Supplementary Document on Solving Trigonometric Moment Problems for Fast Transient Imaging

The only non-trivial step in evaluation of the maximum entropy spectral estimate is the computation of the vectorB−1 ·e0. Generic algorithms with run time O(m) can be used for this purpose (e.g. a Cholesky decomposition). However, if run time is critical, the special structure of the Toeplitz matrix should be exploited. Levinson’s algorithm provides a simple and highly efficient way to do this. It is given in Algorithm 1. Note that cl−1, . . . , c0 denotes the complex conjugate of cl−1, . . . , c0. A correctness proof can be found in [Burg 1975, p. 14 ff].