Sparse recovery for discrete tomography

Discrete tomography (DT) focuses on the reconstruction of a discrete valued image from few projection angles. Prior knowledge about the image can greatly increase the quality of the reconstructed image, especially when a small number of projections are available. In this paper, we show that DT can be formulated as a sparse signal recovery problem. By using a well designed dictionary, it is possible to represent a binary image with very few coefficients. Starting from this concept, we modify the reweighed l₁ algorithm to achieve a sparse solution and preserve the binary property of image. Preliminary simulation results show that our algorithm can outperform conventional continuous reconstruction methods in cases when very limited data is available.