1,267 research outputs found
Blind Sensor Calibration using Approximate Message Passing
The ubiquity of approximately sparse data has led a variety of com- munities
to great interest in compressed sensing algorithms. Although these are very
successful and well understood for linear measurements with additive noise,
applying them on real data can be problematic if imperfect sensing devices
introduce deviations from this ideal signal ac- quisition process, caused by
sensor decalibration or failure. We propose a message passing algorithm called
calibration approximate message passing (Cal-AMP) that can treat a variety of
such sensor-induced imperfections. In addition to deriving the general form of
the algorithm, we numerically investigate two particular settings. In the
first, a fraction of the sensors is faulty, giving readings unrelated to the
signal. In the second, sensors are decalibrated and each one introduces a
different multiplicative gain to the measures. Cal-AMP shares the scalability
of approximate message passing, allowing to treat big sized instances of these
problems, and ex- perimentally exhibits a phase transition between domains of
success and failure.Comment: 27 pages, 9 figure
Inferring Sparsity: Compressed Sensing using Generalized Restricted Boltzmann Machines
In this work, we consider compressed sensing reconstruction from
measurements of -sparse structured signals which do not possess a writable
correlation model. Assuming that a generative statistical model, such as a
Boltzmann machine, can be trained in an unsupervised manner on example signals,
we demonstrate how this signal model can be used within a Bayesian framework of
signal reconstruction. By deriving a message-passing inference for general
distribution restricted Boltzmann machines, we are able to integrate these
inferred signal models into approximate message passing for compressed sensing
reconstruction. Finally, we show for the MNIST dataset that this approach can
be very effective, even for .Comment: IEEE Information Theory Workshop, 201
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