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Signal estimation with different error metrics

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Signal estimation with different error metrics

1. 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
2. 2. DISK FULL!!!
3. 3. 10 GB
4. 4. 9 GB
5. 5. 8 GB
6. 6. 7 GB
7. 7. How do we model the signal?
8. 8. Image signal Audio signal Vector
9. 9. How do we compress the signal?
10. 10. Sampling matrix Original signal
11. 11. Sampling matrix Original signal Compressed signal
12. 12. How do we model the noise during transmission?
13. 13. noise ObservationsCompressed signal
14. 14. How do we decompress or recover the original signal?
15. 15. noise Observations
16. 16. Observations Efficient algorithm Recovered signal
17. 17. How do we evaluate the quality of the recovery?
18. 18. Error metric Original signal Recovered signal
19. 19. 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
20. 20. Square error Original signal Error metric Recovered signal
21. 21. Hamming distance Original signal Estimated signal Error metric
22. 22. What type of error metric can our algorithm deal with?
23. 23. Any well defined errors Error metric
24. 24. We are going to explain how the algorithm works. It is recommended that the audiences have basic knowledge about compressed sensing.
25. 25. Error metric (averaged error)
26. 26. Error metric
27. 27. Noise Original signal Observations Posterior Probability of x given y
28. 28. Noise Original signal Observations Decoupling principle
29. 29. Noise Original signal Observations Decoupling principle
30. 30. Original signal q Gaussian noise Equivalent observations Decoupling principle Scalar Gaussian channels
31. 31. Original signal q Gaussian noise Decoupling principle Scalar Gaussian channels Equivalent observations
32. 32. Numerical results
33. 33. Signal dimension = 10,000 Our algorithm Number of rows of sampling matrix
34. 34. Signal dimension = 10,000 Number of rows of sampling matrix
35. 35. Summary
36. 36. Decoupling principle Minimize averaged error
37. 37. Thanks!