536 research outputs found
Signal Recovery in Perturbed Fourier Compressed Sensing
In many applications in compressed sensing, the measurement matrix is a
Fourier matrix, i.e., it measures the Fourier transform of the underlying
signal at some specified `base' frequencies , where is the
number of measurements. However due to system calibration errors, the system
may measure the Fourier transform at frequencies
that are different from the base frequencies and where
are unknown. Ignoring perturbations of this nature can lead to major errors in
signal recovery. In this paper, we present a simple but effective alternating
minimization algorithm to recover the perturbations in the frequencies \emph{in
situ} with the signal, which we assume is sparse or compressible in some known
basis. In many cases, the perturbations can be expressed
in terms of a small number of unique parameters . We demonstrate that
in such cases, the method leads to excellent quality results that are several
times better than baseline algorithms (which are based on existing off-grid
methods in the recent literature on direction of arrival (DOA) estimation,
modified to suit the computational problem in this paper). Our results are also
robust to noise in the measurement values. We also provide theoretical results
for (1) the convergence of our algorithm, and (2) the uniqueness of its
solution under some restrictions.Comment: New theortical results about uniqueness and convergence now included.
More challenging experiments now include
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Polca SARA - Full polarization, direction-dependent calibration and sparse imaging for radio interferometry
New generation of radio interferometers are envisaged to produce high
quality, high dynamic range Stokes images of the observed sky from the
corresponding under-sampled Fourier domain measurements. In practice, these
measurements are contaminated by the instrumental and atmospheric effects that
are well represented by Jones matrices, and are most often varying with
observation direction and time. These effects, usually unknown, act as a
limiting factor in achieving the required imaging performance and thus, their
calibration is crucial. To address this issue, we develop a global algorithm,
named Polca SARA, aiming to perform full polarization, direction-dependent
calibration and sparse imaging by employing a non-convex optimization
technique. In contrast with the existing approaches, the proposed method offers
global convergence guarantees and flexibility to incorporate sophisticated
priors to regularize the imaging as well as the calibration problem. Thus, we
adapt a polarimetric imaging specific method, enforcing the physical
polarization constraint along with a sparsity prior for the sought images. We
perform extensive simulation studies of the proposed algorithm. While
indicating the superior performance of polarization constraint based imaging,
the obtained results also highlight the importance of calibrating for
direction-dependent effects as well as for off-diagonal terms (denoting
polarization leakage) in the associated Jones matrices, without inclusion of
which the imaging quality deteriorates
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