180 research outputs found
Signal reconstruction from the magnitude of subspace components
We consider signal reconstruction from the norms of subspace components
generalizing standard phase retrieval problems. In the deterministic setting, a
closed reconstruction formula is derived when the subspaces satisfy certain
cubature conditions, that require at least a quadratic number of subspaces.
Moreover, we address reconstruction under the erasure of a subset of the norms;
using the concepts of -fusion frames and list decoding, we propose an
algorithm that outputs a finite list of candidate signals, one of which is the
correct one. In the random setting, we show that a set of subspaces chosen at
random and of cardinality scaling linearly in the ambient dimension allows for
exact reconstruction with high probability by solving the feasibility problem
of a semidefinite program
Extreme Singular Values of Random Time-Frequency Structured Matrices
In this paper, we investigate extreme singular values of the analysis matrix
of a Gabor frame with a random window . Columns of such
matrices are time and frequency shifts of , and is the set of time-frequency shift indices. Our
aim is to obtain bounds on the singular values of such random time-frequency
structured matrices for various choices of the frame set , and to
investigate their dependence on the structure of , as well as on its
cardinality. We also compare the results obtained for Gabor frame analysis
matrices with the respective results for matrices with independent identically
distributed entries.Comment: 21 pages, 3 figure
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