Boosting spatial resolution by incorporating periodic boundary conditions into single-distance hard-x-ray phase retrieval

Paganin, David M.; Favre‐Nicolin, V.; Mirone, Alessandro; Rack, Alexander; Villanova, Julie; Olbinado, Margie P.; Fernández, Vincent; Silva, Júlio César da; Pelliccia, Daniele

doi:10.1088/2040-8986/abbab9

Cited by 18 publications

(31 citation statements)

References 99 publications

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“…4(e). In particular, the Laplacian-type character of this difference map is a signature of the higher-resolution projected thickness reconstruction associated with the Fokker-Planck analysis [28]. This is especially clear in Fig.…”

Section: Experimental Pbi Datamentioning

confidence: 77%

X-ray dark-field and phase retrieval without optics, via the Fokker-Planck equation

Leatham¹,

Paganin²,

Morgan³

2021

Preprint

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Emerging methods of x-ray imaging that capture phase and dark-field effects are equipping medicine with complementary sensitivity to conventional radiography. These methods are being applied over a wide range of scales, from virtual histology to clinical chest imaging, and typically require the introduction of optics such as gratings. Here, we consider extracting x-ray phase and dark-field signals from bright-field images collected using nothing more than a coherent x-ray source and detector. Our approach is based on the Fokker-Planck equation for paraxial imaging, which is the diffusive generalization of the transport-of-intensity equation. Specifically, we utilize the Fokker-Planck equation in the context of propagation-based phase-contrast imaging, where we show that two intensity images are sufficient for successful retrieval of the projected thickness and dark-field signals associated with the sample. We show the results of our algorithm using both a simulated dataset and an experimental dataset. These demonstrate that the x-ray darkfield signal can be extracted from propagation-based images, and that x-ray phase can be retrieved with better spatial resolution when dark-field effects are taken into account. We anticipate the proposed algorithm will be of benefit in biomedical imaging, industrial settings, and other non-invasive imaging applications.

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Section: Experimental Pbi Datamentioning

confidence: 77%

X-ray dark-field and phase retrieval without optics, via the Fokker-Planck equation

Leatham¹,

Paganin²,

Morgan³

2021

Preprint

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“…As demonstrated in [19], a Taylor series expansion of (4) shows convergence to (2) for spatial frequencies close to the origin of Fourier space, but this can differ greatly when approaching the Nyquist frequency of the Fourier transform. Paganin et al, [19] further shows the GPM filter always suppresses high spatial frequencies to a lesser extent than the PM, providing some first principles justification for the spatial resolution improvement found by users applying sharpening masks alongside the PM algorithm [19]. Paganin et al [19] provide a comparison between the PM and GPM spatial frequency filters by varying δ∆/µW over several orders of magnitude.…”

Section: Introductionmentioning

confidence: 96%

“…Alternative methods have also included adding high spatial frequency information from the phase contrast image back into the retrieved images [18], intended as a compromise between phase retrieval and phase contrast. This motivated Paganin et al [19] to revisit the derivation and find a first principles justification for the success of these approaches [19]. Previous, first-principlessupported methods for increasing the spatial resolution of the PM have broadened the algorithm's scope, such as by reducing the filter strength to account for inherent blurring by the system point spread function (PSF) [20]; however, the new Generalised Paganin Method provides a correction to the PM algorithm itself.…”

Section: Introductionmentioning

confidence: 99%

“…Note that, although (1) includes Fourier transforms, this algorithm is implemented using discrete Fourier transforms, since digital images have discrete sampling. In the GPM derivation presented by Paganin et al [19], this is addressed by employing a 5-point approximation of the transverse Laplacian [21] [22] into which the discrete representation of the Fourier transform is substituted. This representation is then used, in place of the Fourier derivative theorem, to expand the Laplacian that appears in the derivation of the original PM.…”

Section: Introductionmentioning

confidence: 99%

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Enhanced spatial resolution through DFT rederivations of X-ray phase retrieval algorithms

Pollock¹,

Morgan²,

Croton³

et al. 2021

Preprint

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Propagation-based phase-contrast imaging, used in conjunction with the phase retrieval algorithm based on the Transport-of-Intensity Equation (TIE) (Paganin et al., 2002), is commonly used to improve the sensitivity of X-ray imaging. Recently, a 'Generalised Paganin Method' algorithm was published to correct the tendency of the TIE algorithm to over-blur images. The article, Paganin et al. 2020, provided a derivation of the new method and demonstrated a difference in the level of blurring applied by each algorithm. In this manuscript, we quantify the spatial resolution improvement and describe the optimal experimental conditions to observe this improvement. We link the effectiveness of the spatial resolution improvement to the imaging point spread function (PSF), incorporating the PSF to compare the blurring applied by each algorithm. We then validate this model through measurements of spatial resolution in experimental data imaging plastic phantoms and biological tissue, using detectors with different PSFs. By analysing edge-spread functions in CT data captured with indirect detectors with PSFs of several pixels in extent, we show negligible spatial resolution improvement when using the generalised Paganin method. However, a clear improvement in spatial resolution, up to 17%, was observed with direct detectors having PSFs of approximately one pixel in extent. Additionally, we demonstrate clear visual improvement in resolution in CT slices of rat lungs. Finally, we demonstrate the versatility of this improvement by generalising other phase retrieval algorithms, namely for multi-material samples and for spectral decomposition using propagation-based phase contrast, and experimentally verify improvements in spatial resolution.

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“…scheme has been developed recently, based on Paganin's SMO-reconstruction, which is referred to as "generalized Paganin"[141].…”

mentioning

confidence: 99%

Advancing the Characterization of Neuronal Cyto-Architecture by X-ray Phase-Contrast Tomography

Eckermann¹

2021

Göttingen Series in X-Ray Physics

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The Göttingen series in x-ray physics is intended as a collection of research monographs in x-ray science, carried out at the Institute for X-ray Physics at the Georg-August-Universität in Göttingen, and in the framework of its related research networks and collaborations.It covers topics ranging from x-ray microscopy, nano-focusing, wave propagation, image reconstruction, tomography, short x-ray pulses to applications of nanoscale x-ray imaging and biomolecular structure analysis.In most but not all cases, the contributions are based on Ph.D. dissertations. The individual monographs should be enhanced by putting them in the context of related work, often based on a common long term research strategy, and funded by the same research networks. We hope that the series will also help to enhance the visibility of the research carried out here and help others in the field to advance similar projects.

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Boosting spatial resolution by incorporating periodic boundary conditions into single-distance hard-x-ray phase retrieval

Cited by 18 publications

References 99 publications

X-ray dark-field and phase retrieval without optics, via the Fokker-Planck equation

X-ray dark-field and phase retrieval without optics, via the Fokker-Planck equation

Enhanced spatial resolution through DFT rederivations of X-ray phase retrieval algorithms

Advancing the Characterization of Neuronal Cyto-Architecture by X-ray Phase-Contrast Tomography

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