Reduction of variance in spectral estimates for correction of ultrasonic aberration

Astheimer, Jeffrey P.; Pilkington, Wayne C.; Waag, Robert C.

doi:10.1109/tuffc.2006.1588393

Cited by 8 publications

(9 citation statements)

References 6 publications

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“…The random fluctuation is characterized by a standard deviation, defined as the square root of the mean square of the fluctuation. The term variance is usually used in the literature 15,16 and refers to the square of the standard deviation. The standard deviation seems to have more physical meaning though, as the quality of focusing depends on the standard deviation of the phase of the Green's function rather than its variance.…”

Section: Variance and Standard Deviation Of The Estimationmentioning

confidence: 99%

“…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%

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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 Journal of the Acoustical Society of America

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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.

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Section: Variance and Standard Deviation Of The Estimationmentioning

confidence: 99%

Section: Green Function Estimation and Focusing In The Presence Omentioning

confidence: 99%

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 Journal of the Acoustical Society of America

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“…Propagation path effects in aberration estimation and correction in the absence of a point target using statistical methods have been investigated by Waag and Astheimer [64], Astheimer et al . [65], and Tillet et al . [66].…”

Section: Introductionmentioning

confidence: 99%

Pitch-catch phase aberration correction of multiple isoplanatic patches for 3-D transcranial ultrasound imaging

Lindsey

Smith

2013

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Having previously presented the ultrasound brain helmet, a system for simultaneous 3-D ultrasound imaging via both temporal bone acoustic windows, the scanning geometry of this system is utilized to allow each matrix array to serve as a correction source for the opposing array. Aberration is estimated using cross-correlation of RF channel signals, followed by least mean squares solution of the resulting overdetermined system. Delay maps are updated and real-time 3-D scanning resumes. A first attempt is made at using multiple arrival time maps to correct multiple unique aberrators within a single transcranial imaging volume, i.e., several isoplanatic patches. This adaptive imaging technique, which uses steered unfocused waves transmitted by the opposing, or beacon, array, updates the transmit and receive delays of 5 isoplanatic patches within a 64° × 64° volume. In phantom experiments, color flow voxels above a common threshold have also increased by an average of 92%, whereas color flow variance decreased by an average of 10%. This approach has been applied to both temporal acoustic windows of two human subjects, yielding increases in echo brightness in 5 isoplanatic patches with a mean value of 24.3 ± 9.1%, suggesting that such a technique may be beneficial in the future for performing noninvasive 3-D color flow imaging of cerebrovascular disease, including stroke.

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“…To solve this problem, different adaptive focusing approaches [4][5][6][7] based on signal processing of the backscattered echoes were proposed with a limited success in terms of practical applicability. Despite its elegance, the direct application of the iterative time-reversal approach is also unable to converge towards an estimate of the Green's functions in such random media.…”

mentioning

confidence: 99%

Time Reversal of Speckle Noise

2011

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Focusing a wave in an unknown inhomogeneous medium is an open problem in wave physics. This work presents an iterative method able to focus in pulse-echo mode in an inhomogeneous medium containing a random distribution of scatterers. By performing a coherent summation of the random echoes backscattered from a set of points surrounding the desired focus, a virtual bright pointlike reflector is generated. A time-reversal method enables an iterative convergence towards the optimal wave field focusing at the location of this virtual scatterer. Thanks to this iterative time-reversal process, it is possible to focus at any arbitrary point in the heterogeneous medium even in the absence of pointlike source. An experimental demonstration is given for the correction of strongly distorted images in the field of medical ultrasound imaging. This concept enables envisioning many other applications in wave physics.

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Reduction of variance in spectral estimates for correction of ultrasonic aberration

Cited by 8 publications

References 6 publications

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

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

Pitch-catch phase aberration correction of multiple isoplanatic patches for 3-D transcranial ultrasound imaging

Time Reversal of Speckle Noise

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