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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?
22.
Image signal Audio signal Vector
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24.
25.
How do we
compress the signal?
26.
Sampling matrix Original signal
27.
28.
Sampling matrix Original signal Compressed
signal
29.
How do we
model the noise during transmission?
30.
31.
noise ObservationsCompressed signal
32.
How do we
decompress or recover the original signal?
33.
noise Observations
34.
Observations Efficient algorithm Recovered signal
35.
How do we
evaluate the quality of the recovery?
36.
Error metric Original signal
Recovered signal
37.
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
38.
Square error Original signal Error
metric Recovered signal
39.
Hamming distance Original signal
Estimated signal Error metric
40.
What type of
error metric can our algorithm deal with?
41.
Any well defined
errors Error metric
42.
We are going
to explain how the algorithm works. It is recommended that the audiences have basic knowledge about compressed sensing.
43.
Error metric (averaged error)
44.
Error metric
45.
46.
Noise Original signal Observations Posterior Probability of
x given y
47.
Noise Original signal Observations Decoupling principle
48.
Noise Original signal Observations Decoupling principle
49.
Original signal q Gaussian noise
Equivalent observations Decoupling principle Scalar Gaussian channels
50.
Original signal q Gaussian noise Decoupling
principle Scalar Gaussian channels Equivalent observations
51.
52.
53.
Numerical results
54.
Signal dimension =
10,000 Our algorithm Number of rows of sampling matrix
55.
Signal dimension =
10,000 Number of rows of sampling matrix
56.
Summary
57.
Decoupling principle Minimize averaged error
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59.
Thanks!
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