76,393 research outputs found
Adaptive Compressed Sensing for Support Recovery of Structured Sparse Sets
This paper investigates the problem of recovering the support of structured
signals via adaptive compressive sensing. We examine several classes of
structured support sets, and characterize the fundamental limits of accurately
recovering such sets through compressive measurements, while simultaneously
providing adaptive support recovery protocols that perform near optimally for
these classes. We show that by adaptively designing the sensing matrix we can
attain significant performance gains over non-adaptive protocols. These gains
arise from the fact that adaptive sensing can: (i) better mitigate the effects
of noise, and (ii) better capitalize on the structure of the support sets.Comment: to appear in IEEE Transactions on Information Theor
Adaptive sensing performance lower bounds for sparse signal detection and support estimation
This paper gives a precise characterization of the fundamental limits of
adaptive sensing for diverse estimation and testing problems concerning sparse
signals. We consider in particular the setting introduced in (IEEE Trans.
Inform. Theory 57 (2011) 6222-6235) and show necessary conditions on the
minimum signal magnitude for both detection and estimation: if is a sparse vector with non-zero components then it
can be reliably detected in noise provided the magnitude of the non-zero
components exceeds . Furthermore, the signal support can be exactly
identified provided the minimum magnitude exceeds . Notably
there is no dependence on , the extrinsic signal dimension. These results
show that the adaptive sensing methodologies proposed previously in the
literature are essentially optimal, and cannot be substantially improved. In
addition, these results provide further insights on the limits of adaptive
compressive sensing.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ555 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Achieving minimum-error discrimination of an arbitrary set of laser-light pulses
Laser light is widely used for communication and sensing applications, so the
optimal discrimination of coherent states--the quantum states of light emitted
by a laser--has immense practical importance. However, quantum mechanics
imposes a fundamental limit on how well different coher- ent states can be
distinguished, even with perfect detectors, and limits such discrimination to
have a finite minimum probability of error. While conventional optical
receivers lead to error rates well above this fundamental limit, Dolinar found
an explicit receiver design involving optical feedback and photon counting that
can achieve the minimum probability of error for discriminating any two given
coherent states. The generalization of this construction to larger sets of
coherent states has proven to be challenging, evidencing that there may be a
limitation inherent to a linear-optics-based adaptive measurement strategy. In
this Letter, we show how to achieve optimal discrimination of any set of
coherent states using a resource-efficient quantum computer. Our construction
leverages a recent result on discriminating multi-copy quantum hypotheses
(arXiv:1201.6625) and properties of coherent states. Furthermore, our
construction is reusable, composable, and applicable to designing
quantum-limited processing of coherent-state signals to optimize any metric of
choice. As illustrative examples, we analyze the performance of discriminating
a ternary alphabet, and show how the quantum circuit of a receiver designed to
discriminate a binary alphabet can be reused in discriminating multimode
hypotheses. Finally, we show our result can be used to achieve the quantum
limit on the rate of classical information transmission on a lossy optical
channel, which is known to exceed the Shannon rate of all conventional optical
receivers.Comment: 9 pages, 2 figures; v2 Minor correction
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