Sparse recovery for SPECT imaging of inflammation at implants

The treatment of implant loosening requires a diagnosis of its cause for the operation planning of the implant replacement. If the loosening has mechanical reasons the implant may be replaced directly in one surgical intervention. On the contrary, if the loosening is caused by a bacterial inflammation this has to be factored into the operation planning. As the implant is not accessible before an operation it is the aim of this project to develop molecular imaging strategies for the noninvasive detection of bacterial inflammations. For the imaging process, substances which accumulate at bacterial inflammations on implant surfaces are marked with radioactive tracers. The radioactive decay of the tracers is then detected with a SPECT or PET measurement. Due to the fact that the number of radioactive events will be small and that the inflamed surface is embedded in an absorbing and scattering environment a precise attenuation correction, motion correction and an adapted reconstruction strategy is necessary. The attenuation coefficients can be determined by a CT scan, which can be accomplished in advance or simultaneously in case of a combined device. As the presence of metal implants usually results in severe artifacts in the CT reconstruction, these artifacts have to be corrected first to achieve more accurate attenuation values. The spatial distribution of the attenuation values can then be used in the SPECT reconstruction process as a correction term. The usual acquisition time of a SPECT examination ranges between 5 and 30 minutes. As a consequence, the acquisition will include position adjustments of the patient. These position changes provoke motion artifacts in the reconstructed image and may decrease the image quality significantly. Therefore strategies to correct linear as well as nonlinear patient motion have been developed. If the CT measurement is performed with a separate device, the technique also allows for correcting displacements between the CT and the SPECT image. This registration step is essential for a correct alignment of the spatial distribution of the attenuation coefficients. Exploiting the fact that the statistics of radioactive events are low and SPECT images are smoothened, the application of methods from compressed sensing leads to a sparse recovery for SPECT. The measurement can be modeled by the attenuated Radon transform which is a nonlinear operator. Due to discretization and noisy data the reconstruction is generally an ill-posed problem, such that regularization is needed for a stable recovery. The image reconstruction is normally achieved by iterative schemes, which are computational expensive. If sparsity is introduced as an additional constraint, this leads to faster iteration algorithms as only few important coefficients of the sparse expansion are considered. Additionally, the reconstruction with sparsity constraints can deliver images with much sharper contours, which is of interest for particular medical applications such as the presented project.