Discretization schemes and numerical approximations of PDE impainting models and a comparative evaluation on novel real world MRI reconstruction applications

While various PDE models are in discussion since the last ten years and are widely applied nowadays in image processing and computer vision tasks, including restoration, filtering, segmentation and object tracking, the perspective adopted in the majority of the relevant reports is the view of applied mathematician, attempting to prove the existence theorems and devise exact numerical methods for solving them. Unfortunately, such solutions are exact for the continuous PDEs but due to the discrete approximations involved in image processing, the results yielded might be quite unsatisfactory. The major contribution of This work is, therefore, to present, from an engineering perspective, the application of PDE models in image processing analysis, from the algorithmic point of view, the discretization and numerical approximation schemes used for solving them. It is of course impossible to tackle all PDE models applied in image processing in this report from the computational point of view. It is, therefore, focused on image impainting PDE models, that is on PDEs, including anisotropic diffusion PDEs, higher order non-linear PDEs, variational PDEs and other constrained/regularized and unconstrained models, applied to image interpolation/ reconstruction. Apart from this novel computational critical overview and presentation of the PDE image impainting models numerical analysis, the second major contribution of This work is to evaluate, especially the anisotropic diffusion PDEs, in novel real world image impainting applications related to MRI

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

State of the Art in Face Recognition

Notwithstanding the tremendous effort to solve the face recognition problem, it is not possible yet to design a face recognition system with a potential close to human performance. New computer vision and pattern recognition approaches need to be investigated. Even new knowledge and perspectives from different fields like, psychology and neuroscience must be incorporated into the current field of face recognition to design a robust face recognition system. Indeed, many more efforts are required to end up with a human like face recognition system. This book tries to make an effort to reduce the gap between the previous face recognition research state and the future state

Intelligent energy management system - techniques and methods

ABSTRACT Our environment is an asset to be managed carefully and is not an expendable resource to be taken for granted. The main original contribution of this thesis is in formulating intelligent techniques and simulating case studies to demonstrate the significance of the present approach for achieving a low carbon economy. Energy boosts crop production, drives industry and increases employment. Wise energy use is the first step to ensuring sustainable energy for present and future generations. Energy services are essential for meeting internationally agreed development goals. Energy management system lies at the heart of all infrastructures from communications, economy, and society’s transportation to the society. This has made the system more complex and more interdependent. The increasing number of disturbances occurring in the system has raised the priority of energy management system infrastructure which has been improved with the aid of technology and investment; suitable methods have been presented to optimize the system in this thesis. Since the current system is facing various problems from increasing disturbances, the system is operating on the limit, aging equipments, load change etc, therefore an improvement is essential to minimize these problems. To enhance the current system and resolve the issues that it is facing, smart grid has been proposed as a solution to resolve power problems and to prevent future failures. This thesis argues that smart grid consists of computational intelligence and smart meters to improve the reliability, stability and security of power. In comparison with the current system, it is more intelligent, reliable, stable and secure, and will reduce the number of blackouts and other failures that occur on the power grid system. Also, the thesis has reported that smart metering is technically feasible to improve energy efficiency. In the thesis, a new technique using wavelet transforms, floating point genetic algorithm and artificial neural network based hybrid model for gaining accurate prediction of short-term load forecast has been developed. Adopting the new model is more accuracy than radial basis function network. Actual data has been used to test the proposed new method and it has been demonstrated that this integrated intelligent technique is very effective for the load forecast. Choosing the appropriate algorithm is important to implement the optimization during the daily task in the power system. The potential for application of swarm intelligence to Optimal Reactive Power Dispatch (ORPD) has been shown in this thesis. After making the comparison of the results derived from swarm intelligence, improved genetic algorithm and a conventional gradient-based optimization method, it was concluded that swam intelligence is better in terms of performance and precision in solving optimal reactive power dispatch problems

Novel Algorithms for Merging Computational Fluid Dynamics and 4D Flow MRI

Time-resolved three-dimensional spatial encoding combined with three-directional velocity-encoded phase contrast magnetic resonance imaging (termed as 4D flow MRI), can provide valuable information for diagnosis, treatment, and monitoring of vascular diseases. The accuracy of this technique, however, is limited by errors in flow estimation due to acquisition noise as well as systematic errors. Furthermore, available spatial resolution is limited to 1.5mm - 3mm and temporal resolution is limited to 30-40ms. This is often grossly inadequate to resolve flow details in small arteries, such as those in cerebral circulation. Recently, there have been efforts to address the limitations of the spatial and temporal resolution of MR flow imaging through the use of computational fluid dynamics (CFD). While CFD is capable of providing essentially unlimited spatial and temporal resolution, numerical results are very sensitive to errors in estimation of the flow boundary conditions. In this work, we present three novel techniques that combine CFD with 4D flow MRI measurements in order to address the resolution and noise issues. The first technique is a variant of the Kalman Filter state estimator called the Ensemble Kalman Filter (EnKF). In this technique, an ensemble of patient-specific CFD solutions are used to compute filter gains. These gains are then used in a predictor-corrector scheme to not only denoise the data but also increase its temporal and spatial resolution. The second technique is based on proper orthogonal decomposition and ridge regression (POD-rr). The POD method is typically used to generate reduced order models (ROMs) in closed control applications of large degree of freedom systems that result from discretization of governing partial differential equations (PDE). The POD-rr process results in a set of basis functions (vectors), that capture the local space of solutions of the PDE in question. In our application, the basis functions are generated from an ensemble of patient-specific CFD solutions whose boundary conditions are estimated from 4D flow MRI data. The CFD solution that should be most closely representing the actual flow is generated by projecting 4D flow MRI data onto the basis vectors followed by reconstruction in both MRI and CFD resolution. The rr algorithm was used for between resolution mapping. Despite the accuracy of using rr as the mapping step, due to manual adjustment of a coefficient in the algorithm we developed the third algorithm. In this step, the rr algorithm was substituded with a dynamic mode decomposition algorithm to preserve the robustness. These algorithms have been implemented and tested using a numerical model of the flow in a cerebral aneurysm. Solutions at time intervals corresponding to the 4D flow MRI temporal resolution were collected and downsampled to the spatial resolution of the imaging data. A simulated acquisition noise was then added in k-space. Finally, the simulated data affected by noise were used as an input to the merging algorithms. Rigorous comparison to state-of-the-art techniques were conducted to assess the accuracy and performance of the proposed method. The results provided denoised flow fields with less than 1\% overall error for different signal-to-noise ratios. At the end, a small cohort of three patients were corrected and the data were reconstructed using different methods, the wall shear stress (WSS) was calculated using different reconstructed data and the results were compared. As it has been shown in chapter 5, the calculated WSS using different methods results in mutual high and low shear stress regions, however, the exact value and patterns are significantly different