Application Of Field Theory In SPECT Reconstruction

Single photon emission computed tomography (SPECT) is one of the importantnuclear medicine technologies. SPECT takes the advantages of functional imaging anddynamic imaging in contrast with other diagnosing technologies and so plays an importantrole in the clinic diagnosis, especially in the early detection of tumors and the diagnosis ofheart or brain diseases.The existing SPECT reconstruction algorithms can be divided into analytical methodsand iterative methods. In SPECT, the analytical methods are based on the inversion of theattenuated Radon transform. The problem of how to compensate the non-uniformattenuation had not been solved very well, until Novikov and Natterer presented an explicitinversion formula for the attenuated Radon transform with parallel-beam geometry，respectively. In field theory, it is the important part to research the relationship between thefield and the source. One can build the space distribution of the sources by getting the spacedistribution of the field. The application of field theory can help us to understand the imagereconstruction from another angle.From Natterer’s reconstruction formula, we found that the image reconstruction can betreated as the inverse problem in field. So we can analyses and calculate CT reconstructionby using the field theory. Firstly, we build the reconstruction field using Hilbert transformsof projections. The space distribution of the reconstruction field is related to the spacedistribution of image. Then we reconstruct image by solving the divergence of thereconstruction field. Through the relationship between the parallel-beam projection andfan-beam projection, we further derive the field-based fan-beam CT reconstruction formula.In SPECT, We analyses how Natterer’s inversion formula compensate the non-uniformattenuation in SPECT reconstruction. The formula build SPECT reconstruction field thatincludes two parts: One is the real part that is related to the space distribution of SPECTimage, the other one is the imaginary part that is related to the non-uniform attenuation. So if we only use the real part of SPECT reconstruction field to calculate the divergence of thisfield, we can reconstruct SPECT image with non-uniform attenuation compensation.