title: Statistical analysis of nonlinearly reconstructed near-infrared tomographic images. I. Theory and simulations
abstract: Near-infrared (NIR) 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 (MSE) 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
keyphrases: hemoglobin optical diffusion model-based image reconstruction algorithm light flux mean-squared error test image randomly distributed noise bias error optimal solution decreasing regularization parameter lowest image error medical diagnostic imaging oxygen saturation photon migration minimum regularization parameter constraint ill-posed inverse image reconstruction problem regularization spatial property values estimation O/sub 2/