2,273 research outputs found
Approximation algorithms for wavelet transform coding of data streams
This paper addresses the problem of finding a B-term wavelet representation
of a given discrete function whose distance from f is
minimized. The problem is well understood when we seek to minimize the
Euclidean distance between f and its representation. The first known algorithms
for finding provably approximate representations minimizing general
distances (including ) under a wide variety of compactly supported
wavelet bases are presented in this paper. For the Haar basis, a polynomial
time approximation scheme is demonstrated. These algorithms are applicable in
the one-pass sublinear-space data stream model of computation. They generalize
naturally to multiple dimensions and weighted norms. A universal representation
that provides a provable approximation guarantee under all p-norms
simultaneously; and the first approximation algorithms for bit-budget versions
of the problem, known as adaptive quantization, are also presented. Further, it
is shown that the algorithms presented here can be used to select a basis from
a tree-structured dictionary of bases and find a B-term representation of the
given function that provably approximates its best dictionary-basis
representation.Comment: Added a universal representation that provides a provable
approximation guarantee under all p-norms simultaneousl
Scattering amplitudes from finite-volume spectral functions
A novel proposal is outlined to determine scattering amplitudes from
finite-volume spectral functions. The method requires extracting smeared
spectral functions from finite-volume Euclidean correlation functions, with a
particular complex smearing kernel of width which implements the
standard -prescription. In the limit these smeared
spectral functions are therefore equivalent to Minkowskian correlators with a
specific time ordering to which a modified LSZ reduction formalism can be
applied. The approach is presented for general scattering amplitudes
(above arbitrary inelastic thresholds) for a single-species real scalar field,
although generalization to arbitrary spins and multiple coupled channels is
likely straightforward. Processes mediated by the single insertion of an
external current are also considered. Numerical determination of the
finite-volume smeared spectral function is discussed briefly and the interplay
between the finite volume, Euclidean signature, and time-ordered
-prescription is illustrated perturbatively in a toy example.Comment: 22 pages, 2 figures, CERN-TH-2019-035, CP3-Origins-2019-006 DNRF9
Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation
We propose new compressive parameter estimation algorithms that make use of
polar interpolation to improve the estimator precision. Our work extends
previous approaches involving polar interpolation for compressive parameter
estimation in two aspects: (i) we extend the formulation from real non-negative
amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch
between the manifold described by the parameters and its polar approximation.
To quantify the improvements afforded by the proposed extensions, we evaluate
six algorithms for estimation of parameters in sparse translation-invariant
signals, exemplified with the time delay estimation problem. The evaluation is
based on three performance metrics: estimator precision, sampling rate and
computational complexity. We use compressive sensing with all the algorithms to
lower the necessary sampling rate and show that it is still possible to attain
good estimation precision and keep the computational complexity low. Our
numerical experiments show that the proposed algorithms outperform existing
approaches that either leverage polynomial interpolation or are based on a
conversion to a frequency-estimation problem followed by a super-resolution
algorithm. The algorithms studied here provide various tradeoffs between
computational complexity, estimation precision, and necessary sampling rate.
The work shows that compressive sensing for the class of sparse
translation-invariant signals allows for a decrease in sampling rate and that
the use of polar interpolation increases the estimation precision.Comment: 13 pages, 5 figures, to appear in IEEE Transactions on Signal
Processing; minor edits and correction
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