Image restoration algorithms based on the bispectrum

Kang, Moon Gi; Lay, Kuen‐Tsair; Katsaggelos, Aggelos K.

doi:10.1117/12.50406

Cited by 1 publication

(2 citation statements)

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“…Numerous algorithms for phase recovery from the modulo-2π bispectrum have been proposed which build upon the relationship in (1). These can be separated into two categories: recursive algorithms; see, e.g., [5], [6], [10], [23], [24], [25], [26], [27], [28], and nonlinear least-squares formulations; see, e.g., [7], [25], [26], [29], [30], [31]. We look at the second category.…”

Section: Phase Recovery Schemesmentioning

confidence: 99%

“…Recursive strategies fix a small set of known phase values near the center of the Fourier domain and use these known phase values along with the collected bispectrum to recursively compute the remainder of the reconstructed phase. Such strategies are well explored in the literature [5], [6], [10], [23], [24], [25], [26], [27], [28]. One limitation of recursive strategies is poor performance when attempting to reconstruct the phase values associated with high frequency information when using noisy data [7].…”

Section: Introductionmentioning

confidence: 99%

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Gauss–Newton Optimization for Phase Recovery From the Bispectrum

Herring

Nagy

Ruthotto

2020

IEEE Trans. Comput. Imaging

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Phase recovery from the bispectrum is a central problem in speckle interferometry which can be posed as an optimization problem minimizing a weighted nonlinear leastsquares objective function. We look at two different formulations of the phase recovery problem from the literature, both of which can be minimized with respect to either the recovered phase or the recovered image. Previously, strategies for solving these formulations have been limited to gradient descent or quasi-Newton methods. This paper explores Gauss-Newton optimization schemes for the problem of phase recovery from the bispectrum. We implement efficient Gauss-Newton optimization schemes for all the formulations. For the two of these formulations which optimize with respect to the recovered image, we also extend to projected Gauss-Newton to enforce element-wise lower and upper bounds on the pixel intensities of the recovered image. We show that our efficient Gauss-Newton schemes result in better image reconstructions with no or limited additional computational cost compared to previously implemented first-order optimization schemes for phase recovery from the bispectrum. MATLAB implementations of all methods and simulations are made publicly available in the BiBox repository on Github.

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