CS: PECASEs,CS for fusion frames, ADS, CS for Feedback Reduction in MIMO Broadcast Channels, some blog entries

First Congratulations to Justin Romberg and Joel Tropp for meeting president Obama and incidentally for receiving a PECASE :-)

Found on the interwebs, a generalization of CS, adaptive CS and some MIMO work. There are also some blog entries on the subject of CS. Here we go:

Compressed sensing for fusion frames by Petros Boufounos, Gitta Kutyniok, and Holger Rauhut. The abstract reads:

Compressed Sensing (CS) is a new signal acquisition technique that allows sampling of sparse signals using significantly fewer measurements than previously thought possible. On the other hand, a fusion frame is a new signal representation method that uses collections of subspaces instead of vectors to represent signals. This work combines these exciting new fields to introduce a new sparsity model for fusion frames. Signals that are sparse under the new model can be compressively sampled and uniquely reconstructed in ways similar to sparse signals using standard CS. The combination provides a promising new set of mathematical tools and signal models useful in a variety of applications. With the new model, a sparse signal has energy in very few of the subspaces of the fusion frame, although it needs not be sparse within each of the subspaces it occupies. We define a mixed l_1/l_2 norm for fusion frames. A signal sparse in the subspaces of the fusion frame can thus be sampled using very few random projections and exactly reconstructed using a convex optimization that minimizes this mixed l_1/l_2 norm. The sampling conditions we derive are very similar to the coherence and RIP conditions used in standard CS theory.

You can find more about Fusion Frames on this site.


Adaptive compressed image sensing based on wavelet modeling and direct sampling by Shay Deutsch and Amir Averbuch. The abstract reads:

We present Adaptive Direct Sampling (ADS), an algorithm for image acquisition and compression which does not require the data to be sampled at its highest resolution. In some cases, our approach simplifies and improves upon the existing methodology of Compressed Sensing (CS), by replacing the ‘universal’ acquisition of pseudo-random measurements with a direct and fast method of adaptive wavelet coefficient acquisition. The main advantages of this direct approach are that the decoding algorithm is significantly faster and that it allows more control over the compressed image quality, in particular, the sharpness of edges.

Compressive Sensing for Feedback Reduction in MIMO Broadcast Channels by Syed T. Qaseem and Tareq Y. Al-Naffouri. The abstract reads:

We propose a generalized feedback model and compressive sensing based opportunistic feedback schemes for feedback resource reduction in MIMO Broadcast Channels under the assumption that both uplink and downlink channels undergo block Rayleigh fading. Feedback resources are shared and are opportunistically accessed by users who are strong, i.e. users whose channel quality information is above a certain fixed threshold. Strong users send same feedback information on all shared channels. They are identified by the base station via compressive sensing. Both analog and digital feedbacks are considered. The proposed analog & digital opportunistic feedback schemes are shown to achieve the same sum-rate throughput as that achieved by dedicated feedback schemes, but with feedback channels growing only logarithmically with number of users. Moreover, there is also a reduction in the feedback load. In the analog feedback case, we show that the propose scheme reduces the feedback noise which eventually results in better throughput, whereas in the digital feedback case the proposed scheme in a noisy scenario achieves almost the throughput obtained in a noiseless dedicated feedback scenario. We also show that for a fixed given budget of feedback bits, there exist a trade-off between the number of shared channels and thresholds accuracy of the feedback SINR.

Several blogs mentioned compressive sensing in the past week:

• First-order optimization Lianlin Li's Compressive Sensing blog in Chinese.
• Gradient Descent with Sparsification: An Iterative Algorithm for Sparse Recovery with Restricted Isometry Property from the Paper scanner blog and
• Compressive Sensing and Precomputed Radiance Transfer?

Credit: NASA/GSFC/Arizona State University. The central peak and fractured floor of Compton crater as imaged by the LROC Narrow Angle Camera at dawn, image width is ~1720 meters.