Wood is a limited natural resource whose characteristics have been difficult to identify by advanced technology. The most expensive is a hardwood. There is a desire to optimize the production of wood products by minimizing waste and maximizing output. It could be achieved if one had capabilities to evaluate the common wood structures ― knots, rots, empty spaces and other defects. There are many nondestructive testing methods that could be applied to the evaluation of the inner quality of a log. The most successful one is an x-ray computerized tomography. This thesis covers principles of computerized tomography and image reconstruction algorithms. Testing was performed on implementations of tomographic image reconstruction algorithms using synthetic and real data. Research on an application of an x-ray computerized tomography for the analysis of wood structures was made. Inspection of glued zones in glued wooden articles was accomplished using tomographic imaging. Guidelines for the creation of a wood specialized x-ray computerized tomograph were given.

Biomedical optical imaging is capable of providing functional information of the soft bi-ological tissues, whose applications include imaging large tissues, such breastand brain in-vivo. Biomedical optical imaging uses near infrared light (600nm-900nm) as the probing media, givin ganaddedadvantageofbeingnon-ionizingimagingmodality. The tomographic technologies for imaging large tissues encompasses diffuse optical tomogra-phyandphotoacoustictomography. Traditional image reconstruction methods indiffuse optical tomographyemploysa �2-norm based regularization, which is known to remove high frequency no is either econstructed images and make the mappearsmooth. Hence as parsity based image reconstruction has been deployed for diffuse optical tomography, these sparserecov-ery methods utilize the �p-norm based regularization in the estimation problem with 0≤ p<1. These sparse recovery methods, along with an approximation to utilizethe �0-norm, have been used forther econstruction of diffus eopticaltomographic images.The comparison of these methods was performed by increasing the sparsityinthesolu-tion. Further a model resolution matrix based framework was proposed and shown to in-duceblurinthe�2-norm based regularization framework for diffuse optical tomography. This model-resolution matrix framework was utilized in the optical imaged econvolution framework. A basis pursuitdeconvolution based on Split AugmentedLagrangianShrink-ageAlgorithm(SALSA)algorithm was used along with the Tikhonovregularization step making the image reconstruction into a two-step procedure. This new two-step approach was found to be robust with no iseandwasabletobetterdelineatethestructureswhichwasevaluatedusingnumericalandgelatinphantom experiments. Modern diffuse optical imaging systems are multi-modalin nature, where diffuse optical imaging is combined with traditional imaging modalitiessuc has Magnetic Res-onanceImaging(MRI),or Computed Tomography(CT). Image-guided diffuse optical tomography has the advantage of reducingthetota lnumber of optical parameters beingreconstructedtothenumber of distinct tissue types identified by the traditional imaging modality, converting the optical image-reconstruction problem fromunder-determined innaturetoover-determined. In such cases, the minimum required measurements might be farless compared to those of the traditional diffuse optical imaging. An approach to choose these measurements optimally based on a data-resolution matrix is proposed, and it is shown that it drastically reduces the minimum required measurements (typicalcaseof240to6) without compromising the image reconstruction performance. In the last part of the work , a model-based image reconstruction approaches in pho-toacoustic tomography (which combines light and ultra sound) arestudied as it is know that these methods have a distinct advantage compared to traditionalanalytical methods in limited datacase. These model-based methods deployTikhonovbasedregularizationschemetoreconstruct the initial pressure from the boundary acoustic data. Again a model-resolution for these cases tend to represent the blurinduced by the regularization scheme. A method that utilizes this blurringmodelandper forms the basis pursuit econ-volution to improve the quantitative accuracy of the reconstructed photoacoustic image is proposed and shown to be superior compared to other traditional methods. Moreover, this deconvolution including the building of model-resolution matrixis achievedvia the Lanczosbidiagonalization (least-squares QR) making this approach computationally ef-ficient and deployable inreal-time. Keywords Medical imaging, biomedical optical imaging, diffuse optical tomography, photoacous-tictomography, multi-modalimaging, inverse problems,sparse recovery,computational methods inbiomedical optical imaging.

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 uses near infrared (NIR) light as the probing media to re-cover 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. Diffuse optical image reconstruction problem is always rank-deficient, where finding the independent measurements among the available measurements becomes challenging problem. Knowing these independent measurements will help in designing better data acquisition set-ups and lowering the costs associated with it. An optimal measurement selection strategy based on incoherence among rows (corresponding to measurements) of the sensitivity (or weight) matrix for the near infrared diffuse optical tomography is proposed. As incoherence among the measurements can be seen as providing maximum independent information into the estimation of optical properties, this provides high level of optimization required for knowing the independency of a particular measurement on its counterparts. The utility of the proposed scheme is demonstrated using simulated and experimental gelatin phantom data set comparing it with the state-of-the-art methods. The traditional image reconstruction methods employ ℓ2-norm in the regularization functional, resulting in smooth solutions, where the sharp image features are absent. The sparse recovery methods utilize the ℓp-norm with p being between 0 and 1 (0 ≤ p1), along with an approximation to utilize the ℓ0-norm, have been deployed for the reconstruction of diffuse optical images. These methods are shown to have better utility in terms of being more quantitative in reconstructing realistic diffuse optical images compared to traditional methods. Utilization of ℓp-norm based regularization makes the objective (cost) function non-convex and the algorithms that implement ℓp-norm minimization utilizes approximations to the original ℓp-norm function. Three methods for implementing the ℓp-norm were con-sidered, namely Iteratively Reweigthed ℓ1-minimization (IRL1), Iteratively Reweigthed Least-Squares (IRLS), and Iteratively Thresholding Method (ITM). These results in-dicated that IRL1 implementation of ℓp-minimization provides optimal performance in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images. Photoacoustic tomography (PAT) is an emerging hybrid imaging modality combining optics with ultrasound imaging. PAT provides structural and functional imaging in diverse application areas, such as breast cancer and brain imaging. A model-based iterative reconstruction schemes are the most-popular for recovering the initial pressure in limited data case, wherein a large linear system of equations needs to be solved. Often, these iterative methods requires regularization parameter estimation, which tends to be a computationally expensive procedure, making the image reconstruction process to be performed off-line. To overcome this limitation, a computationally efficient approach that computes the optimal regularization parameter is developed for PAT. This approach is based on the least squares-QR (LSQR) decomposition, a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution.