Showing papers by "Eric Todd Quinto published in 2013"
TL;DR: In this article, the authors consider the reconstruction problem for limited angle tomography using filtered backprojection (FBP) and lambda tomography, and they use microlocal analysis to explain why the well-known streak artifacts are present at the end of the limited angular range.
Abstract: 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.
176 citations
TL;DR: In this paper, the microlocal properties of the linearized forward scattering operator F and the normal operator F F (where F is the L 2 adjoint of F) were analyzed in Synthetic Aperture Radar imaging for the common midpoint acquisition geometry.
30 citations
TL;DR: In this article, the authors considered a generalized Radon transform that is used in trasound reflection tomography and showed that R ∗ R is an elliptic pseudodifferential operator.
Abstract: This article is dedicated to Sigurdur Helgason on the occasion of his eighty fifth birthday. We thank him for creating so much beautiful mathematics and for being a friend and mentor to so many people in the field. Abstract. We consider a generalized Radon transform that is used in ul- trasound reflection tomography. In our model, the ultrasound emitter and receiver move at a constant distance apart along a circle. We analyze the microlocal properties of the transform R that arises from this model. As a consequence, we show that, for distributions with support contained in a disc Db sufficiently inside the circle, R ∗ R is an elliptic pseudodifferential operator. We provide a local filtered back projection algorithm, L = R ∗ DR where D is a well-chosen differential operator. We prove that L is an elliptic pseudodiffer- ential operator of order 1 and so for f ∈E � (Db), Lf shows all singularities of f , and we provide reconstructions illustrating this point. Finally, we discuss an extension with some modifications of our result outside of Db.
17 citations
TL;DR: In this article, the authors define a general curvilinear Radon transform in R-3 and develop its microlocal properties, and prove that singularities can be added (or masked) in any backprojection reconstruction method.
Abstract: We define a general curvilinear Radon transform in R-3, and we develop its microlocal properties. We prove that singularities can be added (or masked) in any backprojection reconstruction method fo ...
17 citations