Blind deconvolution


Simultaneous deconvolution and system identification. If you have more than one kernel type, then you have a problem of dictionary learning.

Deconvolving a signal without knowing what it was convolved with (how blurry it is or what kind of blur it was). Say, reconstructing the pure sound of an instrument, and the sound of the echo in a church, from a recording made in a reverberant church, without knowing which church it was.

If you can find some way of making your problem linear-ish, and your signal is “sparse”, this turns out, amazingly, to be sometimes tractable.

🏗 cite Vetterli’s grad student, name TBC.

Ahmed, Ali, Benjamin Recht, and Justin Romberg. 2012. “Blind Deconvolution Using Convex Programming,” November. http://arxiv.org/abs/1211.5608.

Almeida, M. S. C., and M. A. T. Figueiredo. 2013. “Blind Image Deblurring with Unknown Boundaries Using the Alternating Direction Method of Multipliers.” In 2013 IEEE International Conference on Image Processing, 586–90. https://doi.org/10.1109/ICIP.2013.6738121.

Babacan, S. Derin, Rafael Molina, Minh N. Do, and Aggelos K. Katsaggelos. 2012. “Bayesian Blind Deconvolution with General Sparse Image Priors.” In Computer Vision – ECCV 2012, edited by Andrew Fitzgibbon, Svetlana Lazebnik, Pietro Perona, Yoichi Sato, and Cordelia Schmid, 341–55. Lecture Notes in Computer Science 7577. Springer Berlin Heidelberg. http://www.dbabacan.info/papers/Babacan_ECCV_2012.pdf.

Bahmani, Sohail, and Justin Romberg. 2014. “Lifting for Blind Deconvolution in Random Mask Imaging: Identifiability and Convex Relaxation,” December. http://arxiv.org/abs/1501.00046.

Beck, Amir, and Marc Teboulle. 2009. “A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems.” SIAM Journal on Imaging Sciences 2 (1): 183–202. https://doi.org/10.1137/080716542.

Benichoux, Alexis, Emmanuel Vincent, and Rémi Gribonval. 2013. “A Fundamental Pitfall in Blind Deconvolution with Sparse and Shift-Invariant Priors.” In ICASSP-38th International Conference on Acoustics, Speech, and Signal Processing-2013. https://hal.inria.fr/hal-00800770/.

Delaigle, Aurore, and Peter Hall. 2015. “Methodology for Non-Parametric Deconvolution When the Error Distribution Is Unknown.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), February, n/a–n/a. https://doi.org/10.1111/rssb.12109.

Delaigle, Aurore, and Alexander Meister. 2008. “Density Estimation with Heteroscedastic Error.” Bernoulli 14 (2): 562–79. http://www.maths.bristol.ac.uk/research/stats/reports/2005/0523.pdf.

Fan, Jianqing. 1992. “Deconvolution with Supersmooth Distributions.” Canadian Journal of Statistics 20 (2): 155–69. https://doi.org/10.2307/3315465.

Hall, Peter, and Alexander Meister. 2007. “A Ridge-Parameter Approach to Deconvolution.” The Annals of Statistics 35 (4): 1535–58. https://doi.org/10.1214/009053607000000028.

Liu, Guangcan, Shiyu Chang, and Yi Ma. 2012. “Blind Image Deblurring by Spectral Properties of Convolution Operators,” September. http://arxiv.org/abs/1209.2082.

Meister, Alexander. 2008. “Deconvolution from Fourier-Oscillating Error Densities Under Decay and Smoothness Restrictions.” Inverse Problems 24 (1): 015003. https://doi.org/10.1088/0266-5611/24/1/015003.

Schuler, Christian J., Michael Hirsch, Stefan Harmeling, and Bernhard Schölkopf. 2014. “Learning to Deblur,” June. http://arxiv.org/abs/1406.7444.

Smaragdis, Paris. 2004. “Non-Negative Matrix Factor Deconvolution; Extraction of Multiple Sound Sources from Monophonic Inputs.” In Independent Component Analysis and Blind Signal Separation, edited by Carlos G. Puntonet and Alberto Prieto, 494–99. Lecture Notes in Computer Science. Granada, Spain: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-30110-3_63.

Stockham, Jr., T. G., T. M. Cannon, and R. B. Ingebretsen. 1975. “Blind Deconvolution Through Digital Signal Processing.” Proceedings of the IEEE 63 (4): 678–92. https://doi.org/10.1109/PROC.1975.9800.