NUFFT and NUIFFT based reconstruction algorithms for non -Cartesian imaging on small animals

The growing interest in small animal models of human disease requires developments of imaging techniques dedicated to small animals. This dissertation work is motivated to develop efficient non-Cartesian image reconstruction methods to address the dual challenges of signal-to-noise ratio (SNR) and spatio-temporal resolution. Multi-dimensional nonuniform fast Fourier transform (NUFFT) and nonuniform inverse fast Fourier transform algorithms have been developed to efficiently evaluate the nonuniform DFT (NUDFT) and its inverse. Several reconstruction algorithms were proposed for different applications based on NUFFT and NUIFFT. NUFFT reconstruction was developed for 3D cardiac mouse imaging with radial trajectory and 3D multi-spectral brain imaging with rosette trajectory. An NUFFT based interactive density compensation function (DCF) was formulated for the rosette trajectory that had intersections. NUIFFT reconstruction was also developed and applied on radially acquired 2D cardiac mouse data. A sparseness prior was further integrated into this NUIFFT algorithm to tackle the low SNR and high requirement of temporal resolution in dynamic contrast enhanced (DCE) pulmonary perfusion imaging of a rat lung. The sparseness prior iterative reconstruction method was later extended to reconstruct 3D cone-beam micro-CT data acquired with retrospective gating. In each of the applications, the proposed NUFFT and NUIFFT based reconstructions outperformed the conventional reconstruction methods on image qualities and/or reconstruction speeds.