Uncertainty

Below are references / links to PDFs related to the talk on uncertainty principles I gave 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.

Gabor's famous 1946 paper introducing the uncertainty principle 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 again but with more group theory:

AN ENTROPY-BASED UNCERTAINTY PRINCIPLE FOR A LOCALLY COMPACT ABELIAN GROUP; Özaydin, 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