1,717 research outputs found
Phase retrieval from low-rate samples
The paper considers the phase retrieval problem in N-dimensional complex
vector spaces. It provides two sets of deterministic measurement vectors which
guarantee signal recovery for all signals, excluding only a specific subspace
and a union of subspaces, respectively. A stable analytic reconstruction
procedure of low complexity is given. Additionally it is proven that signal
recovery from these measurements can be solved exactly via a semidefinite
program. A practical implementation with 4 deterministic diffraction patterns
is provided and some numerical experiments with noisy measurements complement
the analytic approach.Comment: Preprint accepted for publication in Sampling Theory in Signal and
Image Processing -- Special issue on SampTa 201
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
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