• Optics and Precision Engineering
  • Vol. 30, Issue 18, 2167 (2022)
Yanqiu LIU1,2, Xiangong HU2,3, Heng ZHANG1,2, Hongbo GUO1,2, and Xiaowei HE1,2,3,*
Author Affiliations
  • 1School of Information Sciences and Technology, Northwest University, Xi’an7027, China
  • 2The Xi’an Key Laboratory of Radiomics and Intelligent Perception, Northwest University, Xi'an71017, China
  • 3Network and Data Center, Northwest University, Xi’an710127, China
  • show less
    DOI: 10.37188/OPE.20223018.2167 Cite this Article
    Yanqiu LIU, Xiangong HU, Heng ZHANG, Hongbo GUO, Xiaowei HE. Application of spectral differential strategy in diffusion approximation model and simplified spherical harmonic approximation model[J]. Optics and Precision Engineering, 2022, 30(18): 2167 Copy Citation Text show less

    Abstract

    Bioluminescence tomography (BLT) is a promising in vivo molecular imaging tool that allows non-invasive monitoring of physiological and pathological processes at the cellular and molecular levels. The reconstruction accuracy of BLT is affected by the optical transmission model error and the ill-posedness of the inverse problem. The higher-order optical transmission model was able to improve the precision, while the multi-spectral method was able to alleviate the ill-posedness of the inverse problem. In this study, the spectral differential strategy, combining the spectral differential theory and multi-spectral method, was applied on the optical transmission model based on the diffusion approximation equation (DE) and third simplified spherical harmonic approximation equation (SP3). First, errors in these two radiative transfer equations (RTE) approximations were analyzed, and the attenuation effect on the error was compared when the spectral differential strategy was applied on two types of optical transmission models. The forward simulation experiment results showed that the spectral differential strategy can effectively reduce the model error of the DE and SP3 models. The spectral differential strategy resulted in the transmission accuracy of the DE model resembling that of the SP3 model, and decreased the high requirements on computing time and storage space of high-order approximation. On this basis, the spectral differential strategy was applied on the DE and SP3 optical transmission models for light source reconstruction. The experimental results showed that the spectral differential strategy not only improves the accuracy of the two light transmission models, but also alleviates the ill-condition of the inverse problem in BLT, yields a location error of reconstructed source within 1 mm, and improves the accuracy of the light source reconstruction in target location, shape restoration, and image contrast. The average time required by the SP3 model was approximately 1 525 s. In contrast, the DE model combined with spectral differential strategy had an average time consumption of only approximately 34 s, resulting in balanced reconstruction accuracy and speed.
    ŝϕ(r,ŝ)+μtrϕ(r,ŝ)-μs4πΘŝŝ'ϕr,ŝ'dΩ'-q(r,ŝ)=0,(1)

    View in Article

    -[DΦ(r)]+μaΦ(r)-q(r)=0(2)

    View in Article

    A(DE)S=Φm(3)

    View in Article

    EA(DE)λ=XλY(4)

    View in Article

    EA(DE)diffe=(Xλj-Xλk)Y(5)

    View in Article

    EA(DE)diffe(6)

    View in Article

    -n+12n+11μa,n+1n+22n+3ϕn+2+n+12n+3ϕn-12n+11μa,n-1n2n-1ϕn+n-12n-1ϕn-2+μa,nϕn-q(r)=0,(7)

    View in Article

    -13μa1φ1+μaφ1=q(r)+23μaφ2-815μaφ3+1635μaφ4-17μa3φ2+49μa+59μa2φ2=-23q(r)+23μaφ1+1645μa+49μa2φ3-32105μa+821μa2φ4.(8)

    View in Article

    A(SP3)S=Φm(9)

    View in Article

    EA(SP3)λ=XλY(10)

    View in Article

    EA(SP3)diffe=(Xλj-Xλk)Y(11)

    View in Article

    EA(SP3)diffe(12)

    View in Article

    Aλ1Aλ2Aλ3S=Φλ1mΦλ2mΦλ3m(13)

    View in Article

    AmultiS=Φmultim(14)

    View in Article

    Aλ1-Aλ2Aλ1-Aλ3Aλ2-Aλ3S=Φλ1m-Φλ2mΦλ1m-Φλ3mΦλ2m-Φλ3m(15)

    View in Article

    AdiffeS=Φdiffem(16)

    View in Article

    minS12AdiffeS-Φdiffem22+τSpp,0<P<1(17)

    View in Article

    EEnergy difference=abs(ΦMCλj(k)-ΦDE(SP3)λj(k)),Specific spectrumabs(abs(ΦMCλj-ΦMCλk)-abs (ΦDE(SP3)λj-ΦDE(SP3)λk)),Spectral differential(18)

    View in Article

    eAverage error=i=1NEEnergy differenceiN(19)

    View in Article

    CCosine similarity=cos(θ)=ABAB=i=1nAi×Bii=1n(Ai)2×i=1n(Bi)2,(20)

    View in Article

    ILE=(x-x0)2+(y-y0)2+(z-z0)2(21)

    View in Article

    IDice=2XYX+Y(22)

    View in Article

    ICNR=μROI-μBCK(ωROIσ2ROI+ωBCKσ2BCK)1/2(23)

    View in Article

    Yanqiu LIU, Xiangong HU, Heng ZHANG, Hongbo GUO, Xiaowei HE. Application of spectral differential strategy in diffusion approximation model and simplified spherical harmonic approximation model[J]. Optics and Precision Engineering, 2022, 30(18): 2167
    Download Citation