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.

Electrical Capacitance Tomography (ECT) is an imaging technique that maps the electrical permittivity contrast of the object. This paper studies an Image and a shape reconstruction method for ECT. For Image reconstruction, a regularized Gauss-Newton method has been implemented, based on the inverse finite element technique. For shape reconstruction, a . narrow band level set method has been developed. Using experimental ECT data, a comparative study of these two techniques is the main objective of this paper.

Speckle noise seriously degrades the quality of SAR Images and complicates the Image exploitation using automated Image analysis techniques. Recently, the application of compressed sensing (CS) is explored in the SAR signal processing. In this paper, first, a linear model is derived for speckled SAR data. Then, using this model and the compressed sensing theory, a speckle reduction method is proposed. In the proposed method, the Image backgrounds as well as the bright point targets are also reconstructed together with noise reduction. The important feature of the proposed method is the joint noise reduction simultaneous with the SAR Image formation. Moreover, using simulated and real SAR Images, the performance of the proposed method in noise reduction and preserving Image features is evaluated and compared to the performance of some de-noising approaches.