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
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Arjas, Roininen, Sillanpää, et al. 2020. “Blind Hierarchical Deconvolution.” In.
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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.
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Meister. 2008. “Deconvolution from Fourier-Oscillating Error Densities Under Decay and Smoothness Restrictions.” Inverse Problems.
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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.