rayleigh

Noise simulations.

mr_utils.sim.noise.rayleigh.rayleigh(M, sigma)

Generates Rayleigh distribution of pixel intensity M.

Generates the noise distribution of magnitude MR image areas where only noise is present. This distribution governs the noise in image regions with no NMR signal.

Parameters:

• M (array_like) – measured image pixel intensity
• sigma (float) – standard deviation of the Gaussian noise in the real and the imaginary images (which we assume to be equal)

Returns:

pM – Computed probability distribution of M

Return type:

array_like

Notes

Computes Equation [2] from [1].

References

[1]	Gudbjartsson, Hákon, and Samuel Patz. “The Rician distribution of noisy MRI data.” Magnetic resonance in medicine 34.6 (1995): 910-914.

mr_utils.sim.noise.rayleigh.rayleigh_mean(sigma)

Mean of the Rayleigh distribution with standard deviation sigma.

Parameters:sigma (float) – Standard deviation of Rayleigh distribution. Returns:M_bar – Mean of Rayleigh distribution. Return type:float

Notes

Computes Equation [3] from [2].

References

[2]	Gudbjartsson, Hákon, and Samuel Patz. “The Rician distribution of noisy MRI data.” Magnetic resonance in medicine 34.6 (1995): 910-914.

mr_utils.sim.noise.rayleigh.rayleigh_variance(sigma)

Variance of the Rayleigh distribution with standard deviation sigma.

Parameters:sigma (float) – Standard deviation of Rayleigh distribution. Returns:Variance of Rayleigh distribution. Return type:float

Notes

Computes Equation [4] from [3].

References

[3]	Gudbjartsson, Hákon, and Samuel Patz. “The Rician distribution of noisy MRI data.” Magnetic resonance in medicine 34.6 (1995): 910-914.