Adaptation
Adaptive sensing of sparse signals
Many real-world signals exhibit sparsity in some representation, and compressive sensing has demonstrated the promise of acquiring such signals with few measurements. However, for a given budget of sensing resources, compressive sensing is not the most efficient in terms of signal-to-noise ratio (SNR) because it non-adaptively allocates a large fraction of the budget to dimensions where the signal is absent. An adaptive strategy by contrast can gradually concentrate resources on signal components, as illustrated below, by using knowledge of their locations inferred from past measurements.
We have considered the adaptive allocation of sensing resources over multiple stages to detect and estimate the nonzero values of sparse signals. The problem is formulated as a dynamic program and sensing policies are developed based on the method of open-loop feedback control (OLFC). These policies are optimal for two stages and improve monotonically thereafter with the number of stages. Simulations show dramatic improvements compared to non-adaptive sensing and gains up to several dB compared to other recent adaptive methods. We illustrate how the policies can be applied in radar surveillance to increasingly focus the radar beam on a set of targets instead of constantly scanning the entire field.
- D. Wei and A. O. Hero, "Multistage adaptive estimation of sparse signals," IEEE Journal of Selected Topics in Signal Processing, vol. 7, no. 5, pp. 783-796, October 2013. [pdf] [arXiv] [IEEE Xplore]
- D. Wei and A. O. Hero, "Multistage adaptive estimation of sparse signals," IEEE Workshop on Statistical Signal Processing (SSP), Ann Arbor, MI, August 2012. [pdf] [IEEE Xplore]
The work below provides an analytical characterization of the gains demonstrated above, specifically in the form of tight lower bounds on the gain due to adaptation. The bounds indicate a relationship between the gain and Chernoff coefficients, information-theoretic measures of detectability, and clarify the dependence on key parameters such as the sparsity level and SNR. As the SNR increases, it is shown that the performance converges to that of the oracle, which has perfect prior knowledge of signal locations. The rate of convergence to the oracle is also derived.
- D. Wei and A. O. Hero, "Performance guarantees for adaptive estimation of sparse signals," submitted to IEEE Transactions on Information Theory in November 2013. [arXiv]
- D. Wei and A. O. Hero, "A performance guarantee for adaptive estimation of sparse signals," IEEE Global Conference on Signal and Information Processing (GlobalSIP), Austin, TX, December 2013. (invited) [pdf] [IEEE Xplore]
Extensions of adaptive sensing
We have extended the work above in several directions: 1) generalizing from a Gaussian observation model to a Gamma-distributed model appropriate for adaptive spectrum sensing, where the goal is to focus on a set of peaks or a set of spectrum holes in cognitive radio; 2) adaptive sensing policies for the more difficult problem of tracking and estimating dynamic, moving targets, balancing the benefits of a non-myopic allocation policy with computational complexity; 3) classifying targets according to relative importance for subsequent exploitation in addition to localization and estimation as before.
- G. Newstadt, D. Wei, A. O. Hero, "Adaptive search and tracking of sparse dynamic targets under resource constraints," submitted to IEEE Transactions on Signal Processing, April 2014. [arXiv]
- G. Newstadt, D. Wei, A. O. Hero, "Adaptive search for sparse dynamic targets," IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Saint Martin, December 2013. [pdf] [IEEE Xplore]
- D. Wei and A. O. Hero, "Adaptive spectrum sensing and estimation," IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, May 2013. [pdf] [IEEE Xplore]
Non-uniform sampling based on local bandwidth
Classical Nyquist-Shannon sampling and its generalizations are based on the frequency bandwidth of a signal defined in a global sense. However, many signals such as speech and music are often interpreted, at least informally, as having time-varying frequency content, i.e., "local bandwidth". One would expect that such signals could benefit from non-uniform sampling, sampling more slowly where local bandwidth is low. Our work formalizes this intuition in two ways, one based on time-varying lowpass filters, the other on time-warping of globally bandlimited signals, and corresponding methods for sampling and reconstruction are suggested.
- D. Wei and A. V. Oppenheim, "Sampling based on local bandwidth," Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 2007. [pdf] [IEEE Xplore]
- D. Wei, "Sampling based on local bandwidth," M.Eng. thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, December 2006. [pdf]
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