Fienup Algorithm With Sparsity Constraints: Application to Frequency-Domain Optical-Coherence Tomography

Mukherjee, Subhadip and Seelamantula, Chandra Sekhar (2014) Fienup Algorithm With Sparsity Constraints: Application to Frequency-Domain Optical-Coherence Tomography. In: IEEE TRANSACTIONS ON SIGNAL PROCESSING, 62 (18). pp. 4659-4672.

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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.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON SIGNAL PROCESSING
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	Copy right for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Keywords:	Sparsity; phase retrieval; alternate projections; relaxed averaged alternating reflections; frequency-domain optical-coherence tomography
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	24 Sep 2014 05:47
Last Modified:	24 Sep 2014 05:47
URI:	http://eprints.iisc.ac.in/id/eprint/49915

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