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Mar 17, 2010

Two interesting contributions on sparse reconstruction

Show and Tell-Yonina Eldar. This morning Yonina Eldar presented their practical proposal to spectrum reconstruction [M09] in a Show and Tell session at the ICASSP. This approach, called the modulated wideband converter, is based on mixing the wideband sparse signal of interest with a high frequency periodic signal to produce aliasing in baseband. This aliased signal is then lowpass filtered and sampled at low rate. Using several replicas of this structure in parallel we obtain several low rate signals that can be used to reconstruct a given passband of interest.
The proposed approach allows practical subsampling of sparse signals in the frequency domain today, with available electronic components. Another interesting point is that the reconstruction process, once the occupied bands are detected, is quite simple.
Unfortunately, the Show and Tell session consisted only on the hardware mixing part. While the available hardware was enough to see the baseband aliased signals that allow the reconstruction of the original passband signals, the show would be much more impressive if the actual mixed signals were reconstructed.

Another work related to sparse recovery was presented in the ICASSP's session on Distributed Estimation in Sensor Networks. The work was a practical distributed implementation of the Lasso estimation algorithm [B10] by J. A. Bazerque et al. The proposed algorithm is based on consensus: first the individual nodes perform a local norm-1 based minimization in order to obtain local sparse solutions, then they interchange with the neighbours the obtained solutions that are then incorpored into the next local optimization. This procedure is repeated until consensus is reached.
The interesting part is that the solution obtained after convergence is the same as if the lasso optimization were performed by a centralized with the whole data record.


M. Mishali, Y. C. Eldar and A. Elron Xampling - Part I: Practice. CCIT Report #747 Oct-09, EE Pub No. 1704, EE Dept., Technion - Israel Institute of Technology. [Online] arXiv 0911.0519, Oct. 2009.


Juan Andres Bazerque, Gonzalo Mateos and Georgios B. Giannakis. Distributed Lasso for in-network linear regression. Proc. of Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP). Dallas, USA. March 14-19, 2010.

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