document: Statistical analysis of nonlinearly reconstructed near-infrared tomographic images . I. Theory and simulations Near-infrared -LRB- NIR -RRB- diffuse tomography is an emerging method for imaging the interior of tissues to quantify concentrations of hemoglobin and exogenous chromophores noninvasively in vivo . It often exploits an optical diffusion model-based image reconstruction algorithm to estimate spatial property values from measurements of the light flux at the surface of the tissue . In this study , mean-squared error -LRB- MSE -RRB- over the image is used to evaluate methods for regularizing the ill-posed inverse image reconstruction problem in NIR tomography . Estimates of image bias and image standard deviation were calculated based upon 100 repeated reconstructions of a test image with randomly distributed noise added to the light flux measurements . It was observed that the bias error dominates at high regularization parameter values while variance dominates as the algorithm is allowed to approach the optimal solution . This optimum does not necessarily correspond to the minimum projection error solution , but typically requires further iteration with a decreasing regularization parameter to reach the lowest image error . Increasing measurement noise causes a need to constrain the minimum regularization parameter to higher values in order to achieve a minimum in the overall image MSE
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