Computational imaging has been playing an important role in understanding and analysing the captured images. Both image segmentation and restoration has been in-tegral parts of computational imaging. The studies performed in this thesis has been focussed toward developing novel algorithms for image segmentation and restoration. Study related to usage of Morozov Discrepancy Principle in Di use Optical Imaging was also presented here to show that hyper parameter selection could be performed with ease. The Laplacian of Gaussian (LoG) and Canny operators use Gaussian smoothing be-fore applying the derivative operator for edge detection in real images. The LoG kernel was based on second derivative and is highly sensitive to noise when compared to the Canny edge detector. A new edge detection kernel, called as Helmholtz of Gaussian (HoG), which provides higher di suavity is developed in this thesis and it was shown that it is more robust to noise. The formulation of the developed HoG kernel is similar to LoG. It was also shown both theoretically and experimentally that LoG is a special case of HoG. This kernel when used as an edge detector exhibited superior performance compared to LoG, Canny and wavelet based edge detector for the standard test cases both in one- and two-dimensions. The linear inverse problem encountered in restoration of blurred noisy images is typically solved via Tikhonov minimization. The outcome (restored image) of such min-imitation is highly dependent on the choice of regularization parameter. In the absence of prior information about the noise levels in the blurred image, ending this regular-inaction/hyper parameter in an automated way becomes extremely challenging. The available methods like Generalized Cross Validation (GCV) may not yield optimal re-salts in all cases. A novel method that relies on minimal residual method for ending the regularization parameter automatically was proposed here and was systematically compared with the GCV method. It was shown that the proposed method performance was superior to the GCV method in providing high quality restored images in cases where the noise levels are high Di use optical tomography uses near infrared (NIR) light as the probing media to recover the distributions of tissue optical properties with an ability to provide functional information of the tissue under investigation. As NIR light propagation in the tissue is dominated by scattering, the image reconstruction problem (inverse problem) is non-linear and ill-posed, requiring usage of advanced computational methods to compensate this. An automated method for selection of regularization/hyper parameter that incorporates Morozov discrepancy principle(MDP) into the Tikhonov method was proposed and shown to be a promising method for the dynamic Di use Optical Tomography.

Diffuse optical tomography (DOT) is one of the promising imaging modalities that pro- vides functional information of the soft biological tissues in-vivo, such as breast and brain tissues. The near infrared (NIR) light (600-1000 nm) is the interrogating radiation, which is typically delivered and collected using fiber bundles placed on the boundary of the tissue. The internal optical property distribution is estimated via model-based image reconstruction algorithm using these limited boundary measurements. Image reconstruction problem in DOT is known to be non-linear, ill-posed, and some times under-determined due to the multiple scattering of NIR light in the tissue. Solving this inverse problem requires regularization to obtain meaningful results, with Tikhonov-type regularization being the most popular one. The choice of the regularization parameter dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. An automated method for optimal selection of regularization parameter that is based on regularized minimal residual method (MRM) is proposed and is compared with the traditional generalized cross-validation method. The results obtained using numerical and gelatin phantom data indicate that the MRM-based method is capable of providing the optimal regularization parameter. A new approach that can easily incorporate any generic penalty function into the diffuse optical tomographic image reconstruction is introduced to show the utility of non-quadratic penalty functions. The penalty functions that were used include, quadratic (`2), absolute (`1), Cauchy, and Geman-McClure. The regularization parameter in each of these cases were obtained automatically using the generalized cross-validation (GCV) method. The reconstruction results were systematically compared with each other via utilization of quantitative metrics, such as relative error and Pearson correlation. The reconstruction results indicate that while quadratic penalty may be able to provide better separation between two closely spaced targets, it's contrast recovery capability is limited and the sparseness promoting penalties, such as `1, Cauchy, Geman-McClure have better utility in reconstructing high-contrast and complex-shaped targets with Geman-McClure penalty being the most optimal one. Effective usage of image guidance by incorporating the refractive index (RI) variation in computational modeling of light propagation in tissue is investigated to assess its impact on optical-property estimation. With the aid of realistic patient breast three-dimensional models, the variation in RI for different regions of tissue under investigation is shown to influence the estimation of optical properties in image-guided diffuse optical tomography (IG-DOT) using numerical simulations. It is also shown that by assuming identical RI for all regions of tissue would lead to erroneous estimation of optical properties. The a priori knowledge of the RI for the segmented regions of tissue in IG-DOT, which is difficult to obtain for the in vivo cases, leads to more accurate estimates of optical properties. Even inclusion of approximated RI values, obtained from the literature, for the regions of tissue resulted in better estimates of optical properties, with values comparable to that of having the correct knowledge of RI for different regions of tissue. Image reconstruction in IG-DOT procedure involves reduction of the number of optical parameters to be reconstructed equal to the number of distinct regions identified in the structural information provided by the traditional imaging modality. This makes the image reconstruction problem to be well-determined compared to traditional under- determined case. Still, the methods that are deployed in this case are same as the one used for traditional diffuse optical image reconstruction, which involves regularization term as well as computation of the Jacobian. A gradient-free Nelder-Mead simplex method was proposed here to perform the image reconstruction procedure and shown to be providing solutions that are closely matching with ones obtained using established methods. The proposed method also has the distinctive advantage of being more efficient due to being regularization free, involving only repeated forward calculations.