# Ensemble averaging for multiplicative noise

In my problem there exists a vector

x = [x1,x2, ... x_N]

of length N, and I have M measurements

y_k = x .* e_k, 1 <= k <= M,

where e_k is non-gaussian multiplicative noise.

Currently, I denoise by taking logs of each y_k and averaging the M
replicates. In the ideal case (ie additive mean 0 gaussian noise) this
would improve SNR by a factor of sqrt(M). However, since log(e_k) is not
mean 0 gaussian noise, averaging is probably not the best approach.

This is the first time I've encountered an ensemble of signals. Does anyone

.

• Follow-Ups:

## Relevant Pages

• Re: Transfer Function Estimation - Averaging?
... I have a question about transfer function estimation relating ... The data that I have is daily records of measurement of earth's noise. ... the corresponding part in frequency domain and then added them together ... and averaging in frequency domain with same amount of segmenting and ...
(comp.dsp)
• Re: Dayton Miller Presented His Results in a False and Misleading Manner
... I found Tom Roberts' paper very interesting, ... and then performed calculations to remove noise from the ... smaller number of values produced by averaging. ... Tom argued that error bars should be calculated from data prior to ...
(sci.physics.relativity)
• Re: NMR combating terrorists
... >> Averaging works for a while, but is limited by the varance of the ... > LOL, what an idiot. ... You don't understand noise, do you. ... >> with a very weak mind. ...
(sci.physics)
• Re: Q about noise in time interval measurement averging
... I have a PIC measuring a time interval to 25ns resolution, ... I cant seem to recall how the noise reduces with increasing samples, ... your need to know the sense of the rotation as well as it's speed. ... and averaging wouldn't do as much good as it ...
(sci.electronics.design)
• Re: ALE, the right way to do multi-pass multi-scanning?
... the stepper motor is not very accurate at this level of precision, ... It does not eliminate noise, just improves the signal to noise ratio. ... doing with a 5400dpi scanner, yes, Gaussian blurring with a small sigma can replace scan line averaging without loosing detail. ... Because that works over two dimensions, it can be even more effective than 2x averaging. ...
(comp.periphs.scanners)