Iterative Methods in Image Reconstruction

Emory University, Atlanta GA

Investigators

Abstract

The investigator develops efficient and reliable iterative methods for reconstructing an image from recorded, noisy data. To obtain better resolved images, he develops methods that can effectively handle complicated operators (e.g., spatially variant kernels) and methods that enforce a nonnegativity constraint. The emergence of increasingly sophisticated imaging devices has produced a new generation of very difficult computational problems in which an image is to be reconstructed from recorded data. Such problems arise, for example, in breast cancer detection, where there is a tradeoff between the needs to obtain high resolution images and to limit the radiation dose to the patient. New devices have also been recently proposed for 3-dimensional imaging, where high dimensionality and resolution requirements result in nontrivial computational complexity. Yet another example occurs in new ground-based telescopes, which use adaptive optics techniques. To extract detailed information and take advantage of the increase in resolution that can be obtained from new imaging devices, it is important to develop methods that take into account spatial changes of properties in the imaging mechanisms, which are not amenable to standard fast Fourier transform based methods. New fully 3-dimensional medical imaging devices require a new generation of computational methods to efficiently reconstruct images from recorded data, and in order for these new computational methods to find their way to clinical use, it is important to provide software packages that allow for easy implementation and experimentation. Methods that enforce nonnegativity in the computed solution, and that can efficiently handle spatially variant kernels, are developed. Many of the computational tools developed in this project should be applicable to a wide class of iterative image reconstruction methods, including linear, nonlinear and statistical based methods.