Exponential Vector Field Tomography

• In the exponential Radon transform in R2, the integrals of a scalar function f over lines, with exponential weight functions, are determined. We demonstrate how to define two different kinds of exponential Radon transforms for vector fields in R2 in a natural way. It is shown that having data from these transforms it is possible to reconstruct the vector field uniquely. The motivation for the study of this problem is ultrasound measurements of flows, from which velocity spectra along lines can be determined. The first moment of these can be interpreted by means of one of the exponential vectorial Radon transforms

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

integral equations

image reconstruction

computerised tomography

blood flow measurement

biomedical ultrasonics

medical image processing

Radon transforms

spectral analysis

vectors

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