A unique feature of medical imaging is that the object to be imaged has a compact support. In mathematics, the Fourier transform of a function that has a compact support is an entire function. In theory, an entire function can be uniquely determined by its values in a small region, using, for example, power series expansions. Power series expansions require evaluation of all orders of derivatives of a function, which is an impossible task if the function is discretely sampled. In this paper, we propose an alternative method to perform analytic continuation of an entire function, by using the Nyquist-Shannon sampling theorem. The proposed method involves solving a system of linear equations and does not require evaluation of derivatives of the function. Noiseless data computer simulations are presented. Analytic continuation turns out to be extremely ill-conditioned.
Low-dose computed tomography (CT) can produce noisy images that may contain streaking artifacts. Removal of streaking artifacts normally requires iterative algorithms that model the transmission noise physics. A fast filtered backprojection (FBP) algorithm is introduced in this short paper. This algorithm is very simple and effective in removing the streaking artifacts in low-dose CT.
Magnetic resonance imaging (MRI) using under-sampled k-space data is a common method to shorten the imaging time. Iterative Bayesian algorithms are usually used for its image reconstruction. This paper compares an iterative Bayesian image reconstruction method that uses both spatial and temporal constraints and a non-iterative reconstruction algorithm that does not use temporal constraints. Three patient studies are performed. It is interesting to notice that the images reconstructed by the iterative Bayesian algorithm may introduce more bias than the non-iterative algorithm, even though the images provided by the iterative Bayesian algorithm look less noisy. The bias can be reduced by decreasing the influence of the temporal constraints.