Filter phasor coordinates

Functions for filtering phasor coordinates.

Filtering phasor coordinates improves signal quality by reducing noise while preserving relevant features. Two of the most common filtering methods are median filtering and wavelet filtering.

Import required modules and functions:

from phasorpy.datasets import fetch
from phasorpy.filter import (
    phasor_filter_median,
    phasor_filter_pawflim,
    phasor_threshold,
)
from phasorpy.io import signal_from_imspector_tiff
from phasorpy.lifetime import phasor_calibrate
from phasorpy.phasor import phasor_from_signal
from phasorpy.plot import plot_image, plot_phasor

Get calibrated phasor coordinates

Read a time-correlated single photon counting (TCSPC) histogram from a file. A homogeneous solution of Fluorescein (4.2 ns) was imaged as a reference:

signal = signal_from_imspector_tiff(fetch('Embryo.tif'))
frequency = signal.attrs['frequency']

reference_signal = signal_from_imspector_tiff(fetch('Fluorescein_Embryo.tif'))
assert reference_signal.attrs['frequency'] == frequency

Calculate and calibrate phasor coordinates:

mean, real, imag = phasor_from_signal(signal, axis=0)

reference_mean, reference_real, reference_imag = phasor_from_signal(
    reference_signal, axis=0
)

real, imag = phasor_calibrate(
    real,
    imag,
    reference_mean,
    reference_real,
    reference_imag,
    frequency=frequency,
    lifetime=4.2,
)

Unfiltered

Plot the unfiltered, calibrated phasor coordinates after applying a threshold based on the mean intensity to remove background values:

plot_phasor(
    *phasor_threshold(mean, real, imag, mean_min=1)[1:],
    frequency=frequency,
    title='Unfiltered phasor coordinates',
)

Median filter

Median filtering replaces each pixel value with the median of its neighboring values, reducing noise while preserving edges. The function phasorpy.filter.phasor_filter_median() applies a median filter to phasor coordinates. Typically, applying a 3x3 kernel once to three times is sufficient to remove noise while maintaining important features:

mean_filtered, real_filtered, imag_filtered = phasor_filter_median(
    mean, real, imag, repeat=3, size=3
)

Thresholds should be applied after filtering:

mean_filtered, real_filtered, imag_filtered = phasor_threshold(
    mean_filtered, real_filtered, imag_filtered, mean_min=1
)

Plot the median-filtered and thresholded phasor coordinates:

plot_phasor(
    real_filtered,
    imag_filtered,
    frequency=frequency,
    title='Median-filtered phasor coordinates (3x3 kernel, 3 repetitions)',
)

Increasing the number of repetitions or the filter kernel size can further reduce noise, but may also remove relevant features:

mean_filtered, real_filtered, imag_filtered = phasor_threshold(
    *phasor_filter_median(mean, real, imag, repeat=6, size=5), mean_min=1
)

plot_phasor(
    real_filtered,
    imag_filtered,
    frequency=frequency,
    title='Median-filtered phasor coordinates (5x5 kernel, 6 repetitions)',
)

The smoothing effect of median-filtering is demonstrated by plotting the real components of the filtered and unfiltered phasor coordinates as images:

plot_image(
    phasor_threshold(mean, real, imag, mean_min=1)[1],
    real_filtered,
    vmin=0.4,
    vmax=0.9,
    labels=['Unfiltered', 'Median-filtered'],
    title='Real component of phasor coordinates',
)

pawFLIM wavelet filter

Filtering based on wavelet decomposition is another method to reduce noise. The function phasorpy.filter.phasor_filter_pawflim() is based on the pawFLIM library. While the median filter is applicable to any type of phasor coordinates, the pawFLIM filter requires calibrated phasor coordinates from FLIM measurements and at least one harmonic and its corresponding second harmonic (the 1st and 2nd harmonic in this example):

harmonic = [1, 2]

mean, real, imag = phasor_from_signal(signal, axis=0, harmonic=harmonic)

reference_mean, reference_real, reference_imag = phasor_from_signal(
    reference_signal, axis=0, harmonic=harmonic
)

real, imag = phasor_calibrate(
    real,
    imag,
    reference_mean,
    reference_real,
    reference_imag,
    frequency=frequency,
    lifetime=4.2,
    harmonic=harmonic,
)

Apply the pawFLIM wavelet filter to the calibrated phasor coordinates:

mean_filtered, real_filtered, imag_filtered = phasor_threshold(
    *phasor_filter_pawflim(mean, real, imag, harmonic=harmonic), mean_min=1
)

Plot the pawFLIM-filtered and thresholded phasor coordinates:

plot_phasor(
    real_filtered[0],
    imag_filtered[0],
    frequency=frequency,
    title='pawFLIM-filtered phasor coordinates (sigma=2, levels=1)',
)

Increasing the significance level sigma of the comparison between phasor coordinates or the maximum averaging area levels can reduce noise further:

mean_filtered, real_filtered, imag_filtered = phasor_filter_pawflim(
    mean, real, imag, harmonic=harmonic, sigma=5, levels=3
)

mean_filtered, real_filtered, imag_filtered = phasor_threshold(
    mean_filtered, real_filtered, imag_filtered, mean_min=1
)

plot_phasor(
    real_filtered[0],
    imag_filtered[0],
    frequency=frequency,
    title='pawFLIM-filtered phasor coordinates (sigma=5, levels=3)',
)

Plot the real components of the filtered and unfiltered phasor coordinates as images:

plot_image(
    phasor_threshold(mean, real, imag, mean_min=1)[1],
    real_filtered,
    vmin=0.4,
    vmax=0.9,
    labels=['Unfiltered', 'pawFLIM-filtered'],
    title='Real component of phasor coordinates',
)