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 uses near infrared (NIR) light as the probing media to recover the distributions of tissue optical properties. It has a potential to become an adjunct imaging modality for breast and brain imaging, that is capable of providing functional information of the tissue under investigation. As NIR light propagation in the tissue is dominated by scattering, the image reconstruction problem (inverse problem) tends to be non-linear and ill-posed, requiring usage of advanced computational methods to compensate this. Traditional image reconstruction methods in diffuse optical tomography employ l2 –norm based regularization, which is known to remove high frequency noises in the re-constructed images and make them appear smooth. The recovered contrast in the reconstructed image in these type of methods are typically dependent on the iterative nature of the method employed, in which the non-linear iterative technique is known to perform better in comparison to linear techniques. The usage of non-linear iterative techniques in the real-time, especially in dynamical imaging, becomes prohibitive due to the computational complexity associated with them. In the rapid dynamic diffuse optical imaging, assumption of a linear dependency in the solutions between successive frames results in a linear inverse problem. This new frame work along with the l1–norm based regularization can provide better robustness to noise and results in a better contrast recovery compared to conventional l2 –based techniques. Moreover, it is shown that the proposed l1-based technique is computationally efficient compared to its counterpart(l2 –based one). The proposed framework requires a reasonably close estimate of the actual solution for the initial frame and any suboptimal estimate leads to erroneous reconstruction results for the subsequent frames. Modern diffuse optical imaging systems are multi-modal in nature, where diffuse optical imaging is combined with traditional imaging modalities such as MRI, CT, and Ultrasound. A novel approach that can more effectively use the structural information provided by the traditional imaging modalities in these scenarios is introduced, which is based on prior image constrained- l1 minimization scheme. This method has been motivated by the recent progress in the sparse image reconstruction techniques. It is shown that the- l1 based frame work is more effective in terms of localizing the tumor region and recovering the optical property values both in numerical and gelatin phantom cases compared to the traditional methods that use structural information.

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.

Diffuse optical tomography is a promising imaging modality that provides functional information of the soft biological tissues, with prime imaging applications including breast and brain tissue in-vivo. This modality uses near infrared light( 600nm-900nm) as the probing media, giving an advantage of being non-ionizing imaging modality. The image reconstruction problem in diffuse optical tomography is typically posed as a least-squares problem that minimizes the difference between experimental and modeled data with respect to optical properties. This problem is non-linear and ill-posed, due to multiple scattering of the near infrared light in the biological tissues, leading to infinitely many possible solutions. The traditional methods employ a regularization term to constrain the solution space as well as stabilize the solution, with Tikhonov type regularization being the most popular one. The choice of this regularization parameter, also known as hyper parameter, dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. In this thesis, a simple back projection type image reconstruction algorithm is taken up, as they are known to provide computationally efficient solution compared to regularized solutions. In these algorithms, the hyper parameter becomes equivalent to filter factor and choice of which is typically dependent on the sampling interval used for acquiring data in each projection and the angle of projection. Determining these parameters for diffuse optical tomography is not so straightforward and requires usage of advanced computational models. In this thesis, a computationally efficient simplex Method based optimization scheme for automatically finding this filter factor is proposed and its performances is evaluated through numerical and experimental phantom data. As back projection type algorithms are approximations to traditional methods, the absolute quantitative accuracy of the reconstructed optical properties is poor .In scenarios, like dynamic imaging, where the emphasis is on recovering relative difference in the optical properties, these algorithms are effective in comparison to traditional methods, with an added advantage being highly computationally efficient. In the second part of this thesis, this hyper parameter choice for traditional Tikhonov type regularization is attempted with the help of Least-Squares QR-decompisition (LSQR) method. The established techniques that enable the automated choice of hyper parameters include Generalized Cross-Validation(GCV) and regularized Minimal Residual Method(MRM), where both of them come with higher over head of computation time, making it prohibitive to be used in the real-time. The proposed LSQR algorithm uses bidiagonalization of the system matrix to result in less computational cost. The proposed LSQR-based algorithm for automated choice of hyper parameter is compared with MRM methods and is proven to be computationally optimal technique through numerical and experimental phantom cases.