Tomographic reconstruction in Single Photon Emission Tomography (SPECT) and Positron Emission Tomography (PET), especially for brain and cardiac imaging. Breast cancer detection and imaging using Positron Emission Mammography (PEM), PET, Magnetic Resonance Imaging (MRI) including Contrast – Enhanced (CE) MRI, MR Diffusion Tensor Imaging (DTI) and MR Spectroscopy (MRS). Multimodality (PEM, PET/CT, CE-MRI, x-ray mammography) nonrigid medical image registration and fusion. Quantification of regional blood flow and perfusion defects in brain using SPECT and PET. Dosimetry in Nuclear Medicine.
Physics of Nuclear Medicine and Nuclear Cardiology, emission tomography
Advanced tomographic reconstruction in PET and SPECT. Breast cancer detection and imaging using molecular, MR and x-ray imaging. Nonrigid multimodality breast image registration and fusion. Advanced breast cancer lumpectomy. Ultrafast laser-based x-ray source for biomedical imaging. Advanced tomographic reconstruction in cone-beam micro-CT.
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We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.