• Photonics Research
  • Vol. 9, Issue 3, B45 (2021)
Jianhui Ma1, Zun Piao1, Shuang Huang1, Xiaoman Duan1, Genggeng Qin1, Linghong Zhou1、2、*, and Yuan Xu1、3、*
Author Affiliations
  • 1School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China
  • 2e-mail: smart@smu.edu.cn
  • 3e-mail: yuanxu@smu.edu.cn
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    DOI: 10.1364/PRJ.413486 Cite this Article Set citation alerts
    Jianhui Ma, Zun Piao, Shuang Huang, Xiaoman Duan, Genggeng Qin, Linghong Zhou, Yuan Xu. Monte Carlo simulation fused with target distribution modeling via deep reinforcement learning for automatic high-efficiency photon distribution estimation[J]. Photonics Research, 2021, 9(3): B45 Copy Citation Text show less

    Abstract

    Particle distribution estimation is an important issue in medical diagnosis. In particular, photon scattering in some medical devices extremely degrades image quality and causes measurement inaccuracy. The Monte Carlo (MC) algorithm is regarded as the most accurate particle estimation approach but is still time-consuming, even with graphic processing unit (GPU) acceleration. The goal of this work is to develop an automatic scatter estimation framework for high-efficiency photon distribution estimation. Specifically, a GPU-based MC simulation initially yields a raw scatter signal with a low photon number to hasten scatter generation. In the proposed method, assume that the scatter signal follows Poisson distribution, where an optimization objective function fused with sparse feature penalty is modeled. Then, an over-relaxation algorithm is deduced mathematically to solve this objective function. For optimizing the parameters in the over-relaxation algorithm, the deep Q-network in the deep reinforcement learning scheme is built to intelligently interact with the over-relaxation algorithm to accurately and rapidly estimate a scatter signal with the large range of photon numbers. Experimental results demonstrated that our proposed framework can achieve superior performance with structural similarity >0.94, peak signal-to-noise ratio >26.55 dB, and relative absolute error <5.62%, and the lowest computation time for one scatter image generation can be within 2 s.

    dσRd(cosθ)=πr02F(E,θ,Z)2(1+cos2θ),

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    dσCd(cosθ)=πr02S(E,θ,Z)[P(E,θ)P(E,θ)2sin2θ+P(E,θ)3].

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    P(E,θ)=EE=11+Em0c2(1cosθ),

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    P[x=S^(u)]=S(u)S^(u)S^(u)!eS(u),

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    P(x=S^)=SS^S^!eSdu.

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    argminS(SS^logS)du.

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    S(u)=argminS(SS^logS)du+β2|S|2du,

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    (1S^S)β2S=0.

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    [1S^(i,j)S(i,j)]β2S(i,j)=0,

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    S(k+1)(i,j)=(1ω)S(k)(i,j)+ω4[S(k)(i,j)1β(1S^(i,j)S(k)(i,j))],

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    Qπ(s,a)=E(Gt|st=s,at=a),

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    Gt=rt+γrt+1+γ2rt+2+=m=1γmrt+m,

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    Qπ*(s,a)=maxπQπ(s,a).

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    Qπ*(s,a)=r+γmaxaQπ*(s,a),

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    L=E{[r+γmaxaQπ(s,a;W)Qπ(s,a;W)]2}.

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    L=E{[r+γmaxaQ^π(s,a;W^)Qπ(s,a;W)]2}·

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    L=E{{r+γQ^π{s,argmaxa[Qπ(s,a;W)];W^}Qπ(s,a;W)}2}.

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    SSIM(x,y)=(2μxμy+c1)(2σxy+c2)(μx2+μy2+c1)(σx2+σy2+c2),

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    rt=sgn[SSIM(st+1,sgt)SSIM(st,sgt)],

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    PSNR=10log10(MAX2MSE),

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    RAE=i=1mj=1n|s(i,j)sgt(i,j)||sgt(i,j)|,

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    Jianhui Ma, Zun Piao, Shuang Huang, Xiaoman Duan, Genggeng Qin, Linghong Zhou, Yuan Xu. Monte Carlo simulation fused with target distribution modeling via deep reinforcement learning for automatic high-efficiency photon distribution estimation[J]. Photonics Research, 2021, 9(3): B45
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