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Three dimensional shape, volume and depth of penetration of a skin lesion are significant factors for early diagnosis and prognosis of melanoma. An optical imaging instrument, Nevoscope is pursued in this work to image and reconstruct pigmented lesions, in three dimensions. The Nevoscope provides a set of planar projections of the pigmented inhomogeneity using transillumination. This paper presents a novel and simple algorithm to reconstruct the volume of the skin lesion from the optical projections acquired using the Nevoscope. The annular ring source of the Nevoscope injects light in the visible spectrum into the skin area surrounding the skin lesion. Light in the visible spectrum undergoes absorption and multiple scattering in the skin. Light photons, which are not extinct, are back scattered and re-emerge carrying information of the structure of the skin-lesion. The transilluminated photons are detected by a set of mirrors functioning as detectors to form 2D projections of the skin-lesion. The multiple-scattering phenomenon renders the inverse problem of solving for the volume of lesion non-linear. A diffusion- theory based approach along with the physics of light propagation in superficial layers of the skin results in a proposition of a hybrid model for solving the forward problem. An iterative non-linear inversion method is pursued to solve the inverse problem. Reconstruction of the lesion volume based on iterative algebraic reconstruction technique involves computation of 'weights' (contribution of a given voxel for a given photon path between a source and a detector) to calculate the forward and inverse solution for every iteration. A previously proposed model computes these weights as a product of two fluences. The first is the fluence calculated at a given voxel due to the annular ring source (forward fluence) and the second is the fluence calculated at the same voxel due to an imaginary point source at the detector (adjoint fluence). A diffusion theory based solution for calculation of the weights results in an under-estimation of the volume. This is because, diffusion theory is not accurate for calculation of fluence very near the source. Conventional X-ray CT like approach over-estimates the volume of reconstruction as it assumes an imaginary light source emanating photons in straight-line paths between source and detector from within the volume of the medium, and ignores scattering. The proposed hybrid method uses both the solutions from a diffusion theory based approach and the X-ray CT like approach to solve the forward and the inverse problems. Milk- gelatin phantoms and a skin mole were used to validate the algorithm. The problem is solved using three different approaches; a straight line X-ray CT like approach, a Diffusion Theory approach and finally the proposed hybrid approach. Quantitative results show the hybrid model reconstructs the phantoms with less error as opposed to the other two.
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