A statistical reconstruction model for absorption CT with source uncertainty ^*

Abstract

Reconstruction methods for computed tomography are often based on the assumption that the source intensity and the detector response are known and static. In practice, however, both are unknown and must be estimated. An estimate of the combined source intensity and detector response is typically obtained by acquiring a number of so-called flat-field measurements, but this approach is oblivious to intensity drift, e.g., due to source instabilities, vibrating beamline components, etc. Discrepancies between the estimated response and true response can lead to severe artifacts in the reconstruction, especially for dose-and/or time-limited experiments. We propose a new, extended reconstruction model that jointly estimates the reconstruction, the detector response, and the (possibly time-varying) source intensity. We demonstrate through simulated experiments that the proposed reconstruction model leads to reconstructions with significantly reduced artifacts.

Low-rank flat-field correction for artifact reduction in spectral computed tomography

“…A possible improvement of the model could be the inclusion of the low-rank matrix as parameters of the reconstruction model and jointly estimating the reconstruction and the spectral detector response, e.g., see [19]. A natural initial guess for the low-rank matrix would be the estimate obtained by the LR method.…”

“…Let Y k ∈ R rp denote the measurements for the k'th energy with r detector elements and p projection images and discretize the domain into n pixels, then by appropriate discretization (e.g., see [19]), we can describe the measurements by,…”

Partial source separation from unknown correlation mixture for eliminating unknown periodic disturbances from random measured signals

“…Conventional blind source separation problem has been studied and several separation techniques were presented as well as image recognition [5][6][7][8][9][10][11][12][13]. For example, the blind source separation technique using signal second-order statistics can effectively extract simultaneous uncorrelated sources and mixture [7].…”