Preconditioning Methods for Shift-Variant Image Reconstruction
dc.contributor.author | Fessler, Jeffrey A. | en_US |
dc.date.accessioned | 2011-08-18T18:20:54Z | |
dc.date.available | 2011-08-18T18:20:54Z | |
dc.date.issued | 1997-10-26 | en_US |
dc.identifier.citation | Fessler, J. A. (1997). "Preconditioning Methods for Shift-Variant Image Reconstruction." International Conference on Image Processing 1: 185-188. <http://hdl.handle.net/2027.42/85856> | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/85856 | |
dc.description.abstract | Preconditioning methods can accelerate the convergence of gradient-based iterative methods for tomographic image reconstruction and image restoration. Circulant preconditioners have been used extensively for shift-invariant problems. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. For inverse problems that are approximately shift-invariant (i.e. approximately block-Toeplitz or block-circulant Hessians), circulant or Fourier-based preconditioners can provide remarkable acceleration. However, in applications with nonuniform noise variance (such as arises from Poisson statistics in emission tomography and in quantum-limited optical imaging), the Hessian of the (penalized) weighted least-squares objective function is quite shift-variant, and the Fourier preconditioner performs poorly. Additional shift-variance is caused by edge-preserving regularization methods based on nonquadratic penalty functions. This paper describes new preconditioners that more accurately approximate the Hessian matrices of shift-variant imaging problems. Compared to diagonal or Fourier preconditioning, the new preconditioners lead to significantly faster convergence rates for the unconstrained conjugate-gradient (CG) iteration. Applications to position emission tomography (PET) illustrate the method. | en_US |
dc.publisher | IEEE | en_US |
dc.title | Preconditioning Methods for Shift-Variant Image Reconstruction | en_US |
dc.type | article | en_US |
dc.subject.hlbsecondlevel | Biomedical Engineering | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/85856/1/Fessler147.pdf | |
dc.identifier.doi | 10.1109/ICIP.1997.647442 | en_US |
dc.identifier.source | International Conference on Image Processing | en_US |
dc.owningcollname | Electrical Engineering and Computer Science, Department of (EECS) |
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