Microlocal Analysis in Tomography
نویسندگان
چکیده
In this chapter, we introduce a range of tomography problems, including Xray imaging, limited data problems, electron microscopy and radar imaging. We are interested in the recovery of the singular features of the medium or object rather than exact inversion formulas. Toward this end, we show how microlocal analysis helps researchers understand the strengths and limitations inherent in the reconstruction of these and several other tomography problems. Microlocal analysis aids researchers in understanding those singular features that can be stably recovered, which could be very important when only limited or partial data is available. Furthermore, it helps explain the presence of artifacts present in certain image reconstruction methods and in some cases might help distinguish the true singularities from the false ones. We emphasize these issues in this chapter. In Section 1.2, we will introduce tomography problems including X-ray tomography, electron microscope tomography, and radar imaging. We will present reconstructions for each problem and examine how well they image the original objects with the goal of finding strengths and limitations for each method. In Section 1.3, we introduce some basic properties of some tomographic transforms and then introduce microlocal analysis in Section 1.4. Finally, we give several applications in tomography and radar imaging in Section 1.5 emphasizing the microlocal properties of these transforms. This powerful tool allows us to understand the strengths and limitations that are really intrinsic to the data, as is shown in Section 1.5.
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تاریخ انتشار 2015