page_title: Doppler echocardiography
section_title: Interpolation method (parabolic fit)
hierarchical_section_title: Doppler echocardiography / 2D Doppler imaging / Speckle tracking / Sub pixel accuracy / Interpolation method (parabolic fit)
caption_attribution_description: English: Parabolic fit to find peak
context_page_description: Doppler echocardiography is a procedure that uses Doppler ultrasonography to examine the heart. An echocardiogram uses high frequency sound waves to create an image of the heart while the use of Doppler technology allows determination of the speed and direction of blood flow by utilizing the Doppler effect.
  An echocardiogram can, within certain limits, produce accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the ultrasound beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, any abnormal communications between the left and right side of the heart, any leaking of blood through the valves, calculation of the cardiac output and calculation of E/A ratio. Contrast-enhanced ultrasound-using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.
  An advantage of Doppler echocardiography is that it can be used to measure blood flow within the heart without invasive procedures such as cardiac catheterization.
context_section_description: As shown in the right figure, parabolic fit can help find the real peak of the cross correlation function. The equation for parabolic fit in 1D is:
  where  is the cross correlation function and  is the originally found peak.  is then used to find the displacement of scatterers after  interpolation. For the 2D scenario, this is done in both the axial and lateral dimensions. Some other techniques can be used to improve the accuracy and robustness of the interpolation method, including parabolic fit with bias compensation and matched filter interpolation.
caption: Interpolation to find peak
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