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

Abstract

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.

Reverberation nulling and echo enhancement at low frequency using waveguide invariance

“…Then, a reverberation subspace, denoted by U(R k ,ω-Δω), is obtained from the kth segment data with a certain frequency shift to construct a project matrix P in eq. (15). After that, the projection matrix P is applied to the next segment of the return signal data x(R k+1 ,ω) to null the reverberation component embedded in the (k+1)th segment (i.e.…”

“…To solve the above problem, an echo-to-reverberation enhancement method based on decomposition of the time reversal operator (DORT) [12][13][14][15][16] with forward and backward reverberation nulling has been proposed [17]. This method can focus sound energy at the target while nulling the energy at the bottom near the target range simultaneously, substantially enhancing the echo-to-reverberation ratio without a probe source and prior knowledge about the relative scattering intensity of target and bottom.…”

Time Reversal of Speckle Noise

“…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.…”

Time reversal transfer: Exploring the robustness of time reversed acoustics in media with geometry perturbations

“…2 Typically, when performing noncontact (e.g., vibrometer) measurements, a reciprocal version of the time reversal experiment is used. 1 These properties of TRA were found useful in many fields, such as underwater acoustics and telecommunication, 3 seismology, 4 medical imaging, 5 and non-destructive testing (NDT). The range of TRA applications in NDT is extensive, e.g., the decomposition of the time reversal operator allows selective detection and focusing on individual scatterers; 6 TRA allows location and characterization of acoustic emission sources, 7 structural health monitoring, 8 etc.…”