17,029 research outputs found
Lorentzian Iterative Hard Thresholding: Robust Compressed Sensing with Prior Information
Commonly employed reconstruction algorithms in compressed sensing (CS) use
the norm as the metric for the residual error. However, it is well-known
that least squares (LS) based estimators are highly sensitive to outliers
present in the measurement vector leading to a poor performance when the noise
no longer follows the Gaussian assumption but, instead, is better characterized
by heavier-than-Gaussian tailed distributions. In this paper, we propose a
robust iterative hard Thresholding (IHT) algorithm for reconstructing sparse
signals in the presence of impulsive noise. To address this problem, we use a
Lorentzian cost function instead of the cost function employed by the
traditional IHT algorithm. We also modify the algorithm to incorporate prior
signal information in the recovery process. Specifically, we study the case of
CS with partially known support. The proposed algorithm is a fast method with
computational load comparable to the LS based IHT, whilst having the advantage
of robustness against heavy-tailed impulsive noise. Sufficient conditions for
stability are studied and a reconstruction error bound is derived. We also
derive sufficient conditions for stable sparse signal recovery with partially
known support. Theoretical analysis shows that including prior support
information relaxes the conditions for successful reconstruction. Simulation
results demonstrate that the Lorentzian-based IHT algorithm significantly
outperform commonly employed sparse reconstruction techniques in impulsive
environments, while providing comparable performance in less demanding,
light-tailed environments. Numerical results also demonstrate that the
partially known support inclusion improves the performance of the proposed
algorithm, thereby requiring fewer samples to yield an approximate
reconstruction.Comment: 28 pages, 9 figures, accepted in IEEE Transactions on Signal
Processin
Matching Long and Short Distances in Large-Nc QCD
It is shown, with the example of the experimentally known Adler function,
that there is no matching in the intermediate region between the two asymptotic
regimes described by perturbative QCD (for the very short-distances) and by
chiral perturbation theory (for the very long-distances). We then propose to
consider an approximation of large-Nc QCD which consists in restricting the
hadronic spectrum in the channels with J^P quantum numbers 0^-, 1^-, 0^+ and
1^+ to the lightest state and treating the rest of the narrow states as a
perturbative QCD continuum; the onset of this continuum being fixed by
consistency constraints from the operator product expansion. We show how to
construct the low-energy effective Lagrangian which describes this
approximation. The number of free parameters in the resulting effective
Lagrangian can be reduced, in the chiral limit where the light quark masses are
set to zero, to just one mass scale and one dimensionless constant to all
orders in chiral perturbation theory. A comparison of the corresponding
predictions, to O(p^4) in the chiral expansion, with the phenomenologically
known couplings is also made.Comment: 35 pages, 9 figures, LaTeX. Added a couple of reference
On sparsity averaging
Recent developments in Carrillo et al. (2012) and Carrillo et al. (2013)
introduced a novel regularization method for compressive imaging in the context
of compressed sensing with coherent redundant dictionaries. The approach relies
on the observation that natural images exhibit strong average sparsity over
multiple coherent frames. The associated reconstruction algorithm, based on an
analysis prior and a reweighted scheme, is dubbed Sparsity Averaging
Reweighted Analysis (SARA). We review these advances and extend associated
simulations establishing the superiority of SARA to regularization methods
based on sparsity in a single frame, for a generic spread spectrum acquisition
and for a Fourier acquisition of particular interest in radio astronomy.Comment: 4 pages, 3 figures, Proceedings of 10th International Conference on
Sampling Theory and Applications (SampTA), Code available at
https://github.com/basp-group/sopt, Full journal letter available at
http://arxiv.org/abs/arXiv:1208.233
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