Statistical <i>p</i>-Norm Distribution Analysis of Noise in Photon-Counting Detector Projection Data

Jie Guo; Ailong Cai; Shaoyu Wang; Zhizhong Zheng; Lei Li; Bin Yan

doi:10.3788/AOS231610

Acta Optica Sinica, Volume. 44, Issue 3, 0311003(2024)

Statistical p-Norm Distribution Analysis of Noise in Photon-Counting Detector Projection Data

Jie Guo¹, Ailong Cai², Shaoyu Wang², Zhizhong Zheng¹, Lei Li², and Bin Yan^2、*

Author Affiliations

¹Basic of Department, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, Henan , China

²Henan Key Laboratory of Imaging and Intelligent Processing, Department of Information Systems Engineering, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, Henan , China

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Figures & Tables(6)

Fig. 1. Dataset of bovine bone

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Fig. 2. PDF fitting results of projected data noise in different datasets. (a) Bovine bone B dataset; (b) rabbit head B dataset; (c) bovine bone C dataset; (d) bovine bone A dataset

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Fig. 3. Flowchart for analysis of observation sequences in projection data. (a) Time series of the observations; (b) time series of the first-order differenced sequence; (c) autocorrelation plot of the differenced sequence; (d) partial autocorrelation plot of the differenced sequence; (e) diagnostic of the differenced sequence model; (f) model prediction

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Fig. 4. Restoration results. (a) Mouse thorax phantom (display window is [0.142 0.145] $c m^{- 1}$ ); (b) ground truth projection image; (c) projection image with added noise and outliers; (d) projection image after outlier restoration (display window is [0.345 0.355] $c m^{- 1}$ ); (e) reconstruction results before outlier restoration (display window is [0 0.35] $c m^{- 1}$ ); (f) reconstruction results after outlier restoration (display window is [0 0.35] $c m^{- 1}$ )

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Table 1. Results of goodness-of-fit test

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Table 1. Results of goodness-of-fit test

Dataset	Assessment	Gaussian	Poisson	Gamma	p-norm
Bovine bone-B	p-value	0.1310	0.1418	0.1330	0.3326
	Test statistic	9.8522	10.3419	11.2365	7.3026
	Degrees of freedom	6	8	7	8
	Conclusion	Yes	Yes	No	Yes
Rabbit head-B	p-value	0.5093	0.2059	0.5018	0.5337
	Test statistic	5.0356	8.5148	5.3334	3.0215
	Degrees of freedom	6	7	6	6
	Conclusion	Yes	Yes	Yes	Yes
Bovine bone-C	p-value	0.0327	0.0001	0.0221	0.3125
	Test statistic	13.7325	18.9702	14.7714	10.1526
	Degrees of freedom	6	7	6	7
	Conclusion	No	No	No	Yes
Rabbit head-A	p-value	0.9247	0.9075	0.9524	0.8652
	Test statistic	1.9446	2.7450	1.6020	3.2531
	Degrees of freedom	6	7	6	6
	Conclusion	Yes	Yes	Yes	Yes
Rabbit head-C	p-value	0.0510	0.0612	0.0503	0.0501
	Test statistic	29.0262	23.1069	16.8697	25.3261
	Degrees of freedom	6	7	7	5
	Conclusion	Yes	Yes	Yes	Yes

Table 2. Comparison of the mean and standard deviation for the region of interest in Fig. 4(f)
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Table 2. Comparison of the mean and standard deviation for the region of interest in Fig. 4(f)
Region of interest A B C D
Before restoration $0.0042 \pm 0.0024$ $0.0036 \pm 0.0022$ $0.0149 \pm 0.0208$ $0.0460 \pm 0.0033$
After restoration $0.0039 \pm 0.0018$ $0.0033 \pm 0.0014$ $0.0145 \pm 0.0204$ $0.0440 \pm 0.0028$

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Jie Guo, Ailong Cai, Shaoyu Wang, Zhizhong Zheng, Lei Li, Bin Yan. Statistical p-Norm Distribution Analysis of Noise in Photon-Counting Detector Projection Data[J]. Acta Optica Sinica, 2024, 44(3): 0311003

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