Computer Science – Sound
Scientific paper
Dec 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003invpr..19.....b&link_type=abstract
Inverse Problems, Volume 19, Issue 6, pp. (2003).
Computer Science
Sound
Scientific paper
Imaging is a rapidly growing area in applied sciences. It has an interdisciplinary character and a wide range of applications such as medicine, nondestructive evaluation, microscopy and astronomy, as well as many industrial processes. The increasing demand on imaging is due to the change of role of vision. Today vision is not through eyes only but complemented, for instance, by ultrasound, x-ray computerized tomography (CT), electrical impedance tomography (EIT), to name but a few. Moreover, traditional imaging systems such as microscopes and telescopes are now equipped with detection instruments (CCD cameras) and the resulting digital images are currently processed and enhanced. Finally, the relevance of imaging for industry is best documented by a recent feature by Robert West (West R 2003 In industry, seeing is believing Physics World June 2003). Today the scope of imaging has broadened and plays a central role in many different areas ranging, for instance, from remote sensing to seismology.
In most cases the new imaging techniques are based on indirect measurements of physical parameters; therefore they quite naturally lead to the demand of solving (linear or nonlinear) inverse problems. This indicates the central role that inverse problems have in imaging science.
This special section highlights several topics of recent advances in imaging. The first five papers concern problems originating from medical imaging which can have important applications in other domains. The paper by Ji et al covers a new and promising diagnostic tool in medicine: the identification of abnormal tissues by elastic shear wave properties. The two subsequent papers by Louis and by Defrise et al concern 3D cone beam tomography which is the most recent and advanced technique in x-ray CT. Both the case of circular and helical scanning are considered. The paper by Natterer et al is also about tomography but is intended to exploit the mathematical analogies between x-ray CT and synthetic aperture radar, achieving a unified approach to the important problem of estimating resolution in these two completely different imaging techniques. Electrical impedance tomography is an imaging technique originally proposed for medical applications which can be usefully applied also to problems of nondestructive evaluation. Recent progress in the mathematical treatment of this problem is presented in the paper by Hanke and Brühl.
The next three papers are about scattering problems, a fundamental topic in imaging techniques based for instance on ultrasound and microwave sounding. The papers by Kress and by Colton et al are concerned with inverse obstacle problems presenting two different concepts: Kress gives a survey of Newton methods while Colton et al discuss linear sampling methods. Borcea et al cover the problem of detecting and imaging small or extended objects embedded in inhomogeneous media.
Finally Strong and Chan discuss the application of the total variation regularization method to denoising problems and present new results which enlighten the edge-preserving and scale-dependent properties of this method.
Bertero Mario
Scherzer Otmar
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