4,975 research outputs found
A Novel Convex Relaxation for Non-Binary Discrete Tomography
We present a novel convex relaxation and a corresponding inference algorithm
for the non-binary discrete tomography problem, that is, reconstructing
discrete-valued images from few linear measurements. In contrast to state of
the art approaches that split the problem into a continuous reconstruction
problem for the linear measurement constraints and a discrete labeling problem
to enforce discrete-valued reconstructions, we propose a joint formulation that
addresses both problems simultaneously, resulting in a tighter convex
relaxation. For this purpose a constrained graphical model is set up and
evaluated using a novel relaxation optimized by dual decomposition. We evaluate
our approach experimentally and show superior solutions both mathematically
(tighter relaxation) and experimentally in comparison to previously proposed
relaxations
Probing quantum state space: does one have to learn everything to learn something?
Determining the state of a quantum system is a consuming procedure. For this
reason, whenever one is interested only in some particular property of a state,
it would be desirable to design a measurement setup that reveals this property
with as little effort as possible. Here we investigate whether, in order to
successfully complete a given task of this kind, one needs an informationally
complete measurement, or if something less demanding would suffice. The first
alternative means that in order to complete the task, one needs a measurement
which fully determines the state. We formulate the task as a membership problem
related to a partitioning of the quantum state space and, in doing so, connect
it to the geometry of the state space. For a general membership problem we
prove various sufficient criteria that force informational completeness, and we
explicitly treat several physically relevant examples. For the specific cases
that do not require informational completeness, we also determine bounds on the
minimal number of measurement outcomes needed to ensure success in the task.Comment: 23 pages, 4 figure
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