15,164 research outputs found
Communications-Inspired Projection Design with Application to Compressive Sensing
We consider the recovery of an underlying signal x \in C^m based on
projection measurements of the form y=Mx+w, where y \in C^l and w is
measurement noise; we are interested in the case l < m. It is assumed that the
signal model p(x) is known, and w CN(w;0,S_w), for known S_W. The objective is
to design a projection matrix M \in C^(l x m) to maximize key
information-theoretic quantities with operational significance, including the
mutual information between the signal and the projections I(x;y) or the Renyi
entropy of the projections h_a(y) (Shannon entropy is a special case). By
capitalizing on explicit characterizations of the gradients of the information
measures with respect to the projections matrix, where we also partially extend
the well-known results of Palomar and Verdu from the mutual information to the
Renyi entropy domain, we unveil the key operations carried out by the optimal
projections designs: mode exposure and mode alignment. Experiments are
considered for the case of compressive sensing (CS) applied to imagery. In this
context, we provide a demonstration of the performance improvement possible
through the application of the novel projection designs in relation to
conventional ones, as well as justification for a fast online projections
design method with which state-of-the-art adaptive CS signal recovery is
achieved.Comment: 25 pages, 7 figures, parts of material published in IEEE ICASSP 2012,
submitted to SIIM
Quantum entanglement enhances the capacity of bosonic channels with memory
The bosonic quantum channels have recently attracted a growing interest,
motivated by the hope that they open a tractable approach to the generally hard
problem of evaluating quantum channel capacities. These studies, however, have
always been restricted to memoryless channels. Here, it is shown that the
classical capacity of a bosonic Gaussian channel with memory can be
significantly enhanced if entangled symbols are used instead of product
symbols. For example, the capacity of a photonic channel with 70%-correlated
thermal noise of one third the shot noise is enhanced by about 11% when using
3.8-dB entangled light with a modulation variance equal to the shot noise.Comment: 4 pages, 4 figure
Information transmission via entangled quantum states in Gaussian channels with memory
Gaussian quantum channels have recently attracted a growing interest, since
they may lead to a tractable approach to the generally hard problem of
evaluating quantum channel capacities. However, the analysis performed so far
has always been restricted to memoryless channels. Here, we consider the case
of a bosonic Gaussian channel with memory, and show that the classical capacity
can be significantly enhanced by employing entangled input symbols instead of
product symbols.Comment: 13 pages, 5 figures, Workshop on Quantum entanglement in physical and
information sciences, Pisa, December 14-18, 200
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