Singularities of the radon transform
نویسندگان
چکیده
منابع مشابه
Singularities of the Radon Transform
Singularities of the Radon transform of a piecewise smooth function f(x), x e R" , n > 2, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of f(x) are calculated by applying the Legendre transform to the functions, which appear in the equations of the discontinuity surfaces of the Radon transform of f(x) ; examples are gi...
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In many applications of tomography one is interested in finding the discontinuities of the unknown piecewise smooth function from the knowledge of the Radon transform of this function. For example, one could think about finding the boundaries of a crack in a solid, say aircraft wing or engine, or a rupture in a tissue in medical diagnostics. The aim of this paper is twofold. First, we want to s...
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where S + x denotes the setf-s + x i s e S ) . Thus, the Radon transform can be thought of as a way of replacing/by a "smeared out" version of /. This form of the transform represents a simplified model of the kind of averaging which occurs in certain applied settings, such as various types of tomography and recent statistical averaging techniques. A fundamental question which arises in connect...
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ژورنال
عنوان ژورنال: Applicable Analysis
سال: 2001
ISSN: 0003-6811,1563-504X
DOI: 10.1080/00036810108840967