]> Adding Synthetic Noise

Adding Synthetic Noise

When modeling system performance or testing algorithms, it is important to add noise to the simulated "data" to accurately model system performance. The PMI toolbox includes routines for adding both Gaussian-distributed noise (e.g., electronic amplifier noise) and Poisson-distributed noise (e.g., detector shot noise) to simulated "data".

Function Summary

Syntax:	Phi = addElecNoise(SD, MeasList, Phi0, SNR);
Inputs:	SD	SD structure
	MeasList	Measurement List that corresponds to Phi0
	Phi0	Original noise-free data
	SNR	average signal-to-noise ratio (linear, not dB)
Outputs:	Phi	Phi0 with added Gaussian noise

Syntax:	Phi = addShotNoise(SD, MeasList, Phi0, gain, bwidth);
Inputs:	SD	SD structure
	MeasList	Measurement List that corresponds to Phi0
	Phi0	Original noise-free data
	gain	Model detector gain
	bwdith	Model detector bandwidth (Hz)
Outputs:	Phi	Phi0 with added Poisson noise

Detailed Descriptions

Gaussian noise is sampled from a distribution

φ_{noise} = N (0, σ_{SNR})

where $N (μ, σ)$ is a Gaussian distributed random number with mean value $μ$ and standard deviation $σ$ . In this case, $σ_{SNR}$ is selected such that the RMS signal to noise ratio is equal to the user-requested SNR.

Shot noise is sampled from a Poisson distribution. Before generating the random numbers, however, the measured fluence must be converted into the number (count) of photos received at the detector

N_{γ} = \frac{B}{G} \frac{h c}{λ} |φ_{0}|

where $h$ is Plank's constant, $c$ is the speed of light, $λ$ is the wavelength of the light, $G$ is the electronic gain of the detector, and $B$ is the bandwidth of the detector. Given the number of detected photons, the shot noise is

φ_{noise} = (\frac{G}{B} \frac{λ}{h c}) N_{p} (N_{γ}) - φ_{0}

where $N_{p} (ν)$ is a Poisson random process with mean value $ν$ . For complex-valued $φ$ , independent random numbers with mean $N_{γ} / \sqrt{2}$ are added to both the real and the imaginary components.