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• W2024017636 abstract "Ill-posed linear systems occur in many different fields. A class of regularization methods, called constrained optimization, aims to determine the extremum of a penalty function whilst constraining an objective function to a likely value. We propose here a novel heuristic way to screen the local extrema satisfying the discrepancy principle. A modified version of the Landweber algorithm is used for the iteration process. After finding a local extremum, a bound is performed to the 'farthest' estimate in the data space still satisfying the discrepancy principle. Afterwards, the modified Landweber algorithm is again applied to find a new local extremum. This bound-iteration process is repeated until a satisfying solution is reached. For evaluation in nuclear medicine tomography, a novel penalty function that preserves the edge steps in the reconstructed solution was evaluated on Monte Carlo simulations and using real SPECT acquisitions as well. Surprisingly, the first bound always provided a significantly better solution in a wide range of statistics." @default.
• W2024017636 created "2016-06-24" @default.
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• W2024017636 date "2009-10-05" @default.
• W2024017636 modified "2023-10-17" @default.
• W2024017636 title "Improved solution for ill-posed linear systems using a constrained optimization ruled by a penalty: evaluation in nuclear medicine tomography" @default.
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• W2024017636 doi "https://doi.org/10.1088/0266-5611/25/11/115004" @default.
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