Table I.
Comparison of main MRA approaches. F(N) denotes the complexity of inverting the bispectrum. For instance, for the FM algorithm, F(N) = O(N2). Storage requirements include the possibility of streaming computations where possible.
| Method | Computational complexity | Storage requirement | Comments |
|---|---|---|---|
| Template alignment | O(MN log N) | O(N) | Fails at moderate SNR (see Figure I.1) |
| Angular synchronization | O(M2N log N) | O(M2) | Fails at low SNR |
| Expectation maximization | O(TMN log N) | O(MN) | Empirically accurate; #iterations T grows with noise level |
| Invariant features (this paper) | O(MN2 + F(N)) | O(N2) | Under mild conditions, accurate estimation if M grows as σ6 |