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Optimal inversion of the noisy Radon transform on classes defined by a degree of the Laplace operator. (English) Zbl 1384.65092

Summary: A general optimal recovery problem is to approximate a value of a linear operator on a subset (class) in linear space from a value of another linear operator (called information), measured with an error in given metric. We use this formulation to investigate the classical computerized tomography problem of inversion of the noisy Radon transform.

MSC:

65R10 Numerical methods for integral transforms
44A12 Radon transform
65R32 Numerical methods for inverse problems for integral equations
92C55 Biomedical imaging and signal processing
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