Fast Transient Imaging
A Python framework revolving around reconstruction of impulse responses from AMCW lidar measurements.
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Functions | |
def | GetMaximumEntropySpectralEstimate (TrigonometricMoments, X) |
This function evaluates a special density function at the given location X (in radians) and returns the result as array of shape identical to that of X. More... | |
def | GetMaximumEntropySpectralEstimateCumulative (TrigonometricMoments, X) |
This function evaluates the cumulative density of the density function given by GetMaximumEntropySpectralEstimate(). More... | |
def | GetPisarenkoEstimate (TrigonometricMoments) |
Given a vector of trigonometric moments without (!) a zeroth moment this function computes a distribution consisting of TrigonometricMoments.size Dirac-delta distributions which describes this measurement correctly. More... | |
def | GetMaximumEntropySpectralEstimateMoment (TrigonometricMoments, MomentIndex) |
This function computes trigonometric moments of the distribution provided by GetMaximumEntropySpectralEstimate(). More... | |
def | GetValidMomentCircle (TrigonometricMoments) |
Given a vector of m trigonometric moments, this function returns the circle containing all acceptable values for trigonometric moment m+1. More... | |
def Reconstruction.GetMaximumEntropySpectralEstimate | ( | TrigonometricMoments, | |
X | |||
) |
This function evaluates a special density function at the given location X (in radians) and returns the result as array of shape identical to that of X.
The density function produces the prescribed trigonometric moments (starting with the zeroth moment) and has minimal Burg entropy. If the given moments do not admit a positive density, it returns None.
def Reconstruction.GetMaximumEntropySpectralEstimateCumulative | ( | TrigonometricMoments, | |
X | |||
) |
This function evaluates the cumulative density of the density function given by GetMaximumEntropySpectralEstimate().
The integral is computed numerically using the trapezoidal rule, so X should provide a sufficiently dense sampling. If the given moments do not admit a positive density, it returns None.
def Reconstruction.GetPisarenkoEstimate | ( | TrigonometricMoments | ) |
Given a vector of trigonometric moments without (!) a zeroth moment this function computes a distribution consisting of TrigonometricMoments.size Dirac-delta distributions which describes this measurement correctly.
def Reconstruction.GetMaximumEntropySpectralEstimateMoment | ( | TrigonometricMoments, | |
MomentIndex | |||
) |
This function computes trigonometric moments of the distribution provided by GetMaximumEntropySpectralEstimate().
TrigonometricMoments | The prescribed trigonometric moments of the distribution starting with the zeroth moment. |
MomentIndex | The integer index of the requested moments. This can be an array of integers in which case the moments for all these indices are computed. |
def Reconstruction.GetValidMomentCircle | ( | TrigonometricMoments | ) |
Given a vector of m trigonometric moments, this function returns the circle containing all acceptable values for trigonometric moment m+1.