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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 RF to B-Mode Generation
Ultrasound imaging employs acoustic pressure waves to gather information describing changes in tissue permeability. A transducer emits an ultrasound beam at discrete time intervals and translates the pressure wave echo into radio frequency waves. These electromagnetic waves are then readable with an analog-to-digital converter for machine input.
The following example notebook showcases how the ITK Ultrasound module may be used to generate a human-readable brightness-mode (B-Mode) image from RF-Mode input collected from a transducer. The input image MouseLiverRF.mha describes one ultrasound capture representing axial, lateral, and time dimensions. The itk.b_mode_image_filter function performs envelope detection on the RF signal along the axial direction and applies a logarithmic intensity transform to the image output for visibility.
Step1:  Read RF Image
The example RF image represents raw transducer output describing a mouse liver sample. Taken alone, the RF sample fails to deliver good insight into the mouse liver image. We must perform envelope detection and brightness filtering on the image in order to generate a BMode image for analysis.
Step2:  The RF image represents transducer results over a certain time period with regards to the axial direction (along the beam) and the lateral direction (normal to the beam). Data along the axial direction describes how the ultrasound wave echo propagated through the image medium. Here we use matplotlib to visualize the waveform at a fixed lateral position at T=0.
Step3:  Perform Envelope Detection
To understand how the pressure wave echo travelled through the imaging medium we apply amplitude demodulation through envelope detection.
Step4:  Apply Logarithmic Transform
To get data on a more useful scale for analysis we apply a log10 transform over the intensity image. Other transforms such as smoothing and clamping may also be applied to help translate the intensity image into a human-interpretable format.
Step5:  Use BModeImageFilter for RF-to-BMode image generation
itk.BModeImageFilter combines envelope detection and logarithmic transformation to produce a straightforward pipeline for BMode image generation. Note that MouseLiverB.mha is produced using a similar method but with additional transformations for visibility and is intended only for general comparison here.
Step6:  Beamline Over Time
We can plot pixel values along the axial direction over time to investigate how the BMode filter transforms data.
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Python Code:
# Install notebook dependencies
import sys
#!{sys.executable} -m pip install itk itk-ultrasound numpy matplotlib itkwidgets
import itk
from matplotlib import pyplot as plt
from itkwidgets import view, compare
Explanation: RF to B-Mode Generation
Ultrasound imaging employs acoustic pressure waves to gather information describing changes in tissue permeability. A transducer emits an ultrasound beam at discrete time intervals and translates the pressure wave echo into radio frequency waves. These electromagnetic waves are then readable with an analog-to-digital converter for machine input.
The following example notebook showcases how the ITK Ultrasound module may be used to generate a human-readable brightness-mode (B-Mode) image from RF-Mode input collected from a transducer. The input image MouseLiverRF.mha describes one ultrasound capture representing axial, lateral, and time dimensions. The itk.b_mode_image_filter function performs envelope detection on the RF signal along the axial direction and applies a logarithmic intensity transform to the image output for visibility.
End of explanation
SAMPLING_FREQUENCY = 40e6 # Hz
SAMPLING_PERIOD = SAMPLING_FREQUENCY ** -1
# Image dimensions: [axial, lateral, frame]
rf_image = itk.imread('Input/MouseLiverRF.mha', itk.F)
print(itk.size(rf_image))
view(rf_image)
Explanation: Read RF Image
The example RF image represents raw transducer output describing a mouse liver sample. Taken alone, the RF sample fails to deliver good insight into the mouse liver image. We must perform envelope detection and brightness filtering on the image in order to generate a BMode image for analysis.
End of explanation
def visualize_beam_waveform(image, lateral_idx=0, time_idx=0):
    arr = itk.array_view_from_image(image)
    x_labels = [idx * SAMPLING_PERIOD for idx in range(0,arr.shape[2])]
    plt.plot(x_labels,arr[time_idx,lateral_idx,:])
    plt.xlabel('Sampling Time ($\mu$s)')
    plt.ylabel('Response')
    plt.show()
# Visualize one RF waveform
visualize_beam_waveform(rf_image)
Explanation: The RF image represents transducer results over a certain time period with regards to the axial direction (along the beam) and the lateral direction (normal to the beam). Data along the axial direction describes how the ultrasound wave echo propagated through the image medium. Here we use matplotlib to visualize the waveform at a fixed lateral position at T=0.
End of explanation
# Note that dimension in direction of analytic signal filter must be
# a multiple of 2,3,5 for the FFT to be valid
padded_image = itk.fft_pad_image_filter(rf_image)
complex_image = itk.analytic_signal_image_filter(rf_image,direction=0)
modulus_image = itk.complex_to_modulus_image_filter(complex_image)
visualize_beam_waveform(modulus_image)
view(modulus_image)
Explanation: Perform Envelope Detection
To understand how the pressure wave echo travelled through the imaging medium we apply amplitude demodulation through envelope detection.
End of explanation
log_image = itk.log10_image_filter(modulus_image)
visualize_beam_waveform(log_image)
view(log_image)
Explanation: Apply Logarithmic Transform
To get data on a more useful scale for analysis we apply a log10 transform over the intensity image. Other transforms such as smoothing and clamping may also be applied to help translate the intensity image into a human-interpretable format.
End of explanation
bmode_image = itk.imread('Input/MouseLiverB.mha', itk.F)
filtered_image = itk.b_mode_image_filter(rf_image,direction=1)
compare(filtered_image, bmode_image)
Explanation: Use BModeImageFilter for RF-to-BMode image generation
itk.BModeImageFilter combines envelope detection and logarithmic transformation to produce a straightforward pipeline for BMode image generation. Note that MouseLiverB.mha is produced using a similar method but with additional transformations for visibility and is intended only for general comparison here.
End of explanation
# BMode Image (calculated)
visualize_beam_waveform(filtered_image)
# BMode Image (expected)
arr = itk.array_view_from_image(bmode_image)
plt.plot(arr[0,:,0])
plt.show()
Explanation: Beamline Over Time
We can plot pixel values along the axial direction over time to investigate how the BMode filter transforms data.
End of explanation
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