Statistical estimation of propagation path parameters for ultrasonic aberration correction

The decomposition of the time reversal operator, known by the French acronym DORT, is widely used to detect, locate, and focus on scatterers in various domains such as underwater acoustics, medical ultrasound, and nondestructive evaluation. In the case of point-scatterers, the theory is well understood: The number of nonzero eigenvalues is equal to the number of scatterers, and the eigenvectors correspond to the scatterers Green's function. In the case of extended objects, however, the formalism is not as simple. It is shown here that, in the Fraunhofer approximation, analytical solutions can be found and that the solutions are functions called prolate spheroidal wave-functions. These functions have been studied in information theory as a basis of band-limited and time-limited signals. They also arise in optics. The theoretical solutions are compared to simulation results. Most importantly, the intuition that for an extended objects, the number of nonzero eigenvalues is proportional to the number of resolution cell in the object is justified. The case of three-dimensional objects imaged by a two-dimensional array is also dealt with. Comparison with previous solutions is made, and an application to super-resolution of scatterers is presented.

Section: B Application To Green's Function Estimation and Focusingmentioning

confidence: 99%

The prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the Fraunhofer approximation

Robert

Fink

2009

“…Then the differential delays can be integrated to yield the wave-front profile. Implementations in the time 28 and temporal frequency domain 10,16 exist. This would be equivalent to integrating the phase of the coefficients of the first diagonal ͑KK H ͒ m,m+1 of the FDORT matrix, corresponding to correlation between neighbors.…”

Section: Green Function Estimation and Focusing In The Presence Omentioning

confidence: 99%

“…This was enough to obtain a good estimate of the Green's functions in both simulations and experimental results. With a twodimensional ͑2D͒ array, 10,19 and 3D imaging, the number of realizations can be increased by taking additional realizations in the elevation dimension ͑the third dimension͒. In Refs.…”

Section: Variance and Standard Deviation Of The Estimationmentioning

confidence: 99%

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Green’s function estimation in speckle using the decomposition of the time reversal operator: Application to aberration correction in medical imaging

Robert

Fink²

2008

The FDORT method (French acronym for decomposition of the time reversal operator using focused beams) is a time reversal based method that can detect point scatterers in a heterogeneous medium and extract their Green's function. It is particularly useful when focusing in a heterogeneous medium. This paper generalizes the theory of the FDORT method to random media (speckle), and shows that it is possible to extract Green's functions from the speckle signal using this method. Therefore it is possible to achieve a good focusing even if no point scatterers are present. Moreover, a link is made between FDORT and the Van Cittert-Zernike theorem. It is deduced from this interpretation that the normalized first eigenvalue of the focused time reversal operator is a well-known focusing criterion. The concept of an equivalent virtual object is introduced that allows the random problem to be replaced by an equivalent deterministic problem and leads to an intuitive understanding of FDORT in speckle. Applications to aberration correction are presented. The reduction of the variance of the Green's function estimate is discussed. Finally, it is shown that the method works well in the presence of strong interfering scatterers.

“…Versions of the aberration correction algorithms have been verified in experiments to produce essentially diffractionlimited focusing. 5,6 Quantification of resolution limits in the presence of aberration and with the use of aberration correction will lead to development of improved focusing techniques. These techniques could also be used to tailor transducer apertures to obtain the best balance between resolution and cost for commercial systems that image in vivo human tissues, resulting in improved diagnostic capabilities.…”

Section: Introductionmentioning

confidence: 99%

Comparison of temporal and spectral scattering methods using acoustically large breast models derived from magnetic resonance images

Hesford

Tillett

Astheimer

et al. 2014

Self Cite

Accurate and efficient modeling of ultrasound propagation through realistic tissue models is important to many aspects of clinical ultrasound imaging. Simplified problems with known solutions are often used to study and validate numerical methods. Greater confidence in a timedomain k-space method and a frequency-domain fast multipole method is established in this paper by analyzing results for realistic models of the human breast. Models of breast tissue were produced by segmenting magnetic resonance images of ex vivo specimens into seven distinct tissue types. After confirming with histologic analysis by pathologists that the model structures mimicked in vivo breast, the tissue types were mapped to variations in sound speed and acoustic absorption. Calculations of acoustic scattering by the resulting model were performed on massively parallel supercomputer clusters using parallel implementations of the k-space method and the fast multipole method. The efficient use of these resources was confirmed by parallel efficiency and scalability studies using large-scale, realistic tissue models. Comparisons between the temporal and spectral results were performed in representative planes by Fourier transforming the temporal results. An RMS field error less than 3% throughout the model volume confirms the accuracy of the methods for modeling ultrasound propagation through human breast.