Section:
New Results
Inferring Sparsity: Compressed Sensing
Using Generalized Restricted Boltzmann Machines
In [23] 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 .