Nonlinear diffusion regularization for transport of intensity phase imaging

Tian, Lei; Petruccelli, Jonathan C.; Barbastathis, George

doi:10.1364/ol.37.004131

Cited by 65 publications

(34 citation statements)

References 18 publications

(21 reference statements)

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“…The latter suggests the use of regularization to stabilize the solutions. Tikhonov [24] and total variation (TV) [25]- [27] regularizations have been considered.…”

Section: A Overview Of Previous Approachesmentioning

confidence: 99%

“…Assuming periodic boundary conditions, these linear methods can be directly solved using the fast Fourier transform [33]. The case p = 1 gives the total variation (TV) regularization [34], which has been considered in [25] and [27] in the context of TIE. More importantly, if weighting is nontrivial and Tikhonov regularization is considered, the solution is given bỹ…”

Section: B Discrete Formulationmentioning

confidence: 99%

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Variational Phase Imaging Using the Transport-of-Intensity Equation

Bostan

Froustey

Nilchian

et al. 2016

IEEE Trans. on Image Process.

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Abstract-We introduce a variational phase retrieval algorithm for the imaging of transparent objects. Our formalism is based on the transport-of-intensity equation (TIE), which relates the phase of an optical field to the variation of its intensity along the direction of propagation. TIE practically requires one to record a set of defocus images to measure the variation of intensity. We first investigate the effect of the defocus distance on the retrieved phase map. Based on our analysis, we propose a weighted phase reconstruction algorithm yielding a phase map that minimizes a convex functional. The method is nonlinear and combines different ranges of spatial frequencies-depending on the defocus value of the measurements-in a regularized fashion. The minimization task is solved iteratively via the alternatingdirection method of multipliers. Our simulations outperform commonly used linear and nonlinear TIE solvers. We also illustrate and validate our method on real microscopy data of HeLa cells.

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“…The latter suggests the use of regularization to stabilize the solutions. Tikhonov [24] and total variation (TV) [25]- [27] regularizations have been considered.…”

Section: A Overview Of Previous Approachesmentioning

confidence: 99%

Section: B Discrete Formulationmentioning

confidence: 99%

Variational Phase Imaging Using the Transport-of-Intensity Equation

Bostan

Froustey

Nilchian

et al. 2016

IEEE Trans. on Image Process.

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show abstract

“…In digital holography and other interference based imaging methods, the regular reference beam adopted always makes the setup complicated and sensitive to the outside disturbance [3][4][5]. Transport of intensity equation (TIE) method, which is a non-interference phase imaging technique, has much simpler setup and lower requirement on the working environment [6][7][8][9][10][11][12][13], and recently developed Fourier ptychographic microscopy [14,15] is another non-interference phase imaging technique that can provide complex amplitude of sample, however like other lens aided imaging methods, the accuracy of these two techniques is dependent to the used optics.…”

Section: Introductionmentioning

confidence: 99%

Ultra-high speed digital micro-mirror device based ptychographic iterative engine method

Sun¹,

He²,

Kong³

et al. 2017

Biomed. Opt. Express

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Abstract:To reduce the long data acquisition time of the common mechanical scanning based Ptychographic Iterative Engine (PIE) technique, the digital micro-mirror device (DMD) is used to form the fast scanning illumination on the sample. Since the transverse mechanical scanning in the common PIE is replaced by the on/off switching of the micromirrors, the data acquisition time can be reduced from more than 15 minutes to less than 20 seconds for recording 12 × 10 diffraction patterns to cover the same field of 147.08 mm 2 . Furthermore, since the precision of DMD fabricated with the optical lithography is always higher than 10 nm (1 μm for the mechanical translation stage), the time consuming positionerror-correction procedure is not required in the iterative reconstruction. These two improvements fundamentally speed up both the data acquisition and the reconstruction procedures in PIE, and relax its requirements on the stability of the imaging system, therefore remarkably improve its applicability for many practices. It is demonstrated experimentally with both USAF resolution target and biological sample that, the spatial resolution of 5.52 μm and the field of view of 147.08 mm 2 can be reached with the DMD based PIE method. In a word, by using the DMD to replace the translation stage, we can effectively overcome the main shortcomings of common PIE related to the mechanical scanning, while keeping its advantages on both the high resolution and large field of view.

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“…There have been attempts to improve the recovery of low spatial frequency information in the context of the TIE by reformulating it as a total-variation optimization problem, [19,20]; however, these approaches require a piecewise constant phase. Other approaches include the application of structured illumination [21]; the experimentally much more complicated interferometric setup [22]; or prior knowledge of the measurement variation [23].…”

Section: Introductionmentioning

confidence: 99%

Recovering low spatial frequencies in wavefront sensing based on intensity measurements

Parvizi

Broek

Koch

2016

Adv Struct Chem Imag

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The transport of intensity equation (TIE) offers a convenient method to retrieve the phase of a wave function from maps of the irradiance (images) recorded at different planes along the optic axis of an optical system. However, being a second-order partial differential equation, even for noise-free data a unique solution of the TIE requires boundary conditions to be specified which are generally not accessible experimentally, jeopardizing retrieval of the low-frequency information in particular. Here we introduce an iterative algorithm which forgoes the need for explicit boundary conditions and combines the well-known reciprocal space solution of the TIE with the charge-flipping algorithm that has originally been developed to solve the crystallographic phase problem in X-ray diffraction. Application of this algorithm to experimental data and comparison with conventionally used algorithms demonstrates an improved retrieval of the low spatial frequencies of the phase.

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Nonlinear diffusion regularization for transport of intensity phase imaging

Abstract: We demonstrate a nonlinear diffusion (NLD) regularization method to solve the transport of intensity equation (TIE). A novel NLD regularization function is proposed to enforce piecewise-constant priors and to remove low-frequency artifacts in the TIE solution.

Cited by 65 publications

References 18 publications

Variational Phase Imaging Using the Transport-of-Intensity Equation

Variational Phase Imaging Using the Transport-of-Intensity Equation

Ultra-high speed digital micro-mirror device based ptychographic iterative engine method

Recovering low spatial frequencies in wavefront sensing based on intensity measurements

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