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The depth of invasion and three-dimensional characteristics of skin lesions are important parameters in the early diagnosis and prognosis of malignant melanoma. `Nevoscopy' (Nevus - pigmented skin lesion), an optical trans-illumination based modality, has previously been proposed for the non-invasive assessment of skin tumors. The skin area surrounding a lesion is illuminated with a visible light source in contact with the skin, avoiding all surface illumination. The Nevoscope with its mirrors at different angles and orientations provides multiple 2D views of the trans-illuminated lesions. Nevoscopy together with image analysis has the potential to quantify all the parameters used in melanoma diagnosis. This paper describes the development of reconstruction algorithms for application to Nevoscopy. Initially, x-ray CT algorithms were applied to Nevoscopy data under heuristic assumptions of linear source-detector relationships. In reality, the reconstruction from scattered optical radiation is a nonlinear inverse problem which is typically solved by progressively solving linear inverse problems. The problem defaults to determination of influence of increased localized absorption on a given source-detector measurement. Photon transport theory and its surrogate diffusion theory are employed to compute this local contribution or `weight.' A three-point diffusion theory model, based on diploe solutions to the diffusion equation, is proposed as a deterministic method to compute the voxel weights for a discrete representation of a homogeneous medium. Simulations of 2D Nevoscope-like imaging geometries indicate that the weights computed by this method approximate those computed by rigorous statistical Monte Carlo statistical procedure. Reconstructions of embedded absorber in homogeneous media using the three-point diffusion weights are comparable to those obtained using Monte Carlo weights. The proposed three point diffusion model was extended to the existing image geometry and applied to reconstruct volumes from the projections of phantom and skin images. Results are presented. Direct extension of the three point diffusion model to the existing Nevoscope geometry has brought into light some of the deficiencies of both the current geometry of the system and the model.
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