An introductory video about our recent research

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

11. DISK FULL!!!

14. 10 GB

15. 9 GB

16. 8 GB

17. 7 GB

21. How do we model the signal?

22. Image signal
Audio signal
Vector

25. How do we compress the signal?

26. Sampling matrix
Original signal

28. Sampling matrix
Original signal
Compressed signal

29. How do we model the noise
during transmission?

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
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3
0
0
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0
3
0
0
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3
0
0
2
0
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1
3
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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

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

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

59. Thanks!