Level estimation for sparse reconstruction in discrete tomography

In discrete tomography (DT), the goal is to reconstruct from multiple linear projections an unknown image, which is known to have few distinct pixel level intensities. Such images arise in tomography problems where very high contrast is expected, e.g., in angiography medical imaging. A common assumption for DT is that the set of possible intensity levels is known in advance. However, determining the intensity levels is a difficult problem, coupled with measurement calibration and the used reconstruction algorithm. We introduce an unsupervised DT algorithm that jointly reconstructs the image and estimates the unknown intensity levels. Our algorithm alternates between (i) an l₁ sparse recovery step with a reweighed cost function that pushes the reconstructed values close to the estimated intensities, and (ii) an estimation step for the most likely intensity levels. We experimentally demonstrate that the proposed algorithm successfully estimates the unknown levels and leads to high quality reconstruction of angiographic images.