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A major challenge in computed tomography (CT) is to reduce X-ray dose to a low or even ultra-low level while maintaining the high quality of reconstructed images. We propose a new method for CT reconstruction that combines penalized weighted-least squares reconstruction (PWLS) with regularization based on a sparsifying transform (PWLS-ST) learned from a dataset of numerous CT images. We adopt an alternating algorithm to optimize the PWLS-ST cost function that alternates between a CT image update step and a sparse coding step. We adopt a relaxed linearized augmented Lagrangian method with ordered-subsets (relaxed OS-LALM) to accelerate the CT image update step by reducing the number of forward and backward projections. Numerical experiments on the XCAT phantom show that for low dose levels, the proposed PWLS-ST method dramatically improves the quality of reconstructed images compared to PWLS reconstruction with a nonadaptive edge-preserving regularizer (PWLS-EP).

In previous work, we proposed a Poisson statistical model for gated PET data in which the distribution was parametrized in terms of both image intensity and motion parameters. The motion parameters related the activity image in each gate to that of a base image in some fixed gate. By doing maximum loglikelihood (ML) estimation of all parameters simultaneously, one obtains an estimate of the base gate image that exploits the full set of measured sinogram data. Previously, this joint ML approach was compared, in a highly simplified single-slice setting, to more conventional methods. Performance was measured in terms of the recovery of tracer uptake in a synthetic lung nodule. This paper reports the extension to 3D with much more realistic simulated motion. Furthermore, in addition to pure ML estimation, we consider the use of side information from a breath-hold CT scan to facilitate regularization, while preserving hot lesions of the kind seen in FDG oncology studies.

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Statistical methods for tomographic image reconstruction lead to improved spatial resolution and noise properties in PET. Penalized-likelihood (PL) image reconstruction methods involve maximizing an objective function that is based on the log-likelihood of the sinogram measurements and on a roughness penalty function to control noise. In emission tomography, PL methods (and MAP methods) based on conventional quadratic regularization functions lead to nonuniform and anisotropic spatial resolution, even for idealized shift-invariant imaging systems. We have previously addressed this problem for parallel-beam 2D emission tomography [1], and for fan-beam 2D transmission tomography [2] by designing data-dependent, shift-variant regularizers that improve resolution uniformity and isotropy. even for idealized shift-invariant imaging systems. This paper extends those methods to 3D cylindrical PET, using an analytical design approach that is numerically efficient.