18,616 research outputs found
Dealing with missing data: An inpainting application to the MICROSCOPE space mission
Missing data are a common problem in experimental and observational physics.
They can be caused by various sources, either an instrument's saturation, or a
contamination from an external event, or a data loss. In particular, they can
have a disastrous effect when one is seeking to characterize a
colored-noise-dominated signal in Fourier space, since they create a spectral
leakage that can artificially increase the noise. It is therefore important to
either take them into account or to correct for them prior to e.g. a
Least-Square fit of the signal to be characterized. In this paper, we present
an application of the {\it inpainting} algorithm to mock MICROSCOPE data; {\it
inpainting} is based on a sparsity assumption, and has already been used in
various astrophysical contexts; MICROSCOPE is a French Space Agency mission,
whose launch is expected in 2016, that aims to test the Weak Equivalence
Principle down to the level. We then explore the {\it inpainting}
dependence on the number of gaps and the total fraction of missing values. We
show that, in a worst-case scenario, after reconstructing missing values with
{\it inpainting}, a Least-Square fit may allow us to significantly measure a
Equivalence Principle violation signal, which is
sufficiently close to the MICROSCOPE requirements to implement {\it inpainting}
in the official MICROSCOPE data processing and analysis pipeline. Together with
the previously published KARMA method, {\it inpainting} will then allow us to
independently characterize and cross-check an Equivalence Principle violation
signal detection down to the level.Comment: Accepted for publication in Physical Review D. 12 pages, 6 figure
PhaseMax: Convex Phase Retrieval via Basis Pursuit
We consider the recovery of a (real- or complex-valued) signal from
magnitude-only measurements, known as phase retrieval. We formulate phase
retrieval as a convex optimization problem, which we call PhaseMax. Unlike
other convex methods that use semidefinite relaxation and lift the phase
retrieval problem to a higher dimension, PhaseMax is a "non-lifting" relaxation
that operates in the original signal dimension. We show that the dual problem
to PhaseMax is Basis Pursuit, which implies that phase retrieval can be
performed using algorithms initially designed for sparse signal recovery. We
develop sharp lower bounds on the success probability of PhaseMax for a broad
range of random measurement ensembles, and we analyze the impact of measurement
noise on the solution accuracy. We use numerical results to demonstrate the
accuracy of our recovery guarantees, and we showcase the efficacy and limits of
PhaseMax in practice
- …