So today we have some example of blind deconvolution as Phil Schniter just sent me the following:
I'm writing to tell you of an exciting body of work that we have recently produced on the topic of Communication over Channels with Sparse Impulse Responses. As you know, this application is frequently cited as one of the motivating examples for Compressive Sensing. While most previous works on "Compressed Channel Sensing" focus solely on sparse-channel estimation, we focus on the larger problem of jointly estimating the sparse-channel, equalizing the sparse-channel, and decoding the bits.
In brief, our work started with an information-theoretic analysis of communication over sparse channels, where we established the following: for an L-length S-sparse N-block-fading channel, the prelog factor of the high-SNR ergodic capacity equals 1-S/N. Since this factor depends on the sparsity S and not the length L, the effect of channel sparsity on link performance becomes clear.
Next, we showed that recent message-passing algorithms to compressed sensing, such as Relaxed Belief Propagation and Generalized-AMP, can be embedded in a larger factor-graph via the "turbo" framework, where they not only estimate the sparse channel, but also jointly equalize and decode the bits. Amazingly, our simulations show that such an approach achieves exactly the pre-log factor predicted by the information theory.
We then further extended our message-passing approach to enable exploitation of structured sparsity, as exhibited by real-world communication channels, and we demonstrated that the resulting approach offers huge gains over the traditional "compressed channel sensing" approach based on LASSO, even when LASSO is embedded in a turbo loop.
More details, including matlab code and a complete list of references, can be found at http://www2.ece.ohio-state.edu/~schniter/turboGAMPdecoding
We hope that your readers will enjoy learning about this work.
Thanks Phil . I am also adding TurboGAMP to the sparse signal recovery section of the big picture.
Liked this entry ? subscribe to the Nuit Blanche feed, there's more where that came from