Sparse-View X-Ray CT Reconstruction Using $\ell_1$ Prior with Learned Transform
This addresses the challenge of maintaining image quality in medical CT imaging while lowering radiation exposure, representing an incremental improvement over prior sparse-view reconstruction techniques.
The paper tackles the problem of reconstructing high-quality images from sparse-view X-ray CT scans to reduce radiation dose, proposing a model combining penalized weighted-least squares with an ℓ1 prior and learned sparsifying transform, which improves image quality over existing methods and achieves comparable or better results with shorter runtime in some cases.
A major challenge in X-ray computed tomography (CT) is reducing radiation dose while maintaining high quality of reconstructed images. To reduce the radiation dose, one can reduce the number of projection views (sparse-view CT); however, it becomes difficult to achieve high-quality image reconstruction as the number of projection views decreases. Researchers have applied the concept of learning sparse representations from (high-quality) CT image dataset to the sparse-view CT reconstruction. We propose a new statistical CT reconstruction model that combines penalized weighted-least squares (PWLS) and $\ell_1$ prior with learned sparsifying transform (PWLS-ST-$\ell_1$), and a corresponding efficient algorithm based on Alternating Direction Method of Multipliers (ADMM). To moderate the difficulty of tuning ADMM parameters, we propose a new ADMM parameter selection scheme based on approximated condition numbers. We interpret the proposed model by analyzing the minimum mean square error of its ($\ell_2$-norm relaxed) image update estimator. Our results with the extended cardiac-torso (XCAT) phantom data and clinical chest data show that, for sparse-view 2D fan-beam CT and 3D axial cone-beam CT, PWLS-ST-$\ell_1$ improves the quality of reconstructed images compared to the CT reconstruction methods using edge-preserving regularizer and $\ell_2$ prior with learned ST. These results also show that, for sparse-view 2D fan-beam CT, PWLS-ST-$\ell_1$ achieves comparable or better image quality and requires much shorter runtime than PWLS-DL using a learned overcomplete dictionary. Our results with clinical chest data show that, methods using the unsupervised learned prior generalize better than a state-of-the-art deep "denoising" neural network that does not use a physical imaging model.