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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