Uncertainty: Difference between revisions
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The following is a list of the papers / links to the PDFs which I referenced in my talk on Friday. | |||
-Jascha, 9/11/06 | |||
If you want a reference for the uncertainty principle in physics I highly recommend Griffiths "Introduction to Quantum Mechanics." It is sitting on my desk for the borrowing. | If you want a reference for the uncertainty principle in physics I highly recommend Griffiths "Introduction to Quantum Mechanics." It is sitting on my desk for the borrowing. | ||
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Below are PDFs of the various papers I referenced during my talk: | Below are PDFs of the various papers I referenced during my talk: | ||
Theory of Communication; Gabor | Uncertainty principle is introduced to signal processing: | ||
Theory of Communication; Gabor | |||
[http://redwood.berkeley.edu/w/images/b/b6/Gabor.pdf link] | |||
Discrete, unordered, uncertainty principle (and its relation to signal recovery . . . think roots of compressed sensing): | |||
UNCERTAINTY PRINCIPLES AND SIGNAL RECOVERY; | UNCERTAINTY PRINCIPLES AND SIGNAL RECOVERY; | ||
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[http://redwood.berkeley.edu/w/images/5/53/SMM000906.pdf link] | [http://redwood.berkeley.edu/w/images/5/53/SMM000906.pdf link] | ||
Entropy-Based Uncertainty Measures | |||
Uniqueness of sparse representations (and applicability to identifying cases where the L0 norm solution is also the L1 norm solution): | |||
Uncertainty Principles and Ideal Atomic Decomposition; | |||
Donoho, Huo | |||
[http://redwood.berkeley.edu/w/images/6/6e/00959265.pdf link] | |||
and a followup paper which tightens the inequality: | |||
A Generalized Uncertainty Principle and Sparse Representation in Pairs of Bases; | |||
Elad, Bruckstein | |||
[http://redwood.berkeley.edu/w/images/e/e6/10_Sparseness_IT.pdf link] | |||
An entropy based uncertainty principle | |||
Entropy-Based Uncertainty Measures for L2(Rn), | |||
l2(Z), and l2(Z/NZ) With a Hirschman Optimal | |||
Transform for l2(Z/NZ); DeBrunner, Havlicek, Przebinda, Özaydın | |||
[http://redwood.berkeley.edu/w/images/9/9f/01468465.pdf link] | |||
and with more group theory | |||
AN ENTROPY-BASED UNCERTAINTY PRINCIPLE | |||
FOR A LOCALLY COMPACT ABELIAN GROUP; | |||
ÄOzaydin, Przebinda | |||
[http://redwood.berkeley.edu/w/images/9/95/2002-26.pdf link] | |||
Application of uncertainty principle in 2-dimensions: | |||
Uncertainty relation for resolution in space, spatial | |||
frequency, and orientation optimized by two-dimensional | |||
visual cortical filters; | |||
Daugman | |||
[http://redwood.berkeley.edu/w/images/b/b7/89E36D3B-BDB9-137E-CC149B33AE9BE4E9_1160.pdf link] | |||
A group theoretic paper I didn't understand, but I suspect it and its predecessor are highly applicable ("In this work we study the possibility of designing a window shape that is optimal with respect to all the possible parameters of the two-dimensional affine | |||
transform."): | |||
Scale-Space Generation via Uncertainty | |||
Principles; | |||
Sagiv, Sochen, Zeevi | |||
[http://redwood.berkeley.edu/w/images/c/c5/Fulltext.pdf link] | |||
The powerpoint file for the talk itself is [http://redwood.berkeley.edu/w/images/e/e7/Uncertainty.ppt here] | The powerpoint file for the talk itself is [http://redwood.berkeley.edu/w/images/e/e7/Uncertainty.ppt here] |
Revision as of 08:00, 12 September 2006
The following is a list of the papers / links to the PDFs which I referenced in my talk on Friday.
-Jascha, 9/11/06
If you want a reference for the uncertainty principle in physics I highly recommend Griffiths "Introduction to Quantum Mechanics." It is sitting on my desk for the borrowing.
Below are PDFs of the various papers I referenced during my talk:
Uncertainty principle is introduced to signal processing:
Theory of Communication; Gabor link
Discrete, unordered, uncertainty principle (and its relation to signal recovery . . . think roots of compressed sensing):
UNCERTAINTY PRINCIPLES AND SIGNAL RECOVERY; Donoho, Stark link
Uniqueness of sparse representations (and applicability to identifying cases where the L0 norm solution is also the L1 norm solution):
Uncertainty Principles and Ideal Atomic Decomposition; Donoho, Huo link
and a followup paper which tightens the inequality:
A Generalized Uncertainty Principle and Sparse Representation in Pairs of Bases; Elad, Bruckstein link
An entropy based uncertainty principle
Entropy-Based Uncertainty Measures for L2(Rn), l2(Z), and l2(Z/NZ) With a Hirschman Optimal Transform for l2(Z/NZ); DeBrunner, Havlicek, Przebinda, Özaydın link
and with more group theory
AN ENTROPY-BASED UNCERTAINTY PRINCIPLE FOR A LOCALLY COMPACT ABELIAN GROUP; ÄOzaydin, Przebinda link
Application of uncertainty principle in 2-dimensions:
Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters; Daugman link
A group theoretic paper I didn't understand, but I suspect it and its predecessor are highly applicable ("In this work we study the possibility of designing a window shape that is optimal with respect to all the possible parameters of the two-dimensional affine
transform."):
Scale-Space Generation via Uncertainty Principles; Sagiv, Sochen, Zeevi link
The powerpoint file for the talk itself is here