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Signal estimation with different error metrics
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Signal estimation with different error metrics
1.
Signal Estimation with Different
Error Metrics Jin Tan and Dror Baron North Carolina State University Supported by NSF CCF-1217749 and ARO W911NF-04-D-0003
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DISK FULL!!!
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10 GB
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9 GB
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8 GB
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7 GB
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How do we
model the signal?
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Image signal Audio signal Vector
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How do we
compress the signal?
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Sampling matrix Original signal
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Sampling matrix Original signal Compressed
signal
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How do we
model the noise during transmission?
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noise ObservationsCompressed signal
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How do we
decompress or recover the original signal?
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noise Observations
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Observations Efficient algorithm Recovered signal
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How do we
evaluate the quality of the recovery?
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Error metric Original signal
Recovered signal
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0 0 3 0 0 3 0 0 0 0 3 0 0 0 3 0 0 2 0 0 0 1 3 0 Error metric Absolute error Original
signal Recovered signal
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Square error Original signal Error
metric Recovered signal
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Hamming distance Original signal
Estimated signal Error metric
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What type of
error metric can our algorithm deal with?
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Any well defined
errors Error metric
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We are going
to explain how the algorithm works. It is recommended that the audiences have basic knowledge about compressed sensing.
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Error metric (averaged error)
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Error metric
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Noise Original signal Observations Posterior Probability of
x given y
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Noise Original signal Observations Decoupling principle
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Noise Original signal Observations Decoupling principle
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Original signal q Gaussian noise
Equivalent observations Decoupling principle Scalar Gaussian channels
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Original signal q Gaussian noise Decoupling
principle Scalar Gaussian channels Equivalent observations
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Numerical results
54.
Signal dimension =
10,000 Our algorithm Number of rows of sampling matrix
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Signal dimension =
10,000 Number of rows of sampling matrix
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Summary
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Decoupling principle Minimize averaged error
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Thanks!
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