def inverse_anscombe(x):
"""Compute the inverse transform
This uses an approximation of the exact unbiased inverse.
Reference: Makitalo, M., & Foi, A. (2011). A closed-form
approximation of the exact unbiased inverse of the Anscombe
variance-stabilizing transformation. Image Processing.
"""
# should be positive
# should wotk for dataframe and numpy arrays
return (1.0 / 4.0 * np.power(x, 2) +
1.0 / 4.0 * np.sqrt(3.0 / 2.0) * np.power(x, -1.0) -
11.0 / 8.0 * np.power(x, -2.0) +
5.0 / 8.0 * np.sqrt(3.0 / 2.0) * np.power(x, -3.0) - 1.0 / 8.0)
def normpdf(x, mu, sigma):
"""Return the normal pdf evaluated at *x*; args provides *mu*, *sigma*"
.. note:: same as scipy.stats.norm but implemented to avoid scipy dependency
"""
return 1. / (np.sqrt(2 * np.pi) * sigma) * np.exp(-0.5 * (1. / sigma *
(x - mu))**2)
def generalized_anscombe(x, mu, sigma, gain=1.0):
"""Compute the generalized anscombe variance stabilizing transform
Data should be a mixture of poisson and gaussian noise.
The input signal z is assumed to follow the Poisson-Gaussian noise
model::
x = gain * p + n
where gain is the camera gain and mu and sigma are the read noise
mean and standard deviation. X should contain only positive values.
Negative values are ignored. Biased for low counts
"""
try:
# If a dataframe, we do not want to change it
y = gain * x + (gain**2) * 3.0 / 8.0 + sigma**2 - gain * mu
return (2.0 / gain) * np.sqrt(np.maximum(y, 0.0))
except:
x = np.array(x)
y = gain * x + (gain**2) * 3.0 / 8.0 + sigma**2 - gain * mu
return (2.0 / gain) * np.sqrt(np.maximum(y, 0.0))
def anscombe(x):
r"""Compute the anscombe variance stabilizing transform.
:param x: noisy Poisson-distributed data
:return: data with variance approximately equal to 1.
Reference: Anscombe, F. J. (1948), "The transformation of Poisson,
binomial and negative-binomial data", Biometrika 35 (3-4): 246-254
For Poisson distribution, the mean and variance are not independent. The
anscombe transform aims at transforming the data so that the variance
is about 1 for large enough mean; For mean zero, the varaince is still
zero. So, it transform Poisson data to approximately Gaussian data with
mean :math:`\sqrt{x+3/8} - 1/(4m^{1/2})`
"""
#if np.mean(x) <4:
# logger.warning("Mean of input data below 4")
try:
# If a dataframe, we do not want to change it
return 2.0 * np.sqrt(x + 3.0 / 8.0)
except:
return 2.0 * np.sqrt(np.array(x) + 3.0 / 8.0)
def get_var_coef(self):
return np.sqrt(self.df["cov"].var()) / self.get_mean_cov()