Sparse Recovery for Discrete Tomography

Discrete tomography (DT) focuses on the reconstruction of a dis-crete 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 possi-ble 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. Pre-liminary simulation results show that our algorithm can outperform conventional continuous reconstruction methods in cases when very limited data is available. Index Terms — Discrete tomography, sparse signal recovery, compressive sensing 1