Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix

A variable shaping matrix in the generalized Landweber iteration is used to solve the large linear system of equations arising in the image reconstruction problem of emission tomography. The method used is based on the property that once a spatial frequency image component is recovered in the generalized Landweber iteration, this component will not change during subsequent iterations, even if a different shaping matrix is used. Two different shaping matrices are used: the first recovers low-frequency image components and the second may be used either to accelerate the reconstruction of high-frequency image components or to attenuate these components to filter the image. The variable shaping matrix gives results similar to truncated inverse filtering, but requires much less computation and memory, since it does not rely on singular value decomposition.<>