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We describe and examine an algorithm for tomographic image reconstructionwhere prior knowledge about the solution is available in the form of trainingimages. We first construct a nonnegative dictionary based on prototype elementsfrom the training images; this problem is formulated as a regularizednon-negative matrix factorization. Incorporating the dictionary as a prior in aconvex reconstruction problem, we then find an approximate solution with asparse representation in the dictionary. The dictionary is applied tonon-overlapping patches of the image, which reduces the computationalcomplexity compared to other algorithms. Computational experiments clarify thechoice and interplay of the model parameters and the regularization parameters,and we show that in few-projection low-dose settings our algorithm iscompetitive with total variation regularization and tends to include moretexture and more correct edges.

Tomographic Image Reconstruction using Training images