Attenuation estimation by repeatedly solving the forward scattering problem

Fast linear least-squares method for ultrasound attenuation and backscatter estimation

“…It can be observed from equation ( 2) that the attenuation term has a depth-dependence. Existing methods like [25] deal with the local attenuation estimation at each depth within the probed region. To be more precise, the attenuation estimation for a homogeneous medium was performed in [25] using a non-linear least squares (NLS) framework where an optimum attenuation coefficient was computed at each depth by minimizing the squared error between the model (ignoring the diffraction effects and the backscatter coefficient in (2)) and the spectrum of the recorded backscattered signal at that particular depth.…”

“…Existing methods like [25] deal with the local attenuation estimation at each depth within the probed region. To be more precise, the attenuation estimation for a homogeneous medium was performed in [25] using a non-linear least squares (NLS) framework where an optimum attenuation coefficient was computed at each depth by minimizing the squared error between the model (ignoring the diffraction effects and the backscatter coefficient in (2)) and the spectrum of the recorded backscattered signal at that particular depth. For the estimation, a sliding window technique was used, dividing the axis into overlapping windows 1 While we work with the magnitude spectrum of the backscattered signal, it is straightforward to relate the parameters of interest in this model with those in the backscattered power spectrum model (represented here by (⋅) ′ ) [26].…”

“…Another class of approaches for tissue parameters estimation is based on minimizing the squared error between the measured spectrum of the backscattered signal and a parametric model of the spectrum. One such method for attenuation estimation was proposed in [25], solving a non-linear least squares problem to obtain local attenuation estimates. An exhaustive search was performed over a range of possible attenuation coefficients, making it computationally time consuming and hence, unsuitable for real-time applications.…”

“…Nonetheless, the method focused on computing only an effective attenuation coefficient for the tissue path till the depth of interest. As such, the methods in both [25] and [26], did not exploit the depth information directly. Working in this direction, some regularized approaches have been developed recently that aim to enforce piece-wise continuity of the underlying tissue properties using a suitable regularization term in the cost function to be minimized.…”

Real-time intraoperative ultrasound in brain surgery: neuronavigation and use of contrast-enhanced image fusion

“… A way to correct the attenuation of the sound pulse is called time-gain compensation: this strategy makes equally echogenic tissues look the same even if they are located at different depths (33)(34)(35).  If possible the unscrubbed theatre team can help optimizing the orientation of the surgical table so that at time of IoUS the resection surface is kept horizontal with respect to gravity: this may help to minimize air trapping within the cavity (23,36).…”