Sparse Reconstruction via Bayesian Variable Selection and ...
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Sparse Reconstruction via Bayesian Variable Selection and Bayesian Model Averaging Lee Potter, Phil Schniter, and Subhojit Som Department of Electrical & Computer Engineering Ohio State University with support from AFOSR FA9550-06-1-0324 ATR Center Workshop, February 2009
Transcript of Sparse Reconstruction via Bayesian Variable Selection and ...
Sparse Reconstruction viaBayesian Variable Selection andBayesian Model Averaging
Lee Potter, Phil Schniter, and Subhojit SomDepartment of Electrical & Computer EngineeringOhio State Universitywith support from AFOSR FA9550-06-1-0324
ATR Center Workshop, February 2009
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Sparse Reconstruction
0.51 0.16 0.13 0.09
Variable Selection
[graphic adapted from R. Baraniuk]
Estimation
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Motivating Applications: Channel Estimation
(CW, from top left) Ohio Stadium at X-band; underwater acoustic communications; oximetrywith electronic spin resonance at L-band; ESR resonator; range-Doppler radar; roof-top rail-SAR; through-wall radar imaging.
[graphics: GD_ADS; M. Stojanovic, E. Ertin]
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The Variable Selection Problem
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Bayesian Variable Selection
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Typical Priors in Variable Selection
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Variable Selection: Posteriors
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Connection to AIC/BIC/RIC
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Bayesian Model Averaging
0.51 0.16 0.13 0.09
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Model Averaging: Implementation
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Tipping’s Relevance Vector Machine (RVM)
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BMA versus RVM
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0 5 10 15 20 25 30 35 40−0.8
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Numerical Example: A compressible signal
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NMSE versus decay rate
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−26
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ρ
NM
SE
[dB
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N = 512, M = 128, SNR = 15 dB, Dmax
= 5, Emax
= 20, T = 2000
FBMPmmse
(w/ EM update)
FBMPmap
(w/ EM update)
SparseBayesOMPStOMPGPSRBCSVB−BCS
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Sparsity of estimate versus decay rate
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
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ρ
||xre
cove
ry|| 0
N = 512, M = 128, SNR = 15 dB, Dmax
= 5, Emax
= 20, T = 2000
FBMPmmse
(w/ EM update)
FBMPmap
(w/ EM update)
SparseBayesOMPStOMPGPSRBCS
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Performance Guarantees: MAP variable selection
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Pair-wise Error Probability Analysis
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Conclusion
![Sequential Bayesian Sparse Signal Reconstruction …prior information using linear MMSE reconstruction. Here, we extend the Bayesian approach [13], [14], [15] to sequential Maximum](https://static.fdocuments.net/doc/165x107/5fd55d7c4d7fd26d021e4317/sequential-bayesian-sparse-signal-reconstruction-prior-information-using-linear.jpg)
