Introduction: In this study, we intend to use diffuse optical Tomography (DOT) as a noninvasive, safe and low cost technique that can be considered as a functional imaging method and mention the importance of Image reconstruction in accuracy and procession of Image. One of the most important and fastest methods in Image reconstruction is the boundary element method (BEM). This method is introduced and employed in our works.Method: Generally, to Image a biological tissue we must obtain its optical properties. In order to reach this goal we benefit from diffusion equation because tissue is highly scattering medium. Diffusion equation is solved by boundary element equation (BEM) in our research. First, we assume a double layer phantom with different scattering and absorption coefficients to simulate and verify precession and accuracy of Image reconstruction by BEM. Light absorption can be affected by volume fraction of blood in skin. For a specific skin species the volume fraction is calculated and then the results are compared with the reconstructed values obtained by BEM. Since the depth of tissue is important in light absorption a two layer phantom with known values is made and the depths of layers are reconstructed by BEM then they are compared with the expected values. A homogenous phantom with known scattering and absorption coefficients was made and then these coefficients were reconstructed by BEM. Finally, an inhomogeneous phantom (phantom with defect) whose defect was in a known position was made and the absorption and scattering coefficients were reconstructed and compared with real values.Results: Comparison between real or simulated values and reconstructed values of scattering and absorption coefficients, volume fraction of blood and thickness of phantom layers by BEM shows maximum errors of 24%, 7% and 35%, respectively.Conclusion: Comparison between BEM data and real or simulated values shows an acceptable agreement. Consequently, we can rely on BEM as a beneficial method in diffuse optical tomography Image reconstruction.

A new algorithm for reconstruction of design relation matrix(DRM) is presented. The reconstruction of an unknown DRM is discussed based on some design matrix projections, which was expressed by design experts. The reconstruction algorithm has been formed based on the new concept of DRM. It shows the relation between functional requirements and design parameters that exists in the related design matrix. The specifications of uncoupled, decoupled and coupled design matrices are scrutinizable by the DRM and related concepts such as design set (DS), design row set (DRS) and design column set (DCS). Then, the DRM reconstruction algorithm and algorithm for selecting the unbiased reconstruction from reconstruction family members are presented based on reconstruct ability analysis. The DRM reconstruction algorithm is applicable in reverse engineering, design evaluation and improvement.