Proximal Gradient based Anisotropic TV-L0 Reconstruction for Linear Tomosynthesis

Linear tomosynthesis is an X-ray based imaging modality, which reconstructs slices from a set of low dose X-ray projection images acquired by a flat panel detector over a limited total scan angle. Due to this limitation, the reconstruction problem is extremely ill-posed, which causes many artifacts in the calculated slices. The resolution of the reconstructions is highly anisotropic (poor along the direction of the X-rays) and the noise sensitivity of the reconstruction is also high. Large part of the spectrum of the sagittal slices of the examined volume (in conventional imaging geometry) is not measured by the projection images. This implies the necessity of utilizing maximum a posterior (MAP) estimation based reconstruction methods. Such an approach is the TV-L0 regularized reconstruction [1], which prefers reconstructions with sparse gradient vector field. TV-L0 regularization can highly reduce the tomographic blur of the reconstructions in the case of linear tomosynthesis, however the underlying large scale numerical optimization (estimates more than 1E9 variables) tries to minimize a highly non-convex and extremely badly conditioned function. This paper introduces a possible acceleration and combination of the reconstruction methods described in [1] and [2] by utilizing direction dependent weights in the penalty term on the components of the gradient vector field and examines its effect based on quantitative and qualitative comparison. For this purpose, reconstructions calculated from simulated projections are examined. Based on this examination, the paper concludes improvement in the reconstruction error (especially in the early iterations).