10,376 research outputs found
Dictionary Learning for Blind One Bit Compressed Sensing
This letter proposes a dictionary learning algorithm for blind one bit
compressed sensing. In the blind one bit compressed sensing framework, the
original signal to be reconstructed from one bit linear random measurements is
sparse in an unknown domain. In this context, the multiplication of measurement
matrix \Ab and sparse domain matrix , \ie \Db=\Ab\Phi, should be
learned. Hence, we use dictionary learning to train this matrix. Towards that
end, an appropriate continuous convex cost function is suggested for one bit
compressed sensing and a simple steepest-descent method is exploited to learn
the rows of the matrix \Db. Experimental results show the effectiveness of
the proposed algorithm against the case of no dictionary learning, specially
with increasing the number of training signals and the number of sign
measurements.Comment: 5 pages, 3 figure
Experimentally exploring compressed sensing quantum tomography
In the light of the progress in quantum technologies, the task of verifying
the correct functioning of processes and obtaining accurate tomographic
information about quantum states becomes increasingly important. Compressed
sensing, a machinery derived from the theory of signal processing, has emerged
as a feasible tool to perform robust and significantly more resource-economical
quantum state tomography for intermediate-sized quantum systems. In this work,
we provide a comprehensive analysis of compressed sensing tomography in the
regime in which tomographically complete data is available with reliable
statistics from experimental observations of a multi-mode photonic
architecture. Due to the fact that the data is known with high statistical
significance, we are in a position to systematically explore the quality of
reconstruction depending on the number of employed measurement settings,
randomly selected from the complete set of data, and on different model
assumptions. We present and test a complete prescription to perform efficient
compressed sensing and are able to reliably use notions of model selection and
cross-validation to account for experimental imperfections and finite counting
statistics. Thus, we establish compressed sensing as an effective tool for
quantum state tomography, specifically suited for photonic systems.Comment: 12 pages, 5 figure
Blind calibration for compressed sensing by convex optimization
We consider the problem of calibrating a compressed sensing measurement
system under the assumption that the decalibration consists in unknown gains on
each measure. We focus on {\em blind} calibration, using measures performed on
a few unknown (but sparse) signals. A naive formulation of this blind
calibration problem, using minimization, is reminiscent of blind
source separation and dictionary learning, which are known to be highly
non-convex and riddled with local minima. In the considered context, we show
that in fact this formulation can be exactly expressed as a convex optimization
problem, and can be solved using off-the-shelf algorithms. Numerical
simulations demonstrate the effectiveness of the approach even for highly
uncalibrated measures, when a sufficient number of (unknown, but sparse)
calibrating signals is provided. We observe that the success/failure of the
approach seems to obey sharp phase transitions
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