Studies of signal estimation bias in grating-based x-ray multicontrast imaging

Ji, Xu; Ge, Yongshuai; Zhang, Ran; Li, Ké; Chen, Guang-Hong

doi:10.1002/mp.12235

Cited by 12 publications

(13 citation statements)

References 29 publications

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“…In previous studies, it has been found that the estimated

{\overset{false^}{ϕ}}^{o}

should follow a wrapped normal distribution as a result of the Arg( z ) operation . The wrapped normal distribution is given as

g false({\overset{false^}{ϕ}}^{o} false) = \sum_{k = - \infty}^{+ \infty} \frac{1}{\sqrt{2 π σ^{2}}} \exp [- \frac{{false({\overset{false^}{ϕ}}^{o} - ϕ^{o} + 2 k π false)}^{2}}{2 σ^{2}}], {\overset{ϕ}{true}}^{o} \in false[- π, π false),

where σ is the standard deviation of

{\overset{false^}{ϕ}}^{o}

of the original normal distribution before the phase wrapping effect is taken into account [See Eq.…”

Section: Methodsmentioning

confidence: 99%

“…For a relatively small σ (for example, σ < 1), it was found that the mean of the wrapped normal distribution can be approximated as

false⟨ \overset{ϕ}{true} (S) false⟩ = \int_{- π}^{π} \overset{false^}{ϕ} f false(\overset{ϕ}{true} false) d \overset{false^}{ϕ} \approx S θ + π [erf (A_{-}) - erf (A_{+})],

where erf(·) is the so‐called error function and variable

A_{\pm}

is defined as

A_{\pm} = \frac{π \pm S θ}{\sqrt{2} σ}

. The additional item

π [erf false(A_{-} false) - erf false(A_{+} false)]

is referred to as the signal bias . Due to the existence of bias,

⟨ \overset{false^}{ϕ} ⟩

may no longer be proportional to S .…”

Section: Methodsmentioning

confidence: 99%

“…. Six phase steps were used ( M = 6) and the visibility ( ε ) was assumed to be 0.2 to represent our benchtop grating‐based phase contrast system . The refraction angle ( θ ) was assumed to be

1 \times 10^{- 6} π

.…”

Section: Methodsmentioning

confidence: 99%

“…In previous studies, it has been found that the estimated / o should follow a wrapped normal distribution as a result of the Arg(z) operation. 18,19 The wrapped normal distribution is given as…”

Section: A Theoretical Analysis Of Snr Of the Phase Shiftmentioning

confidence: 99%

“…The additional item p½erfðA À Þ À erfðA þ Þ is referred to as the signal bias. 19 Due to the existence of bias, h/i may no longer be proportional to S. The variance of the wrapped normal distribution, denoted as r 2 w , can be approximated as…”

Section: A Theoretical Analysis Of Snr Of the Phase Shiftmentioning

confidence: 99%

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Is high sensitivity always desirable for a grating‐based differential phase contrast imaging system?

Zhang

et al. 2020

Medical Physics

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Purpose In grating‐based x‐ray differential phase contrast (DPC) imaging, the measured signal amplitude of the phase shift induced by an image object is proportional to the so‐called system sensitivity. Therefore, to achieve a better signal‐to‐noise (SNR) for improved imaging performance, it is generally believed that one should increase the system sensitivity by reducing the period of the analyzer grating or increasing the distance between the phase grating and analyzer grating. The purpose of this work is to theoretically and experimentally demonstrate that there is an optimal system sensitivity to attain the highest SNR for a given task provided that the standard phase‐stepping acquisition and phase retrieval methods are used. When system sensitivity goes beyond this optimal value, SNR decreases and the imaging performance deteriorates. Methods Due to the fundamental fact that the measured phase signal is a cyclic variable, the phase wrapping effect is inevitable in DPC imaging when the system sensitivity increases. The phase wrapping effect appears in both signal and noise measurements. The effect in the signal measurement is manifested in the so‐called signal statistical bias and such effect often impacts the accuracy of the measurement. The phase wrapping effect also appears in the noise variance measurement and impacts the precision of the measurement. A thorough theoretical analysis was performed in this work to demonstrate the quantitative impacts of phase wrapping on both signal bias and noise variance and thus on the actual system SNR. The joint effect of phase wrapping in both the signal bias and noise variance yields an optimal system sensitivity to achieve the highest SNR. Both extensive numerical simulation studies and experimental studies were performed to validate the theoretical analysis. Results Both theoretical analysis and experimental studies show that the SNR of the DPC signal is not always proportional to the sensitivity due to the cyclic nature of the signal and the phase wrapping effect. For a given refraction angle and exposure level, there exists an optimal sensitivity factor that maximizes the SNR, beyond which, increasing the sensitivity will decrease the SNR. Conclusions Increase of system sensitivity does not always improve x‐ray DPC imaging performance provided that the standard phase‐stepping acquisition and phase retrieval methods are used.

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“…In previous studies, it has been found that the estimated

{\overset{false^}{ϕ}}^{o}

should follow a wrapped normal distribution as a result of the Arg( z ) operation . The wrapped normal distribution is given as

g false({\overset{false^}{ϕ}}^{o} false) = \sum_{k = - \infty}^{+ \infty} \frac{1}{\sqrt{2 π σ^{2}}} \exp [- \frac{{false({\overset{false^}{ϕ}}^{o} - ϕ^{o} + 2 k π false)}^{2}}{2 σ^{2}}], {\overset{ϕ}{true}}^{o} \in false[- π, π false),

where σ is the standard deviation of

{\overset{false^}{ϕ}}^{o}

of the original normal distribution before the phase wrapping effect is taken into account [See Eq.…”

Section: Methodsmentioning

confidence: 99%

“…For a relatively small σ (for example, σ < 1), it was found that the mean of the wrapped normal distribution can be approximated as

false⟨ \overset{ϕ}{true} (S) false⟩ = \int_{- π}^{π} \overset{false^}{ϕ} f false(\overset{ϕ}{true} false) d \overset{false^}{ϕ} \approx S θ + π [erf (A_{-}) - erf (A_{+})],

where erf(·) is the so‐called error function and variable

A_{\pm}

is defined as

A_{\pm} = \frac{π \pm S θ}{\sqrt{2} σ}

. The additional item

π [erf false(A_{-} false) - erf false(A_{+} false)]

is referred to as the signal bias . Due to the existence of bias,

⟨ \overset{false^}{ϕ} ⟩

may no longer be proportional to S .…”

Section: Methodsmentioning

confidence: 99%

1 \times 10^{- 6} π

.…”

Section: Methodsmentioning

confidence: 99%

Section: A Theoretical Analysis Of Snr Of the Phase Shiftmentioning

confidence: 99%

Section: A Theoretical Analysis Of Snr Of the Phase Shiftmentioning

confidence: 99%

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Is high sensitivity always desirable for a grating‐based differential phase contrast imaging system?

Zhang

et al. 2020

Medical Physics

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A deep learning reconstruction framework for low dose phase contrast computed tomography via inter-contrast enhancement

Zhang

Zhu

et al. 2023

Measurement

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X-ray dark-field computed tomography for monitoring of tissue freezing

John,

Gottwald,

Berthe

et al. 2024

Sci Rep

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Accurately monitoring the extent of freezing in biological tissue is an important requirement for cryoablation, a minimally invasive cancer treatment that induces cell death by freezing tissue with a cryoprobe. During the procedure, monitoring is required to avoid unnecessary harm to the surrounding healthy tissue and to ensure the tumor is properly encapsulated. One commonly used monitoring method is attenuation-based computed tomography (CT), which visualizes the ice ball by utilizing its hypoattenuating properties compared to unfrozen tissue. However, the contrast between frozen and unfrozen tissue remains low. In a proof-of-principle experiment, we show that the contrast between frozen and unfrozen parts of a porcine phantom mimicking breast tissue can be greatly enhanced by acquiring X-ray dark-field images that capture the increasing small-angle scattering caused by the ice crystals formed during the procedure. Our results show that, compared to X-ray attenuation, the frozen region is detected significantly better in dark-field radiographs and CT scans of the phantom. These findings demonstrate that X-ray dark-field imaging could be a potential candidate for improved monitoring of cryoablation procedures.

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Studies of signal estimation bias in grating-based x-ray multicontrast imaging

Cited by 12 publications

References 29 publications

Is high sensitivity always desirable for a grating‐based differential phase contrast imaging system?

Is high sensitivity always desirable for a grating‐based differential phase contrast imaging system?

A deep learning reconstruction framework for low dose phase contrast computed tomography via inter-contrast enhancement

X-ray dark-field computed tomography for monitoring of tissue freezing

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