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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.