patch_denoise.space_time.utils.marchenko_pastur_median

patch_denoise.space_time.utils.marchenko_pastur_median(beta, eps=1e-07)

Compute the median of the Marchenko-Pastur Distribution.

Parameters:

• beta (float) – aspect ratio of a matrix.

• eps (float) – Precision Parameter

Returns:

float

Return type:

the estimated median

Notes

This method Solve \(F(x) = 1/2\) by dichotomy with .. math

F(x) = \int_{\beta_-}^{x} \frac{\sqrt{(\beta_+-t)(t-\beta_-)}}{2\pi\beta t} dt

The integral is computed using scipy.integrate.quad