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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 boundaries of any objects inside this region can be recovered stably. Otherwise some sharp details become blurred. One can identify in advance the parts of the boundaries that will be affected if the detection view is insufficient. If the detector scans along a circle in a two-dimensional case, acquiring a sufficient view might require covering more than a -, or less than a -arc of the trajectory depending on the position of the object. Similar results hold in a three-dimensional case. In order to support our theoretical conclusions, three types of reconstruction methods are utilized: a filtered backprojection ͑FBP͒ approximate inversion, which is shown to work well for limited-view data, a local-tomography-type reconstruction that emphasizes sharp details ͑e.g., the boundaries of inclusions͒, and an iterative algebraic truncated conjugate gradient algorithm used in conjunction with FBP. Computations are conducted for both numerically simulated and experimental data. The reconstructions confirm our theoretical predictions.

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We report our theoretical and experimental investigations on a new imaging modality, magnetoacoustic tomography with magnetic induction (MAT-MI). In MAT-MI, the sample is located in a static magnetic field and a time-varying (micros) magnetic field. The time-varying magnetic field induces an eddy current in the sample. Consequently, the sample will emit ultrasonic waves by the Lorentz force. The ultrasonic signals are collected around the object to reconstruct images related to the electrical impedance distribution in the sample. MAT-MI combines the good contrast of electrical impedance tomography with the good spatial resolution of sonography. MAT-MI has two unique features due to the solenoid nature of the induced electrical field. Firstly, MAT-MI could provide an explicit or simple quantitative reconstruction algorithm for the electrical impedance distribution. Secondly, it promises to eliminate the shielding effects of other imaging modalities in which the current is applied directly with electrodes. In the theoretical part, we provide formulae for both the forward and inverse problems of MAT-MI and estimate the signal amplitude in biological tissues. In the experimental part, the experimental setup and methods are introduced and the signals and the image of a metal object by means of MAT-MI are presented. The promising pilot experimental results suggest the feasibility of the proposed MAT-MI approach.

For a family of weight functions, hκ, invariant under a finite reflection group on R d , analysis related to the Dunkl transform is carried out for the weighted L p spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a maximal function and use it to prove the almost everywhere convergence.

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An exact time-domain method is proposed to time reverse a transient scalar wave using only the field measured on an arbitrary closed surface enclosing the initial source. Under certain conditions, a timereversed field can be approximated by retransmitting the measured signals in a reversed temporal order. Exact reconstruction for three-dimensional broadband diffraction tomography (a linearized inverse scattering problem) is proposed by time-reversing the measured field back to the time when each secondary source is excited. The algorithm is verified by a numerical simulation. Extension to the case using Green's function in a heterogeneous medium is discussed. DOI: 10.1103/PhysRevLett.92.033902 PACS numbers: 42.30.Wb, 42.25.Fx Time reversal of an acoustic or electromagnetic wave is based on the invariance of the wave equation in a lossless medium under the transform t ! ÿt (t represents the time). Time reversal of a wave can be understood as generating the back-propagation field from the measured forward-propagation field and/or its normal derivative after removing the initial sources. The concept of time reversal has been implemented experimentally and applied to a wide range of studies such as inverse scattering [1], wave-front distortion correction [2,3], and multiple scattering phenomena [4].However, no formula is available for computing the time-reversed (TR) field using only the measured field on a closed surface enclosing the initial source. When both the field and its normal gradient on a closed surface are available, there are formulas [3,5] to derive the TR field. However, it is not practical to measure both the field and its normal gradient simultaneously. For example, the output signal from a piezoelectric transducer is generally a complex combination of these two effects. There are two challenges in deriving the TR field using only the field. First, it is not obvious that Green's function, which is widely used to derive the field in space from the field on a closed surface, can be applied here. This is because the TR field on the closed surface includes both diverging and converging components [3,5]. While the converging component of the TR wave is just the measured signals in the forward propagation in a reversed temporal order (RTO), the diverging component has no counterpart in the forward propagation and, consequently, is not available from measurement in general. Second, in a free space, retransmission of the measured signals in RTO from the detection surface does not reproduce the TR field. This is because the waves retransmitted in one position propagate to the other positions on the surface and change the field there, and, consequently, the field on the surface does not equal the field in the forward propagation in RTO.In this Letter, we find that when time reversal is considered in the time domain, an exact time-reversal method that uses only the field on an arbitrary closed surface can be derived for a wide variety of applications such as tomography with diffracting sources, inverse dif...

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