8,014 research outputs found
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast
Ultrasound Tomography 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 ultrasound tomography, a
fully tomographic method in which the medium to be imaged is surrounded by
ultrasound transducers, has become feasible. In this paper, a comprehensive
derivation and study of a robust framework for large-scale bent-ray ultrasound
tomography 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 three robust, accurate, and efficient ray-linking algorithms are
formulated and demonstrated. 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 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
Tosio Kato (1917–1999)
Tosio Kato was born August 25, 1917, in Kanuma City, Tochigi-ken, Japan. His early training was in physics. He obtained
a B.S. in 1941 and the degree of Doctor of Science in 1951, both at the University of Tokyo. Between these events he published
papers on a variety of subjects, including pair creation by gamma rays, motion of an object in a fluid, and results
on spectral theory of operators arising in quantum mechanics. His dissertation was entitled “On the convergence of the
perturbation method”.
Kato was appointed assistant professor of physics at the University of Tokyo in 1951 and was promoted to professor of
physics in 1958. During this time he visited the University of California at Berkeley in 1954–55, New York University in 1955,
the National Bureau of Standards in 1955–56, and Berkeley and the California Institute of Technology in 1957–58. He was
appointed professor of mathematics at Berkeley in 1962 and taught there until his retirement in 1988. He supervised
twenty-one Ph.D. students at Berkeley and three at the University of Tokyo.
Kato published over 160 papers and 6 monographs, including his famous book Perturbation Theory for Linear
Operators [K66b]. Recognition for his important work included the Norbert Wiener Prize in Applied Mathematics, awarded
in 1980 by the AMS and the Society for Industrial and Applied Mathematics. He was particularly well known for his work on
Schrödinger equations of nonrelativistic quantum mechanics and his work on the Navier-Stokes and Euler equations of
classical fluid mechanics. His activity in the latter area remained at a high level well past retirement and continued until his
death on October 2, 1999
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