Having very few projections of an image does not guarantee the reconstruction even in the case that the original image is only composed of 3 materials.Although previously developed line Mojette algorithm gives a solution in this case,an unicity is required.In order to solve this problem, based on the line Mojette transfrom,the tree decomposition is used to provide the complete set of solutions from a new algorithm denoted as“Tree Line Mojette”in the case that the original image contains only 3 materials (3 discrete values).