# Blind deconvolution

March 1, 2015 — July 27, 2016

convolution

functional analysis

linear algebra

probability

signal processing

sparser than thou

statistics

Simultaneous deconvolution and system identification. 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.

- Blind Image Deblurring With Unknown Boundaries Using the Alternating Direction Method of Multipliers
- Analysis Operator Learning and Its Application to Image Reconstruction
- Image Deconvolution using Sparse Regularization

## 1 References

Ahmed, Recht, and Romberg. 2012. “Blind Deconvolution Using Convex Programming.”

*arXiv:1211.5608 [Cs, Math]*.
Almeida, and Figueiredo. 2013. “Blind Image Deblurring with Unknown Boundaries Using the Alternating Direction Method of Multipliers.” In

*2013 IEEE International Conference on Image Processing*.
Arjas, Roininen, Sillanpää, et al. 2020. “Blind Hierarchical Deconvolution.” In.

Babacan, Molina, Do, et al. 2012. “Bayesian Blind Deconvolution with General Sparse Image Priors.” In

*Computer Vision – ECCV 2012*. Lecture Notes in Computer Science 7577.
Bahmani, and Romberg. 2014. “Lifting for Blind Deconvolution in Random Mask Imaging: Identifiability and Convex Relaxation.”

*arXiv:1501.00046 [Cs, Math, Stat]*.
Beck, and Teboulle. 2009. “A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems.”

*SIAM Journal on Imaging Sciences*.
Benichoux, Vincent, and 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*.
Delaigle, and Hall. 2015. “Methodology for Non-Parametric Deconvolution When the Error Distribution Is Unknown.”

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*.
Delaigle, and Meister. 2008. “Density Estimation with Heteroscedastic Error.”

*Bernoulli*.
Fan. 1992. “Deconvolution with Supersmooth Distributions.”

*Canadian Journal of Statistics*.
Hall, and Meister. 2007. “A Ridge-Parameter Approach to Deconvolution.”

*The Annals of Statistics*.
Liu, Chang, and Ma. 2012. “Blind Image Deblurring by Spectral Properties of Convolution Operators.”

*arXiv:1209.2082 [Cs]*.
Meister. 2008. “Deconvolution from Fourier-Oscillating Error Densities Under Decay and Smoothness Restrictions.”

*Inverse Problems*.
Schuler, Hirsch, Harmeling, et al. 2014. “Learning to Deblur.”

*arXiv:1406.7444 [Cs]*.
Smaragdis. 2004. “Non-Negative Matrix Factor Deconvolution; Extraction of Multiple Sound Sources from Monophonic Inputs.” In

*Independent Component Analysis and Blind Signal Separation*. Lecture Notes in Computer Science.
Stockham, Cannon, and Ingebretsen. 1975. “Blind Deconvolution Through Digital Signal Processing.”

*Proceedings of the IEEE*.