**Publications**(54)

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We have developed POP, phase estimation by onion peeling, an algorithm which unwraps the phase along 1-D paths for a 2-D image obtained with the Dixon method. The unwrapping is initially performed along a closed path enclosing the implant and well separated from it. The recovered phase is expanded using a smooth periodic basis along the path. Then, path-by-path, the estimate is applied to the next path and then the expansion coefficients are estimated to best fit the wrapped measurements. We have successfully tested POP on MRI images of specially constructed phantoms and on a group of patients with hip implants.

In principle, POP can be extended to 3-D imaging. In that case, POP would entail representing phase with a suitably smooth basis over a series of surfaces enclosing the implant (the "onion skins"), again beginning the phase estimation well away from the implant. An approach for this is proposed.

Results are presented for fat and water separation for 2-D images of phantoms and actual patients. The practicality of the method and its employment in clinical MRI are discussed.

*ab initio*phase retrieval using iterative projection algorithms for 2D crystals is presented.

Many technical disciplines (e.g. remote sensing, medical imaging, etc.) require digital processing of data to reconstruct an image. This course presents an analysis of methods and algorithms used for reconstructing images from distorted and/or incomplete data, and the development for specific applications. Topics covered include image formation and degradation, Fourier methods and computations, filtering, projection- and probabilistic-based algorithms, deconvolution (deblurring), and phase retrieval.

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