Imaging in turbid media such as biological tissue is an important emerging technology that can permit functional assessment of biological functions in additional to structural information. The standard approach to this type of imaging is to employ finite element methods to solve the (potentially time-dependent) diffusion equation with arbitrary boundaries. Although this approach can be effective in creating images, insight into the fundamental properties of the reconstructed images (such as their signal-to-noise properties, dependence of spatial resolution on material contrast and types of illumination, etc.) must be obtained by Monte Carlo analyses. If the diffusion equation is simplified to the Helmholtz equation by assuming that the probing illumination is amplitude-modulated light, a diffraction-tomographic approach to modeling the forward problem can be employed that enables the derivation of closed-form expressions to predict spatial resolution as a function of the illumination, detection system, and material properties. In addition, the diffraction tomography problem formulation can be used to develop a backpropagation algorithm to help address the inverse problem.
In this talk, I will present diffraction tomography theory for turbid media and a backpropagation algorithm for solving the inverse problem. Because diffraction tomography assumes that the imaging signal is a weak perturbation from the homogeneous solution (i.e., the Born or Rytov approximation), the homogeneous solution is required to be known to obtain the desired images. Since the homogeneous solution is not known, in general, I will also describe an approach to determining the homogeneous solution using blind deconvolution methods.
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