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Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties

This paper introduces a general reconstruction technique for using unregistered prior images within model-based penalized- likelihood reconstruction. The resulting estimator is implicitly defined as the maximizer of an objective composed of a likelihood term that enforces a fit to data measurements and that incorporates the heteroscedastic statistics of the tomographic problem; and a penalty term that penalizes differences from prior image. Compressed sensing (p-norm) penalties are used to allow for differences between the reconstruction and the prior. Moreover, the penalty is parameterized with registration terms that are jointly optimized as part of the reconstruction to allow for mismatched images. We apply this novel approach to synthetic data using a digital phantom as well as tomographic data derived from a conebeam CT test bench. The test bench data includes sparse data acquisitions of a custom modifiable anthropomorphic lung phantom that can simulate lung nodule surveillance. Sparse reconstructions using this approach demonstrate the simultaneous incorporation of prior imagery and the necessary registration to utilize those priors.