Time-domain diffuse optical tomography using analytic statistical characteristics of photon trajectories

Abstract

We show that the scattering amplitude of four open string scalars or tachyons on the world-volume of a Dp-brane in the bosonic string theory can be written in a universal form. The difference between this amplitude and the corresponding amplitude in the superstring theory is in an extra tachyonic pole. We show that in an α expansion and for slowly varying fields, the amplitude is consistent with the tachyonic DBI action in which the even part of the tachyon potential is V (T ) = e −( √ πT /α) 2 with α = 1 for bosonic theory and α = √ 2 for superstring theory.

Methods for Postprocessing in Single-Step Diffuse Optical Tomography

“…For all objects from Table 1 we used the measurement ratio 32×32 (32 sources and 32 receivers). The circular objects were reconstructed by the backprojection algorithm with convolution filtering 2007b;Lyubimov et al, 2003) and the rectangular ones with the modified multiplicative algebraic reconstruction technique (Konovalov et al, 2006b;2007a). To restore the reconstructed tomograms, in all cases we partitioned the image domain into 5×5 regions and applied the reflexive boundary conditions.…”

“…the problem of radiation propagation through tissue is solved numerically many times and at each step of linearization it is necessary to adjust the matrix of the system of algebraic equations that describe the discrete reconstruction model. As shown in our earlier papers (Kalintsev et al, 2005;Konovalov et al, 2003;2006b;2007a;2007b;Lyubimov et al, 2002;, there exists a unique opportunity to make the reconstruction procedure much faster by changing over in equation (1) from volume integration to integration along an effective trajectory from source to receiver. The photon average trajectory method (PAT method) we have developed finds such a trajectory using a probabilistic interpretation of light energy transfer by photons from source to receiver.…”

“…For the second approach the single-step reconstruction means that the system of algebraic equations describing the discrete model is only once inverted and the matrix needs no adjustment. In our previous papers we provided some examples of 2D reconstruction from data simulated for the time-domain measurement technique to show that the PAT method can be implemented with integral algorithms 2007b;Lyubimov et al, 2003) as well as with algebraic ones (Konovalov et al, 2006b;2007a;Lyubimov et al, 2002). Compared with the multistep algorithms, the former give a terrific gain (a factor of about 100) in calculation time, but are too inaccurate in the reconstruction of optical inhomogeneities near the boundaries of the study object.…”

Algebraic Reconstruction and Post-Processing in Incomplete Data Computed Tomography: from X-rays to Laser Beams

“…The object contains periodic structures created by circular absorbing inhomogeneities. In both cases, the inverse problem is solved using algebraic reconstruction techniques (additive and multiplicative) which we modernized to attain the better convergence of the iterative reconstruction process 2006b). Procedures used to calculate the weight matrices are described in detail.…”

“…In case of DOT, we use model data from the numerical solution of a time-dependent diffusion equation with an instantaneous point source (time-domain measurement technique). We consider a traditional geometry where sources and receivers are on the boundary of a scattering object in the form of a flat layer (Konovalov et al, 2006b). The object contains periodic structures created by circular absorbing inhomogeneities.…”