Investigation of Linear-Mode, Photon Counting HgCdTe APDs for Astronomical Observations
Comments on Rebecca Willett’s paper “Multiscale Analysis of Photon-Limited Astronomical...
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Transcript of Comments on Rebecca Willett’s paper “Multiscale Analysis of Photon-Limited Astronomical...
Comments on Rebecca Willett’s paper“Multiscale Analysis of Photon-Limited
Astronomical Images”
By Jeff ScargleSpace Science Division
NASA Ames Research Center
Good lesson: Try your algorithm out on pure noise!
Cautions for the astronomer:
• Performance = rate of asymptotic convergence( N )
• Oracles … they’re never around when you need them.
• Plethora of methods
• If you have a hammer, each signal looks like a …
Good lesson: Try your algorithm out on pure noise!
Cautions for the astronomer:
• Performance = rate of asymptotic convergence( N )
• Oracles … they’re never around when you need them.
• Plethora of methods
• If you have a hammer, each signal looks like a … hammer!
Theorem:*
For each a > 0 there is an algorithm operating in C (a ) n 2 log(n ) flops which is asymptotically powerful for detecting signals with amplitudes A n = 2 (1 + a ) log n (against unit variance i.i.d Gaussian noise).
* “Near-Optimal Detection of Geometric Objects by Fast Multiscale Methods,” Ery Arias-Castro, David Donoho, Xiaoming Huo, August 18, 2003
The asymptotic behavior of wavelet coefficients in equation (2) of Rebecca’s paper is related to this somwhat magical result.
Trade-off:
Try to detect a signal with known properties(linear transforms, matched filtering, etc.)
Vs.
Try to find what, if any, signal is present:
•Representation in complete basis•Representation in overcomplete bases
•Generic, non-parametric representation
2 gray levels 4 gray levels 8 gray levels16 gray levels 32 gray levels 64 gray levels
8 16 32 40