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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
DISK FULL!!!
10 GB
9 GB
8 GB
7 GB
How do we model the signal?
Image signal
Audio signal
Vector
How do we compress the signal?
Sampling matrix
Original signal
Sampling matrix
Original signal
Compressed signal
How do we model the noise
during transmission?
noise ObservationsCompressed signal
How do we decompress or recover
the original signal?
noise
Observations
Observations
Efficient
algorithm
Recovered signal
How do we evaluate
the quality of the recovery?
Error metric
Original signal Recovered signal
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
Square error
Original signal
Error metric
Recovered signal
Hamming distance
Original signal Estimated signal
Error metric
What type of error metric
can our algorithm deal with?
Any well defined errors
Error metric
We are going to explain how the algorithm works.
It is recommended that
the audiences have basic knowledge about
compressed sensing.
Error metric
(averaged error)
Error metric
Noise
Original signal
Observations
Posterior
Probability of x
given y
Noise
Original signal
Observations
Decoupling principle
Noise
Original signal
Observations
Decoupling principle
Original signal
q
Gaussian noise Equivalent observations
Decoupling principle
Scalar
Gaussian
channels
Original signal
q
Gaussian noise
Decoupling principle
Scalar
Gaussian
channels
Equivalent observations
Numerical results
Signal dimension = 10,000
Our
algorithm
Number of rows of sampling matrix
Signal dimension = 10,000
Number of rows of sampling matrix
Summary
Decoupling
principle
Minimize
averaged
error
Thanks!

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Signal estimation with different error metrics