Compressed sensing based interior tomography
نویسندگان
چکیده
منابع مشابه
Compressed sensing based interior tomography.
While conventional wisdom is that the interior problem does not have a unique solution, by analytic continuation we recently showed that the interior problem can be uniquely and stably solved if we have a known sub-region inside a region of interest (ROI). However, such a known sub-region is not always readily available, and it is even impossible to find in some cases. Based on compressed sensi...
متن کاملSupplemental analysis on compressed sensing based interior tomography.
Recently, in the compressed sensing framework we proved that an interior ROI can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant. In the proofs, we implicitly utilized the property that if an artifact image assumes a constant value within the ROI, then this constant must be zero. Here we prove this property in the space of square integrable functions.
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Recently, in the compressed sensing framework we found that a two-dimensional interior region-of-interest (ROI) can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant (Yu and Wang, 2009). Here we present a general theorem charactering a minimization property for a piecewise constant function defined on a domain in any dimension. Our major mathematical...
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ژورنال
عنوان ژورنال: Physics in Medicine and Biology
سال: 2009
ISSN: 0031-9155,1361-6560
DOI: 10.1088/0031-9155/54/9/014