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