Name
Abstract | ||
|---|---|---|
We address the problem of two-dimensional (2-D) phase retrieval from magnitude of the Fourier spectrum. We consider 2-D signals that are characterized by first-order difference equations, which have a parametric representation in the Fourier domain. We show that, under appropriate stability conditions, such signals can be reconstructed uniquely from the Fourier transform magnitude. We formulate the phase retrieval problem as one of computing the parameters that uniquely determine the signal. We show that the problem can be solved by employing the annihilating filter method, particularly for the case when the parameters are distinct. For the more general case of the repeating parameters, the annihilating filter method is not applicable. We circumvent the problem by employing the algebraically coupled matrix pencil (ACMP) method. In the noiseless measurement setup, exact phase retrieval is possible. We also establish a link between the proposed analysis and 2-D cepstrum. In the noisy case, we derive Cramér-Rao lower bounds (CRLBs) on the estimates of the parameters and present Monte Carlo performance analysis as a function of the noise level. Comparisons with state-of-the-art techniques in terms of signal reconstruction accuracy show that the proposed technique outperforms the Fienup and relaxed averaged alternating reflections (RAAR) algorithms in the presence of noise. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1109/TSP.2014.2370935 | Signal Processing, IEEE Transactions |
Keywords | Field | DocType |
monte carlo methods,filtering theory,signal reconstruction,2-d parametric signals,crlb,cramér-rao lower bounds,fienup,fourier domain,fourier spectrum,fourier transform magnitude,monte carlo performance analysis,algebraically coupled matrix pencil method,annihilating filter method,exact phase retrieval,filter method,first-order difference equations,parametric representation,phase retrieval problem,relaxed averaged alternating reωections,two-dimensional phase retrieval,annihilating filter,finite rate of innovation,phase retrieval,electrical engineering,fourier transforms,stability analysis,imaging,image reconstruction | Iterative reconstruction,Mathematical optimization,Monte Carlo method,Phase retrieval,Matrix pencil,Cepstrum,Fourier transform,Parametric statistics,Mathematics,Signal reconstruction | Journal |
Volume | Issue | ISSN |
63 | 1 | 1053-587X |
Citations | PageRank | References |
6 | 0.53 | 12 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Basty Ajay Shenoy | 1 | 16 | 2.44 |
| Chandra Sekhar Seelamantula | 2 | 48 | 7.95 |