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8 July 1994 Ultrasonic reflection tomography: specific problems and adapted solutions
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Ultrasonic reflection tomography borrows from echography its fundamental physical basis (exploitation of the diffracted echoes by the medium imaged) and from X tomography its numerical procedure of reconstruction. The method results from a linearization of the inverse problem, justified from an acoustical point of view, by the very small inhomogeneities of biological media. One can show that the inverse problem is reduced to a Fourier Synthesis problem based on lacunary data since the measured spectra are angulary equidistributed slices of the Fourier plane. The spectral extent of these cuts isconditioned by the frequency band of the echogrammes, that is, the high frequencies of the image correspond to the high temporal frequencies of the signals. The two problems raised are first the restauration of high frequencies (at the limit the extrapolation of the band analysed) which directly conditions resolution abilities of the instrument. Second, we have to face the problem of the angular interpolation in order to reduce reconstruction noise. Concerning the last point, we have developed a non linear filter operating on the data which contributes (in terms of energy) to the reconstruction of a given pixel. We have shown that these data are distributed on the "contributions circle" where, high frequency components mainly characterized artefacts induced by the reconstruction (backprojection) procedure. On the other hand, lower frequency components result from scattering phenomena. This distinction between useful information and artefact is revealed through a modelization of the interactions between biological interfaces and finite aperture ultrasonic beams. For the extrapolation of the band which allows good image restitution, we have integrated a deconvolution procedure based on a second order statistics filter. This enables us to reduce the input noise by a detection threshold. In addition, the in-line procedure implemented is well adapted to real-time applications. The performances reached, thanks to our experimental tomograph, are described through comparisons of the images obtained.
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Sewa Enyonam Mensah and J. P. Lefebvre "Ultrasonic reflection tomography: specific problems and adapted solutions", Proc. SPIE 2299, Mathematical Methods in Medical Imaging III, (8 July 1994);

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