Abstract
Ultrasound tomography (UST) has seen a revival of interest in the past decade, especially for breast imaging, due to improvements in both ultrasound and computing hardware. In particular, three-dimensional UST, a fully tomographic method in which the medium to be imaged is surrounded by ultrasound transducers, has become feasible. This has led to renewed attention on UST image reconstruction algorithms. In this paper, a comprehensive derivation and study of a robust framework for large-scale bent-ray UST in 3D for a hemispherical detector array is presented. Two ray-tracing approaches are derived and compared. More significantly, the problem of linking the rays between emitters and receivers, which is challenging in 3D due to the high number of degrees of freedom for the trajectory of rays, is analysed both as a minimisation and as a root-finding problem. The ray-linking problem is parameterised for a convex detection surface and two robust, accurate, and efficient derivative-free ray-linking algorithms are formulated and demonstrated and compared with a Jacobian-based benchmark approach. To stabilise these methods, novel adaptive-smoothing approaches are proposed that control the conditioning of the update matrices to ensure accurate linking. The nonlinear UST problem of estimating the sound speed was recast as a series of linearised subproblems, each solved using the above algorithms and within a steepest descent scheme. The whole imaging algorithm was demonstrated to be robust and accurate on realistic data simulated using a full-wave acoustic model and an anatomical breast phantom, and incorporating the errors due to time-of-flight (TOF) picking that would be present with measured data. This method can used to provide a low-artefact, quantitatively accurate, 3D sound speed maps. In addition to being useful in their own right, such 3D sound speed maps can be used to initialise full-wave inversion methods, or as an input to photoacoustic tomography reconstructions.
Highlights
Ultrasound tomography (UST) has received growing interest in the past decade, especially for breast imaging [18, 23, 32, 51, 67, 68]
The hope is that this quantitative information about the tissue properties can be used to aid diagnosis [58]. (It should be noted that UST is very different from conventional ultrasound imaging as widely-used in clinical settings, which is a backward-mode imaging modality that uses a small-area probe to give qualitative reflection images in real time.) In addition, photoacoustic tomography, which has been receiving a great deal of attention in the past decade for 3D breast imaging [38, 49], depends on quantitatively accurate knowledge of the sound speed distribution
Shows the relative error (RE) of the optimal reconstructed images, showing—by comparing to figure 8—that the images reconstructed using the bent-ray approach from the data sets with signal-to-noise ratios (SNR) > 25 dB are more accurate than the image reconstructed using the straight approach from the data sets with 40 dB SNR
Summary
Ultrasound tomography (UST) has received growing interest in the past decade, especially for breast imaging [18, 23, 32, 51, 67, 68]. The acoustic pressure is modelled using the wave equation for heterogeneous media, and the unknown acoustic property (here the sound speed) is iteratively updated using a computation of gradient of the L2-norm of the discrepancy [54] This class of methods can provide high spatial resolution images, are flexible, in the sense that different forward models can be used, and make use of all the information in the measured data. Ray-based methods are commonly used to provide the initial guess for full-wave inversions [39, 44, 67, 68, 70] This approach, initially inspired by x-ray tomography, uses measurements of the time-of-flight (TOF) of the acoustic signals across the imaging target to reconstruct the slowness distribution (the reciprocal of the sound speed) using radon-type inversion techniques [3]. In the appendix A, the approach used for calculation of the TOFs (a slight modification of [33]) is presented
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