Bayesian Approach with Entropy Prior for Open Systems

The Bayesian approach Maximum a Posteriori (MAP) is discussed in the context of solving the image reconstruction problem in nuclear medicine: positron emission tomography (PET) and single photon emission computer tomography (SPECT). Two standard probabilistic forms, Gibbs and entropy prior probabilities, are analyzed. It is shown that both the entropy-based and Gibbs priors in their standard formulations result in global regularization when a single parameter controls the solution. Global regularization leads to over-smoothed images and loss of fine structures. Over-smoothing is undesirable, especially in oncology in diagnosis of cancer lesions of small size and low activity. To overcome the over-smoothing problem and to improve resolution of images, the new approach based on local statistical regularization is developed.

Bayesian Maximum-A-Posteriori Approach with Global and Local Regularization to Image Reconstruction Problem in Medical Emission Tomography

The Bayesian approach Maximum a Posteriori (MAP) provides a common basis for developing statistical methods for solving ill-posed image reconstruction problems. MAP solutions are dependent on a priori model. Approaches developed in literature are based on prior models that describe the properties of the expected image rather than the properties of the studied object. In this paper, such models have been analyzed and it is shown that they lead to global regularization of the solution. Prior models that are based on the properties of the object under study are developed and conditions for local and global regularization are obtained. A new reconstruction algorithm has been developed based on the method of local statistical regularization. Algorithms with global and local regularization were compared in numerical simulations. The simulations were performed close to the real oncologic single photon emission computer tomography (SPECT) study. It is shown that the approach with local regularization produces more accurate images of ‘hot spots’, which is especially important to tumor diagnostics in nuclear oncology.

Global regularization method for planar restricted three-body problem

In this paper, global regularization method for planar restricted three-body problem is purposed by using the transformation z = x+iy = ? cos n(u+iv), where i = ??1, 0 < ? ? 1 and n is a positive integer. The method is developed analytically and computationally. For the analytical developments, analytical solutions in power series of the pseudotime ? are obtained for positions and velocities (u, v, u', v') and (x, y, x?, y?) in both regularized and physical planes respectively, the physical time t is also obtained as power series in ?. Moreover, relations between the coefficients of the power series are obtained for two consequent values of n. Also, we developed analytical solutions in power series form for the inverse problem of finding ? in terms of t. As typical examples, three symbolic expressions for the coefficients of the power series were developed in terms of initial values. As to the computational developments, the global regularized equations of motion are developed together with their initial values in forms suitable for digital computations using any differential equations solver. On the other hand, for numerical evolutions of power series, an efficient method depending on the continued fraction theory is provided.

3D Building Adjustment Using Planar Half-Space Regularities

The automatic reconstruction of 3D building models with complex roof shapes is still an active area of research. In this paper we present a novel approach for local and global regularization rules that integrate building knowledge to improve both the shape of the reconstructed building models and their accuracy. These rules are defined for the planar half-space representation of our models and emphasize the presence of symmetries, co-planarity, parallelism, and orthogonality. By not adjusting building features separately (e.g. ridges, eaves, etc.) we are able to handle more than one feature at a time without considering dependencies between different features. Additionally, we present a new method for reconstructing buildings with concave outlines using half-spaces that avoids the need to partition the models into smaller convex parts. We present both extensions in the context of a fully automatic feature-driven 3D building reconstruction approach where the whole process is suited for processing large urban areas with complex building roofs.

Global Regularization of a Restricted Four-Body Problem

In the n-body problem, a collision singularity occurs when the position of two or more bodies coincide. By understanding the dynamics of collision motion in the regularized setting, a better understanding of the dynamics of near-collision motion is achieved. In this paper, we show that any double collision of the planar equilateral restricted four-body problem can be regularized by using a Birkhoff-type transformation. This transformation has the important property to provide a simultaneous regularization of three singularities due to binary collision. We present some ejection–collision orbits after the regularization of the restricted four-body problem (RFBP) with equal masses, which were obtained by numerical integration.