4 December 2000 Tomographic reconstruction with nonlinear diagonal estimators
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In tomographic reconstruction, the inversion of the Radon transform in the presence of noise is numerically unstable. Reconstruction estimators are studied where the regularization is performed by a thresholding in a wavelet or wavelet packet decomposition. These estimators are efficient and their optimality can be established when the decomposition provides a near-diagonalization of the inverse Radon transform operator and a compact representation of the object to be recovered. Several new estimators are investigated in different decomposition. First numerical results already exhibit a strong metrical and perceptual improvement over current reconstruction methods. These estimators are implemented with fast non-iterative algorithms, and are expected to outperform Filtered Back- Projection and iterative procedures for PET, SPECT and X-ray CT devices.
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Jerome Kalifa, Jerome Kalifa, Andrew F. Laine, Andrew F. Laine, Peter D. Esser, Peter D. Esser, } "Tomographic reconstruction with nonlinear diagonal estimators", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408646; https://doi.org/10.1117/12.408646

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