A comparison of tomographic reconstruction algorithms for acoustic non destructive testing of stone masonry

To avoid instability in matrix inversion, the number of cells must be smaller than the number of measured travel times. If the inverse of L exists it can be directly evaluated.

However, the inverse of L generally doesn’t exist since L is not a square matrix, it is ill-conditioned, and it has not full rank. Thus, other methods have to be used to solve the problem.