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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 2, Iss. 4 — Apr. 1, 2011
  • pp: 850–857
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Clean image synthesis and target numerical marching for optical imaging with backscattering light

Min Xu, Yang Pu, and Wubao Wang  »View Author Affiliations


Biomedical Optics Express, Vol. 2, Issue 4, pp. 850-857 (2011)
http://dx.doi.org/10.1364/BOE.2.000850


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Abstract

Scanning backscattering imaging and independent component analysis (ICA) are used to probe targets hidden in the subsurface of a turbid medium. A new correction procedure is proposed and used to synthesize a “clean” image of a homogeneous host medium numerically from a set of raster-scanned “dirty” backscattering images of the medium with embedded targets. The independent intensity distributions on the surface of the medium corresponding to individual targets are then unmixed using ICA of the difference between the set of dirty images and the clean image. The target positions are localized by a novel analytical method, which marches the target to the surface of the turbid medium until a match with the retrieved independent component is accomplished. The unknown surface property of the turbid medium is automatically accounted for by this method. Employing clean image synthesis and target numerical marching, three-dimensional (3D) localization of objects embedded inside a turbid medium using independent component analysis in a backscattering geometry is demonstrated for the first time, using as an example, imaging a small piece of cancerous prostate tissue embedded in a host consisting of normal prostate tissue.

© 2011 OSA

1. Introduction

Biomedical optical imaging is an imaging modality that uses light to probe structural and functional variations in tissue. One prominent example is the detection of a tumor in a human breast [1

1. S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25(12), 123010 (2009). [CrossRef]

]. With recent developments, wherein a scanning beam and a CCD camera are employed to replace the illumination and detection fiber-optics of the conventional optical tomography system, the size of generated data sets is orders of magnitude larger than those acquired with a fiber-based system and the solutions demand fast inversion algorithms [2

2. W. Cai, S. K. Gayen, M. Xu, M. Zevallos, M. Alrubaiee, M. Lax, and R. R. Alfano, “Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements,” Appl. Opt. 38(19), 4237–4246 (1999). [CrossRef]

, 3

3. S. D. Konecky, A. Mazhar, D. Cuccia, A. J. Durkin, J. C. Schotland, and B. J. Tromberg, “Quantitative optical tomography of sub-surface heterogeneities using spatially modulated structured light,” Opt. Express 17(17), 14780–14790 (2009). [CrossRef]

]. Fast inversion algorithms rely on a linearized inversion procedure on the scattering field produced by the inhomogeneities in the turbid medium, i.e., the difference between the “dirty” image of the medium with embedded targets and the “clean” one due to the (homogeneous) host medium alone. As an alternative approach, Optical Imaging using Independent Component Analysis (OPTICA) first unmixes the signal from targets embedded in a turbid medium buried in the scattering field using independent component analysis (ICA). It then detects, locates, and characterizes targets based on the analysis of unmixed independent components [4–6

4. M. Xu, M. Alrubaiee, S. K. Gayen, and R. R. Alfano, “Optical imaging of turbid media using independent component analysis: Theory and Simulation,” J. Biomed. Opt. 10(5), 051705 (2005). [CrossRef]

]. OPTICA has been demonstrated to detect and locate small absorptive [6

6. M. Xu, M. Alrubaiee, S. K. Gayen, and R. R. Alfano, “Optical diffuse imaging of an ex vivo model cancerous human breast using independent component analysis,” IEEE J. Sel. Top. Quantum Electron. 14(1), 43–49 (2008). [CrossRef]

, 7

7. M. Xu, M. Alrubaiee, S. K. Gayen, and R. R. Alfano, “Three-dimensional localization and optical imaging of objects in turbid media with independent component analysis,” Appl. Opt. 44(10), 1889–1897 (2005). [CrossRef]

], scattering [8

8. M. Alrubaiee, M. Xu, S. K. Gayen, and R. R. Alfano, “Three-dimensional optical tomographic imaging of scattering objects in tissue-simulating turbid media using independent component analysis,” Appl. Phys. Lett. 87, 191112 (2005). [CrossRef]

], or fluorescent targets [5

5. M. Alrubaiee, M. Xu, S. K. Gayen, and R. R. Alfano, “Localization and cross section reconstruction of fluorescent targets in ex vivo breast tissue using independent component analysis,” Appl. Phys. Lett. 89(13), 133902 (2006). [CrossRef]

] in tissue phantoms and model breast samples in a transmission geometry.

2. Theory

2.1. Clean image synthesis

Fast inversion algorithms require as input the scattering field due to the sought-after targets. This scattering field is the difference between the measured intensity distribution of backscattering light and a clean image of the homogeneous host medium without any embedded targets. The image for a target-free host medium is not available in most applications and must be generated from the measured data set of the medium with targets embedded inside. Denote the recorded images I(ρd,ρs) where ρd covers the whole 2D array (for example, ρd enumerates all pixels on a CCD image) for a series of beam scanning positions at ρs on the sample surface (zd = zs = 0). One crude method to obtain the image of the host medium is simply the average of all the array images after shifting the scanning position to the origin. This results in, however, only a distorted version of the real background image. To illustrate this point, assume one thin slice absorptive object δμa of volume ΔV is located at r′ = (ρ′, z′) with the extension Δz ≪ 1 along the axial direction (δμa is constant within ΔV and 0 outside), denote the exact Green's function for light propagation in the host medium G 0 and the intensity of the incident pencil beam I 0, the measured array image is given by

I(ρd,ρs)=I0G0(rd,rs)I0ΔzG0(rd;ρ,z)δμa(ρ,z)G0(ρ,z;rs)d2ρ.
(1)

We have set the speed of light to be unity for clarity. Scattering targets can be treated in a similar fashion.

The average of shifted array images (shifting the scanning position for each image ρs to the origin 0) gives

I¯(ρd,0)=I0G0(rd,0)h1(ρd,0;z)
(2)

where the error term is given by

h11NsI0ΔzG0(rd;ρ,z)u(ρ,z)G0(ρ,z;0)d2ρ=1AsI0δμΔVG0(rd;ρ,z)G0(ρ,z;0)d2ρ,
(3)

with u(ρ,z)=Σρsδμa(ρρs,z) the superposition of the absorber at all possible shifted positions, Ns is the total number of scanning positions, and AsNsa 2 s is the total area of the scanning grid with step size as, provided that the scanning area As is sufficiently large and the pitch as is fine enough such that the scanning area covers the whole range of the Green's function above the noise floor on the z = z′ plane and the value of the Green's function does not change appreciably within one scanning grid.

When a total of N slices of strength δμjΔVj are located on z = zj planes (j = 1,2,...,N), the averaging over the shifted images yields

I¯(ρd,0)=I0G0(rd,0)h(ρd,0)
(4)

where h = Σj h 1(ρd,0;zj) and the difference image between the dirty images and Ī can be written as:

ΔI(ρd,ρs)=ΣjI0G0(rd;ρ,z)δμaj(ρ,z)G0(ρ,z;rs)d2ρdz+h(ρdρs,0).
(5)

Here the error term h in Eqs. (4) and (5) only depends on ρdρs and is shared for the difference images ΔI(ρd,ρs) obtained at all scanning positions ρs. Hence a simple estimation of h is provided by averaging all shifted difference images which are minimally perturbed by the embedded objects, such as,

h(ρdρs,0)=1NBΣρsBΔI(ρdρs,0)
(6)

where B denotes the perimeter of the scanning grid which contains a total of NB scanning positions. After h has been obtained, the clean image of the host medium and the difference between the dirty images and the clean one are given by, Ic¯=I¯(ρd,0)+h(ρd,0) and ΔIc = ΔI(ρd,ρs)−h(ρdρs,0), respectively.

2.2. Numerical target marching

After the difference images ΔIc(ρd,ρs) have been obtained, ICA can be used to unmix the signal arising from individual targets and obtain the independent intensity distribution due to the jth target (j = 1,2,...,N). The jth independent component constitutes the projection of the Green's functions, G 0(rs, rj) and G 0(rd, rj), on the source and detector plane, respectively [4

4. M. Xu, M. Alrubaiee, S. K. Gayen, and R. R. Alfano, “Optical imaging of turbid media using independent component analysis: Theory and Simulation,” J. Biomed. Opt. 10(5), 051705 (2005). [CrossRef]

]. In the reflection geometry, the intensity of the backscattering light under illumination of a pencil incident beam is strongly peaked at the point of incidence. There is no analytical solution for the Green's function in this case and numerical simulations such as Monte Carlo techniques have been commonly used instead to generate the Green's function [9

9. E. M. C. Hillman, D. A. Boas, A. M. Dale, and A. K. Dunn, “Laminar optical tomography: demonstration of millimeter-scale depth resolved imaging in turbid media,” Opt. Lett. 29(14), 1650–1652 (2004). [CrossRef]

].

To overcome these difficulties, we approximate light propagation from rj to rd by a two-step process: forward propagating light first bouncing back by the bottom semi-infinite medium (z > zj), and then diffusing from the layer z = zj to the top surface z = zd < zj. This approximation is justified as the probing beam still retains its forward direction at the shallow depth (|zjzs| ~ a few lt) whereas the propagation direction of the bounced back light is randomized within the backward hemisphere, and light backscattered without interaction first with the bottom semi-infinite medium is negligible. The main advantage of this approximation is that the light propagator for the first process of light backscattering from the host medium, i.e., the Green's function G 0(ρd,0), is exactly the clean image, Ic¯ , which has been computed directly from the measured data set as outlined above without assumption of any particular light propagation model in the medium. Another advantage of using the clean image from experimentally measured data set as the Green's function G 0(ρd,0) is that this light propagator automatically incorporates the blurring effect due to the unknown superficial structure and surface roughness of a biological sample.

The projection of the Green's functions for the jth target, G 0(rd, rj), on the detector plane can now be rewritten as:

G0(rd,rj)=12πG0(ρρj,0)g(ρdρ,zd,zj)zjd2ρ
(7)

using the first Rayleigh-Sommerfeld integral [10

10. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (World Scientific, 2006).

, 11

11. J. Ripoll and V. Ntziachristos, “From Finite to Infinite Volumes: Removal of Boundaries in Diffuse Wave Imaging,” Phys. Rev. Lett. 96(17), 173903 (2006). [CrossRef]

] where the integration is performed over the z = zj plane and g is the Green's function inside an infinite homogeneous medium for a diffuse photon density wave [12

12. M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69(18), 2658–2661 (1992). [CrossRef]

]. Performing Fourier transform over the lateral coordinates, a simple relationship is obtained:

G0j(q)=12πG0(q,0)g(q,zd,zj)zj.
(8)

Here G0j(q) is the Fourier transform of the jth independent intensity on the detector plane, G 0(q,0) is the Fourier transform of the clean image, Ic¯ , and g(q, zd, zj) is the Fourier transform of g(ρ, zd, zj) representing the propagation of a plane wave of spatial modulation frequency q from the z = zj plane to the surface z = zd.

To incorporate the detection condition where only photons escaping the medium in the normal direction is being detected, we first use the optical reciprocal property [13

13. K. M. Case, “Transfer problems and the reciprocity principle,” Rev. Mod. Phys. 29(4), 651–663 (1957). [CrossRef]

] and consider instead for a normally incident beam at rd migrating to the z = zj plane. In the center-moved diffusion model [14–16

14. W. Cai, M. Lax, and R. R. Alfano, “Analytical solution of the elastic Boltzmann transport equation in an infinite uniform medium using cumulant expansion,” J. Phys. Chem. B 104(16), 3996–4000 (2000). [CrossRef]

], g(ρ, zd, zj) = exp(−κr)/r where κ=(μa0iω)D0 is the attenuation coefficient for incident beam of intensity modulation frequency ω, D0 = lt/3 is the diffusion coefficient, lt is the transport mean free path, μa0 is the absorption coefficient for the host medium, r=ρ2+(zjzd*)2 , and z * d = zd + lt is the location of the effective source by displacing the incident point of the collimated beam one lt along the incident direction. The Green's function g in the Fourier space is given by g(q, zd, zj) = 2π exp(−Q|zjz * d|)/Q and Eq. (8) is simplified to:

G0j(q)=G0(q,0)exp(Qzjzd*)
(9)

where Qq2+κ2 .

Equation (9) is the main expression for numerical target marching. The deeper the target is hidden inside the medium, the stronger damping of the high spatial frequency details in the independent intensity distribution corresponding to that target. The degree to which the independent intensity distribution flattens and loses its high spatial frequency details comparing to the clean image provides the basis to obtain the depth of the target.

The position of the jth target is obtained by fitting G 0(rd, rj) from inverse Fourier transform of Eq. (9) to the retrieved jth independent intensity distribution on the detector plane. G 0(rd, rj) needs to be deconvoluted with the incident beam profile before fitting to remove the effect of the beam profile on the clean image.

3. Experiment

Figure 1 displays the schematic diagram of the experimental setup. The sample is illuminated by a collimated diode laser (635 nm) in the direction close to the normal to the surface. Two galvanometric mirrors and controllers (General Scanning Inc. Lumonics-GSIL, Bedford, M.A., Model DSC W/HCI) are used to scan the illuminating beam along the x- and y-directions on the front surface of the sample. The two dimensional image of the backscattering light from the sample in the normal direction is recorded by a CCD camera (Photometrix CH350L, 1024 × 1024 pixels, 16 bit) after passing through a neutral density filter (NF) and lens (L). A custom software (GSIL, WinMCL Plus) is used to control the scanning speed, the two dimensional scanning grid, and to trigger the recording of the backscattering image at each scanning position. A CCD control board (Photometrix PCI-X 01-490-400 with PVCAM driver) and the corresponding imaging software (Digital Optics V++) are used to record the 2D backscattering images. The spot size of the scanning beam is ~ 500µm. The sample studied consists of a large piece of normal prostate tissue with a small piece of cancerous prostate tissue (4mm × 4mm × 1.5mm) embedded inside at a depth of z = 3.0 mm from the front surface. The thickness of the whole sample is 10 mm and with lateral dimensions of 45 × 38mm2. The embedded and the host prostate tissue were verified to be cancerous and normal, respectively, by pathology. The scanning grid is 8 × 8 with a step size of 2.13 mm. The scanning window could be adjusted and/or enlarged to contain the target if the target is found to be not well contained inside the scanning window. The CCD camera captures the backscattering light within a front surface window of size 87.8 × 87.8mm2. One pixel of the image corresponds to 0.086×0.086mm2 on the sample surface.

The optical property of prostate tissue reported in the literature varies over a wide range [17–19

17. J. H. Ali, W. B. Wang, M. Zevallos, and R. R. Alfano, “Near infrared spectroscopy and imaging to probe differences in water content in normal and cancer human prostate tissues,” Technol. Cancer Res. Treat. 3, 491–497 (2004).

]. The absorption and reduced scattering coefficients for normal prostate tissue (the host medium) in this study were μa00.026mm1 and μs ≃ 0.53mm−1, respectively, from fitting the diffusion model to the clean image for the source-detector separation larger than 9mm. The cancerous prostate tissue has a much smaller μa (about 10 times smaller) than the normal prostate tissue whereas the cancerous prostate tissue has a slightly larger μs than the normal prostate tissue at the probing wavelength 635 nm [20

20. Y. Pu, “Time-resolved spectroscopy and near infrared imaging for prostate cancer detection: receptor-targeted and native biomarker,” Ph D. thesis (City University of New York, 2010).

]. The piece of cancerous prostate tissue embedded inside the model prostate tissue sample behaves predominantly as an absorption inhomogeneity.

4. Results

The clean host image Ic¯ and the correction ratio image hIc¯ is shown in Fig. 2. The correction is computed using a total of 30 images measured on the perimeter of the scanning grid. The clean image is shown in a 10-base logarithm scale. The correction ratio is displayed on the right pane. The clean image Ic¯ represents the propagator, G 0(rd,0), the intensity distribution of backscattering light from a collimated beam incident at the origin.

Figure 3 displays the line profile of the clean image, the independent component originating from the cancerous prostate target, and the fitting of the Green's function to the independent component along the vertical direction. The full width at half maximum (FWHM) is 0.56mm for the clean host image and FWHM expands to 3.98mm for the independent intensity distribution on the detector plane arising from the target. The depth of the target is obtained by numerically marching the host image through the medium via Eq. (9) after deconvolution with the beam profile in the Fourier space until it matches the independent intensity on the detector plane. The depth from data fit is 3.01 mm, in excellent agreement with the known value. For comparison, the same analysis without applying the correction procedure and using the uncorrected difference images (ΔI) yields the depth for the target at 2.75 mm, performing much worse.

5. Discussion and conclusion

Fig. 1. Experiment setup.
Fig. 2. The clean host image and the correction ratio. The clean image is shown in a 10-base logarithm scale. The correction ratio ( (hIc¯) ) is displayed on the right pane.
ΣjfjδμajΔVj=AshIc¯
(10)

where fj is the scaling factor for the jth target.

One major challenge of applying backscattering light to probe the subsurface (at the depth up to a few transport mean free paths) of a turbid medium is that the diffusion approximation to radiative transfer is inadequate in this case and computationally much expensive methods need to be used [3

3. S. D. Konecky, A. Mazhar, D. Cuccia, A. J. Durkin, J. C. Schotland, and B. J. Tromberg, “Quantitative optical tomography of sub-surface heterogeneities using spatially modulated structured light,” Opt. Express 17(17), 14780–14790 (2009). [CrossRef]

, 9

9. E. M. C. Hillman, D. A. Boas, A. M. Dale, and A. K. Dunn, “Laminar optical tomography: demonstration of millimeter-scale depth resolved imaging in turbid media,” Opt. Lett. 29(14), 1650–1652 (2004). [CrossRef]

]. The novelty of numerical target marching is that it alleviates this difficulty using the Green's function G 0(rd,0) of light reflection from a semi-infinite medium, i.e., the clean image of the host medium, obtained directly from experimentally measured array images. As the result, no light propagation model is assumed in obtaining this Green's function G 0(rd,0), and the blurring effect due to the unknown superficial structure and surface roughness of a biological sample on light propagation is automatically incorporated in G 0(rd,0). This new approach, which builds the proper Green's function for optical imaging from experimentally measured clean image, should be applicable in modeling light propagation in general when the commonly used diffusion model is inadequate or incorrect.

Fig. 3. The line profile of the clean host image (Left), the independent component originating from the cancerous prostate target (Middle), and the fitting of the Green's function to the independent component along the vertical direction (Right).

The geometry of choice to detect prostate cancer is to use backscattering light through rectum. As the rectal wall is relatively thin (~2.5–3.0mm) [22

22. C. H. Huh, M. S. Bhutani, and E. B. Farfan, “andW. E. Bolch, “Individual variations in mucosa and total wall thickness in the stomach and rectum assessed via endoscopic ultrasound,” Clin. Phys. Physiol. Meas. 24(15–N), 22 (2003).

], backscattering light can penetrate the rectal wall and examine the peripheral zone where most prostate cancer initiates. The developed methods are, in particular, useful for optical imaging of prostate cancer through rectum in the backscattering geometry. We have demonstrated in our prior work that optical imaging using independent component analysis to be an effective method to locate and characterize absorption, scattering, or fluorescent targets as small as several millimeters in the transmission geometry [5–8

5. M. Alrubaiee, M. Xu, S. K. Gayen, and R. R. Alfano, “Localization and cross section reconstruction of fluorescent targets in ex vivo breast tissue using independent component analysis,” Appl. Phys. Lett. 89(13), 133902 (2006). [CrossRef]

]. As the FWHM of the Green's function for light backscattering from subsurface in the reflection geometry is much smaller than that of the Green's function for light transmission through a slab in the transmission geometry, we expect even smaller size of inhomogeneity can be detected in the backscattering geometry provided a sufficient signal to noise ratio.

In conclusion, clean image synthesis of a host medium and target numerical marching have been presented for optical imaging. These techniques are, in particular, useful for imaging in a reflection (backscattering) geometry. Employing clean image synthesis and target numerical marching, three-dimensional localization of objects embedded inside a turbid medium using independent component analysis in a backscattering geometry has been demonstrated for the first time with an example imaging a small piece of cancerous prostate tissue embedded in a host consisting of normal prostate tissue.

Acknowledgments

This research is supported by USAMRMC through grants of W81XWH-08-1-0717 and W81XWH-10-1-0526. M.X. acknowledges additional support from Research Corporation and NIH (1R15EB009224).

References and links

1.

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25(12), 123010 (2009). [CrossRef]

2.

W. Cai, S. K. Gayen, M. Xu, M. Zevallos, M. Alrubaiee, M. Lax, and R. R. Alfano, “Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements,” Appl. Opt. 38(19), 4237–4246 (1999). [CrossRef]

3.

S. D. Konecky, A. Mazhar, D. Cuccia, A. J. Durkin, J. C. Schotland, and B. J. Tromberg, “Quantitative optical tomography of sub-surface heterogeneities using spatially modulated structured light,” Opt. Express 17(17), 14780–14790 (2009). [CrossRef]

4.

M. Xu, M. Alrubaiee, S. K. Gayen, and R. R. Alfano, “Optical imaging of turbid media using independent component analysis: Theory and Simulation,” J. Biomed. Opt. 10(5), 051705 (2005). [CrossRef]

5.

M. Alrubaiee, M. Xu, S. K. Gayen, and R. R. Alfano, “Localization and cross section reconstruction of fluorescent targets in ex vivo breast tissue using independent component analysis,” Appl. Phys. Lett. 89(13), 133902 (2006). [CrossRef]

6.

M. Xu, M. Alrubaiee, S. K. Gayen, and R. R. Alfano, “Optical diffuse imaging of an ex vivo model cancerous human breast using independent component analysis,” IEEE J. Sel. Top. Quantum Electron. 14(1), 43–49 (2008). [CrossRef]

7.

M. Xu, M. Alrubaiee, S. K. Gayen, and R. R. Alfano, “Three-dimensional localization and optical imaging of objects in turbid media with independent component analysis,” Appl. Opt. 44(10), 1889–1897 (2005). [CrossRef]

8.

M. Alrubaiee, M. Xu, S. K. Gayen, and R. R. Alfano, “Three-dimensional optical tomographic imaging of scattering objects in tissue-simulating turbid media using independent component analysis,” Appl. Phys. Lett. 87, 191112 (2005). [CrossRef]

9.

E. M. C. Hillman, D. A. Boas, A. M. Dale, and A. K. Dunn, “Laminar optical tomography: demonstration of millimeter-scale depth resolved imaging in turbid media,” Opt. Lett. 29(14), 1650–1652 (2004). [CrossRef]

10.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (World Scientific, 2006).

11.

J. Ripoll and V. Ntziachristos, “From Finite to Infinite Volumes: Removal of Boundaries in Diffuse Wave Imaging,” Phys. Rev. Lett. 96(17), 173903 (2006). [CrossRef]

12.

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69(18), 2658–2661 (1992). [CrossRef]

13.

K. M. Case, “Transfer problems and the reciprocity principle,” Rev. Mod. Phys. 29(4), 651–663 (1957). [CrossRef]

14.

W. Cai, M. Lax, and R. R. Alfano, “Analytical solution of the elastic Boltzmann transport equation in an infinite uniform medium using cumulant expansion,” J. Phys. Chem. B 104(16), 3996–4000 (2000). [CrossRef]

15.

M. Xu, W. Cai, M. Lax, and R. R. Alfano, “A photon transport forward model for imaging in turbid media,” Opt. Lett. 26(14), 1066–1068 (2001). [CrossRef]

16.

M. Xu, W. Cai, M. Lax, and R. R. Alfano, “Photon migration in turbid media using a cumulant approximation to radiative transfer,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066609 (2002). [CrossRef]

17.

J. H. Ali, W. B. Wang, M. Zevallos, and R. R. Alfano, “Near infrared spectroscopy and imaging to probe differences in water content in normal and cancer human prostate tissues,” Technol. Cancer Res. Treat. 3, 491–497 (2004).

18.

T. C. Zhu, J. C. Finlay, and S. M. Hahn, “Determination of the distribution of light, optical properties, drug concentration, and tissue oxygenation in-vivo in human prostate during motexafin lutetium-mediated photodynamic therapy,” J. Photochem. Photobiol. B 79(3), 231–241 (2005). [CrossRef]

19.

T. Svensson, S. Andersson-Engels, M. Einarsdóttír, and K. Svanberg, “In vivo optical characterization of human prostate tissue using near-infrared time-resolved spectroscopy,” J. Biomed. Opt. 12(1), 014022 (2007). [CrossRef]

20.

Y. Pu, “Time-resolved spectroscopy and near infrared imaging for prostate cancer detection: receptor-targeted and native biomarker,” Ph D. thesis (City University of New York, 2010).

21.

V. A. Markel and J. C. Schotland, “Symmetries, inversion formulas, and image reconstruction for optical tomography,” Phys. Rev. E 70(5), 056616 (2004). [CrossRef]

22.

C. H. Huh, M. S. Bhutani, and E. B. Farfan, “andW. E. Bolch, “Individual variations in mucosa and total wall thickness in the stomach and rectum assessed via endoscopic ultrasound,” Clin. Phys. Physiol. Meas. 24(15–N), 22 (2003).

OCIS Codes
(170.0110) Medical optics and biotechnology : Imaging systems
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.5280) Medical optics and biotechnology : Photon migration
(290.1350) Scattering : Backscattering
(290.1990) Scattering : Diffusion
(290.4210) Scattering : Multiple scattering
(290.7050) Scattering : Turbid media

ToC Category:
Diffuse Optical Imaging

History
Original Manuscript: December 13, 2010
Revised Manuscript: January 28, 2011
Manuscript Accepted: February 25, 2011
Published: March 14, 2011

Citation
Min Xu, Yang Pu, and Wubao Wang, "Clean image synthesis and target numerical marching for optical imaging with backscattering light," Biomed. Opt. Express 2, 850-857 (2011)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-4-850


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References

  1. S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25(12), 123010 (2009). [CrossRef]
  2. W. Cai, S. K. Gayen, M. Xu, M. Zevallos, M. Alrubaiee, M. Lax, and R. R. Alfano, “Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements,” Appl. Opt. 38(19), 4237–4246 (1999). [CrossRef]
  3. S. D. Konecky, A. Mazhar, D. Cuccia, A. J. Durkin, J. C. Schotland, and B. J. Tromberg, “Quantitative optical tomography of sub-surface heterogeneities using spatially modulated structured light,” Opt. Express 17(17), 14780–14790 (2009). [CrossRef]
  4. M. Xu, M. Alrubaiee, S. K. Gayen, and R. R. Alfano, “Optical imaging of turbid media using independent component analysis: Theory and Simulation,” J. Biomed. Opt. 10(5), 051705 (2005). [CrossRef]
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