/CIP.2012.6232892

  • Figueiredo, M., & Bioucas-Dias, J. (2010). Restoration of Poissonian images using alternating direction optimization. IEEE Transactions on Image Processing, 19, 3133-3145 - http://dx.doi.org/10.1109/TIP.2010.2053941

  • Teodoro, A., Bioucas-Dias, J., & Figueiredo, M. (2016). Image restoration and reconstruction using variable splitting and class-adapted image priors. IEEE International Conference on Image Processing, 3518-3522 - http://dx.doi.org/10.1109/ICIP.2016.7533014

  • Teodoro, A., Almeida, M., & Figueiredo, M. (2015). Single-frame image denoising and inpainting using Gaussian mixtures. In M. De Marsico, M. Figueiredo, & A. Fred (Eds.). Proceedings of the International Conference on Pattern Recognition Applications and Methods, (pp. 283-288) - http://dx.doi.org/10.5220/0005256502830288


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