Sparsity driven deterministic sampling strategy for coded aperture X-ray Computed Tomography

The subsampling strategies in X-ray Computed Tomography (CT) gained importance due to their practical relevance. In this direction of research, also known as coded aperture X-ray computed tomography (CAXCT), both random and deterministic strategies were proposed in the literature. Of the techniques available, the ones based on Compressive Sensing (CS) recently gained more traction as CS based ideas efficiently exploit inherent duplication present in the system. The quality of the reconstructed CT images, nevertheless, depends on the sparse signal recovery properties (SRPs) of the sub-sampled Radon matrices. In the present work, we determine CAXCT deterministically in such a way that the corresponding sub-sampled Radon matrices remain close to the incoherent unit norm tight frames (IUNTFs) for better numerical behaviour. We show that this optimization, via Khatri-Rao product, leads to non-negative sparse approximation. While comparing and contrasting our method with its existing counterparts, we show that the proposed algorithm is computationally less involved. Finally, we demonstrate efficacy of the proposed deterministic sub-sampling strategy in recovering CT images both in noiseless and noisy cases.

Deterministic Sampling from Univariate Normal Distributions with Sierpinski Space-Filling Curves

This work addresses the problem of sampling from Gaussian probability distributions by means of uniform samples obtained deterministically and directly from space-filling curves (SFCs), a purely topological concept. To that end, the well-known inverse cumulative distribution function method is used, with the help of the probit function,which is the inverse of the cumulative distribution function of the standard normal distribution. Mainly due to the central limit theorem, the Gaussian distribution plays a fundamental role in probability theory and related areas, and that is why it has been chosen to be studied in the present paper. Numerical distributions (histograms) obtained with the proposed method, and in several levels of granularity, are compared to the theoretical normal PDF, along with other already established sampling methods, all using the cited probit function. Final results are validated with the Kullback-Leibler and two other divergence measures, and it will be possible to draw conclusions about the adequacy of the presented paradigm. As is amply known, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. That said, sequences resulting from this kind of procedure are not truly random. Even so, and to be coherent with the literature, the expression ”random number” will be used along the text to mean ”pseudo-random number”.

Урбанизация национальных республик Саяно-Алтая сквозь призму теории модернизации

Introduction. In the national republics of the Sayan-Altai Region — Altai, Tuva and Khakassia — urbanization has been essentially delayed and is, hence, accelerated. The first urban settlements appeared here only in the 20th century, and many of them were referred to as urban de jure only. Despite the growth of publications studying various aspects of the urbanization in Siberia, there are almost no research works dealing with the development of this historical, cultural, complicated social process and compiled from materials of this region proper. The paper provides a first attempt to assess the features and patterns of urbanization in the Sayan-Altai Region through the prism of modernization theory. Goals. The article aims to analyze urbanization as the most important aspect of modernization through materials collected across Altai, Tuva and Khakassia in the 20th – early 21st centuries. Materials and Methods. The article primarily investigates official statistical data that make it possible to trace the actual urbanization dynamics (for both populations and territories), as well as the process of transformation experienced by material components of city life. Empirically, the study rests on materials of surveys conducted in the Republic of Khakassia (2018) and in the Republics of Tuva and Altai (2019). The total number of interviewees is 2000. The study employs deterministic sampling methods. Results. The work concludes the urbanization development pattern examined in the region is non-linear, which was determined by the difficult and indirect modernization processes nationwide and those in its certain parts in particular. In the history of the ethnic federal subjects of the Sayan-Altai Region, local features of urbanization are more evident than those in other regions of the country, which is largely due to the influence of the ethnic factor, specifics of indigenous cultures and worldviews. Urbanization as a process is studied on the regional materials in two main perspectives: on the one hand, the paper provides analysis of quantitative indicators of urbanization, such as the dynamics of urban population and growth of urban settlements; on the other hand, an important role in the study of urbanization is assigned to its qualitative indicators, the latter including the transformed structure of urban population and evolution of its living standards.

Progressive von Mises–Fisher Filtering Using Isotropic Sample Sets for Nonlinear Hyperspherical Estimation

In this work, we present a novel scheme for nonlinear hyperspherical estimation using the von Mises–Fisher distribution. Deterministic sample sets with an isotropic layout are exploited for the efficient and informative representation of the underlying distribution in a geometrically adaptive manner. The proposed deterministic sampling approach allows manually configurable sample sizes, considerably enhancing the filtering performance under strong nonlinearity. Furthermore, the progressive paradigm is applied to the fusing of measurements of non-identity models in conjunction with the isotropic sample sets. We evaluate the proposed filtering scheme in a nonlinear spherical tracking scenario based on simulations. Numerical results show the evidently superior performance of the proposed scheme over state-of-the-art von Mises–Fisher filters and the particle filter.