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An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary preassigned orthonormal basis. We prove that replacing the usual quadratic regularizingExpand
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Exact and approximate rebinning algorithms for 3-D PET data
This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. Expand
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Symmetric Phase-Only Matched Filtering of Fourier-Mellin Transforms for Image Registration and Recognition
Presents a new method to match a 2D image to a translated, rotated and scaled reference image using symmetric phase-only matched filtering. Expand
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Image reconstruction from fan-beam projections on less than a short scan.
This work is concerned with 2D image reconstruction from fan-beam projections. It is shown that exact and stable reconstruction of a given region-of-interest in the object does not require all linesExpand
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Truncated Hilbert transform and image reconstruction from limited tomographic data
A data sufficiency condition for 2D or 3D region-of-interest (ROI) reconstruction from a limited family of line integrals has recently been introduced using the relation between the backprojection ofExpand
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A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection
An exact inversion formula written in the form of shift-variant filtered-backprojection (FBP) is given for reconstruction from cone-beam data taken from any orbit satisfying H. Tuy's sufficiency conditions. Expand
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Iterative reconstruction for helical CT: a simulation study.
Iterative reconstruction algorithms for helical CT are presented. The algorithms are derived from two-dimensional reconstruction algorithms, by adapting the projector/backprojector to the helicalExpand
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A solution to the long-object problem in helical cone-beam tomography.
This paper presents a new algorithm for the long-object problem in helical cone-beam (CB) computerized tomography (CT). This problem consists in reconstructing a region-of-interest (ROI) bounded byExpand
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Tiny a priori knowledge solves the interior problem
Based on the differentiated backprojection (DBP) framework [1-3], this paper shows that the solution to the interior problem in computed tomography is unique if a tiny a priori knowledge on theExpand
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The case of incomplete tomographic data for a compactly supported attenuation function is studied. When the attenuation function is a priori known in a subregion, we show that a reduced set ofExpand
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