Name
Title | ||
|---|---|---|
Fienup Algorithm With Sparsity Constraints: Application to Frequency-Domain Optical-Coherence Tomography |
Abstract | ||
|---|---|---|
We address the problem of reconstructing a sparse signal from its DFT magnitude. We refer to this problem as the sparse phase retrieval (SPR) problem, which finds applications in tomography, digital holography, electron microscopy, etc. We develop a Fienup-type iterative algorithm, referred to as the Max- K algorithm, to enforce sparsity and successively refine the estimate of phase. We show that the Max- K algorithm possesses Cauchy convergence properties under certain conditions, that is, the MSE of reconstruction does not increase with iterations. We also formulate the problem of SPR as a feasibility problem, where the goal is to find a signal that is sparse in a known basis and whose Fourier transform magnitude is consistent with the measurement. Subsequently, we interpret the Max- K algorithm as alternating projections onto the object-domain and measurement-domain constraint sets and generalize it to a parameterized relaxation, known as the relaxed averaged alternating reflections (RAAR) algorithm. On the application front, we work with measurements acquired using a frequency-domain optical-coherence tomography (FDOCT) experimental setup. Experimental results on measured data show that the proposed algorithms exhibit good reconstruction performance compared with the direct inversion technique, homomorphic technique, and the classical Fienup algorithm without sparsity constraint; specifically, the autocorrelation artifacts and background noise are suppressed to a significant extent. We also demonstrate that the RAAR algorithm offers a broader framework for FDOCT reconstruction, of which the direct inversion technique and the proposed Max- K algorithm become special instances corresponding to specific values of the relaxation parameter. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/TSP.2014.2338832 | Signal Processing, IEEE Transactions |
Keywords | Field | DocType |
discrete Fourier transforms,image reconstruction,iterative methods,optical tomography,Cauchy convergence properties,DFT magnitude,FDOCT reconstruction,Fienup-type iterative algorithm,Fourier transform,Max-k algorithm,RAAR algorithm,digital holography,direct inversion technique,electron microscopy,frequency-domain optical-coherence tomography,homomorphic technique,measurement-domain constraint sets,object-domain constraint sets,reconstruction performance,relaxation parameter,relaxed averaged alternating reflections algorithm,sparse phase retrieval problem,sparse signal reconstruction,sparsity constraints,Sparsity,alternate projections,frequency-domain optical-coherence tomography,phase retrieval,relaxed averaged alternating reflections | Frequency domain,Mathematical optimization,Phase retrieval,Background noise,Iterative method,Digital holography,Algorithm,Fourier transform,Difference-map algorithm,Mathematics,Autocorrelation | Journal |
Volume | Issue | ISSN |
62 | 18 | 1053-587X |
Citations | PageRank | References |
14 | 0.70 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Subhadip Mukherjee | 1 | 36 | 7.57 |
| Chandra Sekhar Seelamantula | 2 | 48 | 7.95 |