A Total Variation Regularizer With Partially Known Support for Pulse-Echo Speed-of-Sound Imaging

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Pulse amplitude and quality01:17

Pulse amplitude and quality

Pulse amplitude is a crucial indicator of cardiac health because it provides valuable insights into the strength of left ventricular contractions and the overall uniformity of blood circulation within the vasculature. The strength of the pulse is directly related to the force with which the heart contracts and the volume of blood being pumped.
A weak or absent pulse may indicate reduced cardiac output or poor left ventricular contraction, which can be signs of cardiovascular dysfunction or...
Regulation of Pulse01:20

Regulation of Pulse

Pulse regulation involves physiological mechanisms that ensure adequate blood flow throughout the body. The heartbeat, regulated by the autonomic nervous system, is influenced by hormonal balance, physical activity, and emotional state.
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Intensity and Pressure of Sound Waves01:05

Intensity and Pressure of Sound Waves

The intensity of sound waves can be related to displacement and pressure amplitudes by using their wave expressions and the definition of intensity. The critical step to achieve this is to write the power delivered by the particles on the wave as the product of force and velocity and simplify the force per unit area as the pressure. The velocity of the medium's particles can be derived from the displacement.
Unlike the time average of a sinusoidal term, which is zero since it is positive and...