Results 1  10
of
3,291
Uncertainty principles and ideal atomic decomposition
 IEEE Transactions on Information Theory
, 2001
"... Suppose a discretetime signal S(t), 0 t<N, is a superposition of atoms taken from a combined time/frequency dictionary made of spike sequences 1ft = g and sinusoids expf2 iwt=N) = p N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every d ..."
Abstract

Cited by 583 (20 self)
 Add to MetaCart
Suppose a discretetime signal S(t), 0 t<N, is a superposition of atoms taken from a combined time/frequency dictionary made of spike sequences 1ft = g and sinusoids expf2 iwt=N) = p N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every discretetime signal can be represented as a superposition of spikes alone, or as a superposition of sinusoids alone, there is no unique way of writing S as a sum of spikes and sinusoids in general. We prove that if S is representable as a highly sparse superposition of atoms from this time/frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the `1 norm of the coe cients among all decompositions. Here \highly sparse " means that Nt + Nw < p N=2 where Nt is the number of time atoms, Nw is the number of frequency atoms, and N is the length of the discretetime signal.
Uncertainty principles and . . .
, 2010
"... In this paper I am careful to distinguish between the space of signals and the space of their Fourier transforms. Folland and Sitaram [4] give a survey of uncertainty principles in analysis. First we will go through the talk by Emmanuel Candès and Terence Tao, “The uniform uncertainty principle and ..."
Abstract
 Add to MetaCart
In this paper I am careful to distinguish between the space of signals and the space of their Fourier transforms. Folland and Sitaram [4] give a survey of uncertainty principles in analysis. First we will go through the talk by Emmanuel Candès and Terence Tao, “The uniform uncertainty principle
‘uncertainty principle’
"... ‘What could and should the relationship be to our subject matter in science studies – especially when we increasingly work on the same sorts of topic as the people we study?’ This is the question that Trevor Pinch (2011: p. 1) places at the center of his review of Meeting the Universe Halfway (Barad ..."
Abstract
 Add to MetaCart
understandings are significant and telling of important and longstanding differences between feminist and other approaches in science studies. Pinch delivers his answer to the question of the relationship between science and science studies in the form of an ‘uncertainty principle’. As someone who studied quantum physics
Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information
, 2006
"... This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discretetime signal and a randomly chosen set of frequencies. Is it possible to reconstruct from the partial knowledge of its Fourier coefficients on the set? A typical result of this pa ..."
Abstract

Cited by 2632 (50 self)
 Add to MetaCart
This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discretetime signal and a randomly chosen set of frequencies. Is it possible to reconstruct from the partial knowledge of its Fourier coefficients on the set? A typical result of this paper is as follows. Suppose that is a superposition of spikes @ Aa @ A @ A obeying @�� � A I for some constant H. We do not know the locations of the spikes nor their amplitudes. Then with probability at least I @ A, can be reconstructed exactly as the solution to the I minimization problem I aH @ A s.t. ” @ Aa ” @ A for all
AN UNCERTAINTY PRINCIPLE FOR A MODIFIED
"... ABSTRACT. An uncertainty principle is obtained for a modified Yνtransform of order ν. The principle is similar to the classical HeisenbergWeyl uncertainty principle for the Fourier transform on R. ..."
Abstract
 Add to MetaCart
ABSTRACT. An uncertainty principle is obtained for a modified Yνtransform of order ν. The principle is similar to the classical HeisenbergWeyl uncertainty principle for the Fourier transform on R.
On the Uncertainty Principle in Harmonic Analysis
, 2000
"... The Uncertainty Principle (UP) as understood in this lecture is the following informal assertion: a nonzero “object” (a function, distribution, hyperfunction) and its Fourier image cannot be too small simultaneously. “The smallness” is understood in a very broad sense meaning fast decay (at infini ..."
Abstract

Cited by 97 (1 self)
 Add to MetaCart
The Uncertainty Principle (UP) as understood in this lecture is the following informal assertion: a nonzero “object” (a function, distribution, hyperfunction) and its Fourier image cannot be too small simultaneously. “The smallness” is understood in a very broad sense meaning fast decay (at
Results 1  10
of
3,291