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Current reconstruction techniques suffer from limitations\nin their model and implementation. In this paper, we present a new\nreconstruction method that is based on solving a system of linear\nequations using an efficient iterative approach. Image pixel\nintensities are related to the measured frequency domain data\nthrough a set of linear equations. Although the system matrix is\ntoo dense and large to solve by direct inversion in practice, a\nsimple orthogonal transformation to the rows of this matrix is\napplied to convert the matrix into a sparse one up to a certain\nchosen level of energy preservation. The transformed system is\nsubsequently solved using the conjugate gradient method. This\nmethod is applied to reconstruct images of a numerical phantom as\nwell as magnetic resonance images from experimental spiral imaging\ndata. The results support the theory and demonstrate that the\ncomputational load of this method is similar to that of standard\ngridding, illustrating its practical utility.<\/jats:p>","DOI":"10.1155\/ijbi\/2006\/49378","type":"journal-article","created":{"date-parts":[[2006,4,5]],"date-time":"2006-04-05T12:24:41Z","timestamp":1144239881000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Progressive Magnetic Resonance Image Reconstruction Based on Iterative Solution of a Sparse Linear System"],"prefix":"10.1155","volume":"2006","author":[{"given":"Yasser M.","family":"Kadah","sequence":"first","affiliation":[]},{"given":"Ahmed S.","family":"Fahmy","sequence":"additional","affiliation":[]},{"given":"Refaat E.","family":"Gabr","sequence":"additional","affiliation":[]},{"given":"Keith","family":"Heberlein","sequence":"additional","affiliation":[]},{"given":"Xiaoping P.","family":"Hu","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,2,21]]},"reference":[{"volume-title":"Magnetic Resonance Imaging: Physical Principles and Sequence Design","year":"1999","author":"Haacke E. 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