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We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the object with acoustic waves that slightly perturb the conductivity and cause the change in the electric potential measured on(More)
The limited-view problem is studied for thermoacoustic tomography, which is also referred to as photoacoustic or optoacoustic tomography depending on the type of radiation for the induction of acoustic waves. We define a "detection region," within which all points have sufficient detection views. It is explained analytically and shown numerically that the(More)
We investigate the band-gap structure of the spectrum of second-order partial differential operators associated with the propagation of waves in a periodic two-component medium. The medium is characterized by a real-valued position-dependent periodic function "(x) that is the dielectric constant for electromagnetic waves and mass density for acoustic waves.(More)
The paper starts with a comparative discussion of features and limitations of the three types of recent approaches to the reconstruction in thermoacoustic/photoacoustic tomography: backprojection formulas, eigenfunction expansions, and time reversal. The latter method happens to be the least restrictive. It is then considered in more detail, e.g. its(More)
This is the manuscript of the chapter for a planned Handbook of Mathematical Methods in Imaging that surveys the mathematical models, problems, and algorithms of the Thermoacoustic (TAT) and Photoacoustic (PAT) Tomography. TAT and PAT represent probably the most developed of the several novel " hybrid " methods of medical imaging. These new modalities(More)
We consider the two-component dielectric medium consisting of a periodic array of parallel air columns of square cross section embedded into a lossless optically dense host material with the dielectric constant (> 1. We show that if (is large enough and the relative distance 8 between the air columns is such that (8 » 1 and (8 2 « 1, then the corresponding(More)
We introduce and investigate the band gap sturcture of the frequency spectrum for classical electromagnetic and acoustic waves in a high contrast two-component periodic medium. The asymptotics with respect to the high contrast is considered. The limit medium is described in terms of appropriate see-adjoint operators and the convergence to the limit is(More)
The transform considered in the paper integrates a function supported in the unit disk on the plane over all circles centered at the boundary of this disk. Such circular Radon transform arises in several contemporary imaging techniques, as well as in other applications. As it is common for transforms of Radon type, its range has infinite co-dimension in(More)