Iterative Methods in Image Reconstruction

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The investigator develops efficient and reliable iterativemethods for reconstructing an image from recorded, noisy data.To obtain better resolved images, he develops methods that caneffectively handle complicated operators (e.g., spatially variantkernels) and methods that enforce a nonnegativity constraint. The emergence of increasingly sophisticated imaging deviceshas produced a new generation of very difficult computationalproblems in which an image is to be reconstructed from recordeddata. Such problems arise, for example, in breast cancerdetection, where there is a tradeoff between the needs to obtainhigh resolution images and to limit the radiation dose to thepatient. New devices have also been recently proposed for3-dimensional imaging, where high dimensionality and resolutionrequirements result in nontrivial computational complexity. Yetanother example occurs in new ground-based telescopes, which useadaptive optics techniques. To extract detailed information andtake advantage of the increase in resolution that can be obtainedfrom new imaging devices, it is important to develop methods thattake into account spatial changes of properties in the imagingmechanisms, which are not amenable to standard fast Fouriertransform based methods. New fully 3-dimensional medical imagingdevices require a new generation of computational methods toefficiently reconstruct images from recorded data, and in orderfor these new computational methods to find their way to clinicaluse, it is important to provide software packages that allow foreasy implementation and experimentation. Methods that enforcenonnegativity in the computed solution, and that can efficientlyhandle spatially variant kernels, are developed. Many of thecomputational tools developed in this project should beapplicable to a wide class of iterative image reconstructionmethods, including linear, nonlinear and statistical basedmethods.