Spiral sampling in magnetic resonance imaging-the effect of inhomogeneities

A study of a spiral scan echo planar method in the presence of static field inhomogeneities is presented. The approach consists of obtaining the samples over the Fourier plane trajectory of the spiral scan, as modified by the inhomogeneities. The resulting images are compared to a Cartesian scan echo-planar method also subjected to inhomogeneities in the static field. The conclusion is that the spiral scan is more sensitive to this type of inhomogeneity. The possibility of compensating for the inhomogeneities during the reconstruction procedure is suggested by a preliminary experimental result.     

One-step image reconstruction from incomplete data in computer tomography

The authors develop a projection operator that simultaneously projects onto the set of all functions satisfying raysum constraints in parallel-beam CT. The projector can be directly extended to the fan-beam case through the process of rebinning. The projector generates a solution that is closest to the initial estimate among all the functions that are consistent with the available raysum data. It realizes the ART (algebraic reconstruction technique) in one step. The projector furnishes the one-step projection reconstruction (OSPR) for any arbitrary configurations of missing data. Because the projection is one-step, there can be a significant reduction in the number of online computations and memory requirements, especially when the missing data exhibit some pattern within a view or between views.     

Tighter Approximation Bounds for Minimum CDS in Unit Disk Graphs

Connected dominating set (CDS) in unit disk graphs has a wide range of applications in wireless ad hoc networks. A number of approximation algorithms for constructing a small CDS in unit disk graphs have been proposed in the literature. The majority of these algorithms follow a general two-phased approach. The first phase constructs a dominating set, and the second phase selects additional nodes to interconnect the nodes in the dominating set. In the performance analyses of these two-phased algorithms, the relation between the independence number α and the connected domination number γ _c of a unit-disk graph plays the key role. The best-known relation between them is a ￡ 3\frac23g_c+1\alpha\leq3\frac{2}{3}\gamma_{c}+1. In this paper, we prove that α≤3.4306γ _c +4.8185. This relation leads to tighter upper bounds on the approximation ratios of two approximation algorithms proposed in the literature.     

Dependence of neuronal correlations on filter characteristics and marginal spike train statistics

Correlated neural activity has been observed at various signal levels (e.g., spike count, membrane potential, local field potential, EEG, fMRI BOLD). Most of these signals can be considered as superpositions of spike trains filtered by components of the neural system (synapses, membranes) and the measurement process. It is largely unknown how the spike train correlation structure is altered by this filtering and what the consequences for the dynamics of the system and for the interpretation of measured correlations are. In this study, we focus on linearly filtered spike trains and particularly consider correlations caused by overlapping presynaptic neuron populations. We demonstrate that correlation functions and statistical second-order measures like the variance, the covariance, and the correlation coefficient generally exhibit a complex dependence on the filter properties and the statistics of the presynaptic spike trains. We point out that both contributions can play a significant role in modulating the interaction strength between neurons or neuron populations. In many applications, the coherence allows a filter-independent quantification of correlated activity. In different network models, we discuss the estimation of network connectivity from the high-frequency coherence of simultaneous intracellular recordings of pairs of neurons.     

Image restoration by the method of convex projections: part 2 applications and numerical results

The image restoration theory discussed in a previous paper by Youla and Webb [1] is applied to a simulated image and the results compared with the well-known method known as the Gerchberg-Papoulis algorithm. The results show that the method of image restoration by projection onto convex sets, by providing a convenient technique for utilizing a priori information, performs significantly better than the Gerchberg-Papoulis method.