Abstract
Recently, we have developed the so-called ‘potato peeler’ perspective forheuristically revealing the existence of redundant information within the datafunction in single-photon emission computed tomography (SPECT) withnon-uniform attenuation. In this work we seek to develop a mathematicalformulation for the potato peeler perspective. Specifically, we introduce theconcept of variable sinograms and derive equations that relate the variablesinograms to the object function and to the measured attenuated Radontransform. Using the variable sinograms and their equations, we show thatredundant information exists within the attenuated Radon transform in SPECTand that an image can uniquely be reconstructed from knowledge of theattenuated Radon transform available in, for example, short-scan SPECT, wherethe scanning configuration includes angular views covering only 180̂. Moreover,the concept of variable sinograms and the associated mathematical formulationmay have significant implications for a variety of tomographic reconstructionproblems.
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