Inferring Sparsity: Compressed Sensing using Generalized Restricted Boltzmann Machines
This work addresses signal reconstruction in compressed sensing for applications like imaging, but it is incremental as it builds on existing methods by incorporating generative models.
The paper tackles compressed sensing reconstruction of structured sparse signals without explicit correlation models by integrating a trained generative statistical model into a Bayesian framework, demonstrating effectiveness on the MNIST dataset even with fewer measurements than sparsity.
In this work, we consider compressed sensing reconstruction from $M$ measurements of $K$-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 $M < K$.