Inverse problems with partial data for a magnetic Schr\"odinger operator in an infinite slab and on a bounded domain

In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of [41], obtained for the Schr\"odinger operator without magnetic potentials. In the case of a bounded domain in $R^n$, $n\ge 3$, extending the results of [2], we show the unique determination of the magnetic field and electric potential from the Dirichlet and Neumann data, given on two arbitrary open subsets of the boundary, provided that the magnetic and electric potentials are known in a neighborhood of the boundary. Generalizing the results of [31], we also obtain uniqueness results for the magnetic Schr\"odinger operator, when the Dirichlet and Neumann data are known on the same part of the boundary, assuming that the inaccessible part of the boundary is a part of a hyperplane

Characterization and reduction of artifacts in limited angle tomography.

We consider the reconstruction problem for limited angle tomography using filtered backprojection (FBP) and lambda tomography. We use microlocal analysis to explain why the well-known streak artifacts are present at the end of the limited angular range. We explain how to mitigate the streaks and prove that our modified FBP and lambda operators are standard pseudodifferential operators, and so they do not add artifacts. We provide reconstructions to illustrate our mathematical results

How to characterize and decrease artifacts in limited angle tomography using microlocal analysis.

The filtered backprojection algorithm (FBP) in limited angle tomography reliably reconstructs only specific features of the original object and creates additional artifacts in the reconstruction. While the former is well understood mathematically, the added artifacts have not been studied very much in the literature. In our paper Inverse Problems 29125007 we mathematically explain why additional artifacts are created by the FBP and Lambda-CT algorithms for a limited angular range, and we derive an artifact reduction strategy using microlocal analysis

Singular FIOs in SAR Imaging, II: transmitter and receiver at different speeds

In this article, we consider two bistatic cases arising in synthetic aperture radar imaging: when the transmitter and receiver are both moving with different speeds along a single line parallel to the ground in the same direction or in the opposite directions. In both cases, we classify the forward operator F as a Fourier integral operator with fold/blowdown singularities. Next we analyze the normal operator F* F in both cases (where F* is the L-2-adjoint of F). When the transmitter and receiver move in the same direction, we prove that F* F belongs to a class of operators associated to two cleanly intersecting Lagrangians, I-p,I-l (Delta, C-1). When they move in opposite directions, F* F is a sum of such operators. In both cases artifacts appear, and we show that they are, in general, as strong as the bona fide part of the image. Moreover, we demonstrate that as soon as the source and receiver start to move in opposite directions, there is an interesting bifurcation in the type of artifact that appears in the image