Results 1  10
of
215,100
Sublinear Fourier Sampling Off the Grid
, 2012
"... We design a sublinear Fourier sampling algorithm for sparse offgrid frequency recovery. ..."
Abstract
 Add to MetaCart
We design a sublinear Fourier sampling algorithm for sparse offgrid frequency recovery.
Quantum fourier sampling simplified
 IN PROCEEDINGS OF THE THIRTYFIRST ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1999
"... We isolate and generalize a technique implicit in many quantum algorithms, including Shor's algorithms for factoring and discrete log. In particular, we show that the distribution sampled after a Fourier transform over Z p can be efficiently approximated by transforming over Z q for any q in a ..."
Abstract

Cited by 19 (2 self)
 Add to MetaCart
We isolate and generalize a technique implicit in many quantum algorithms, including Shor's algorithms for factoring and discrete log. In particular, we show that the distribution sampled after a Fourier transform over Z p can be efficiently approximated by transforming over Z q for any q in a
Sparse Recovery and Fourier Sampling
, 2013
"... the last decade a broad literature has arisen studying sparse recovery, the estimation of sparse vectors from low dimensional linear projections. Sparse recovery has a wide variety of applications such as streaming algorithms, image acquisition, and disease testing. A particularly important subclass ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
subclass of sparse recovery is the sparse Fourier transform, which considers the computation of a discrete Fourier transform when the output is sparse. Applications of the sparse Fourier transform include medical imaging, spectrum sensing, and purely computation tasks involving convolution. This thesis
Simplified Proof of the Fourier Sampling Theorem
 Information Processing Letters 75 (2000
, 2000
"... We give a short and simple proof of Hales and Hallgren's Fourier Sampling Theorem ["Quantum Fourier Sampling Simplified", Proceedings of the ThirtyFirst Annual ACM Symposium on Theory of Computing, ACM Press, May 1999]. The transparency of our prooftechnique allows us to generalize a ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We give a short and simple proof of Hales and Hallgren's Fourier Sampling Theorem ["Quantum Fourier Sampling Simplified", Proceedings of the ThirtyFirst Annual ACM Symposium on Theory of Computing, ACM Press, May 1999]. The transparency of our prooftechnique allows us to generalize
Compressive sampling
, 2006
"... Conventional wisdom and common practice in acquisition and reconstruction of images from frequency data follow the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image, the number of Fourier samples we need to acquire must match the desired res ..."
Abstract

Cited by 1442 (15 self)
 Add to MetaCart
Conventional wisdom and common practice in acquisition and reconstruction of images from frequency data follow the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image, the number of Fourier samples we need to acquire must match the desired
On the Use of Windows for Harmonic Analysis With the Discrete Fourier Transform
 Proc. IEEE
, 1978
"... AhmwThis Pw!r mak = available a concise review of data win compromise consists of applying windows to the sampled daws pad the ^ affect On the Of in the data set, or equivalently, smoothing the spectral samples. '7 of aoise9 m the ptesence of sdroag bar The two operations to which we subject ..."
Abstract

Cited by 668 (0 self)
 Add to MetaCart
AhmwThis Pw!r mak = available a concise review of data win compromise consists of applying windows to the sampled daws pad the ^ affect On the Of in the data set, or equivalently, smoothing the spectral samples. '7 of aoise9 m the ptesence of sdroag bar The two operations to which we
The symmetric group defies strong Fourier sampling
, 2005
"... We resolve the question of whether Fourier sampling can efficiently solve the hidden subgroup problem. Specifically, we show that the hidden subgroup problem over the symmetric group cannot be efficiently solved by strong Fourier sampling, even if one may perform an arbitrary POVM on the coset state ..."
Abstract

Cited by 34 (10 self)
 Add to MetaCart
We resolve the question of whether Fourier sampling can efficiently solve the hidden subgroup problem. Specifically, we show that the hidden subgroup problem over the symmetric group cannot be efficiently solved by strong Fourier sampling, even if one may perform an arbitrary POVM on the coset
Quantum Lower Bound for Recursive Fourier Sampling
 Quantum Information and Computation
, 2003
"... We revisit the oftneglected 'recursive Fourier sampling' (RFS) prob lem, introduced by Bernstein and Vazirani to prove an oracle separation between B]] and BQ] . We show that the known quantum algorithm for RF q is essentially optimal, despite its seemingly wasteful need to un compu ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
We revisit the oftneglected 'recursive Fourier sampling' (RFS) prob lem, introduced by Bernstein and Vazirani to prove an oracle separation between B]] and BQ] . We show that the known quantum algorithm for RF q is essentially optimal, despite its seemingly wasteful need to un
Quantum Fourier Sampling, the Hidden Subgroup Problem, and Beyond
, 2000
"... The Hidden Subgroup Problem (HSP) provides the fundamental framework for most quantum algorithms. Until very recently, all known problems where quantum computation provides a superpolynomial speedup over classical algorithms have been variants of the HSP for particular abelian groups. Examples incl ..."
Abstract
 Add to MetaCart
of dealing with all these variants. The key component of our solution is a new theorem about the robustness of Fourier sampling. The purpose of this theorem is to better understand the structure underlying existing algorithms as well as to provide an algorithmic tool for the construction of future quantum
Results 1  10
of
215,100