A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established.

Simultaneous 3D object tracking and camera parameter estimation by Bayesian methods and transdimensional MCMC sampling

Multi-camera 3D tracking systems with overlapping cameras represent a powerful mean for scene analysis, as they potentially allow greater robustness than monocular systems and provide useful 3D information about object location and movement. However, their performance relies on accurately calibrated camera networks, which is not a realistic assumption in real surveillance environments. Here, we introduce a multi-camera system for tracking the 3D position of a varying number of objects and simultaneously refin-ing the calibration of the network of overlapping cameras. Therefore, we introduce a Bayesian framework that combines Particle Filtering for tracking with recursive Bayesian estimation methods by means of adapted transdimensional MCMC sampling. Addi-tionally, the system has been designed to work on simple motion detection masks, making it suitable for camera networks with low transmission capabilities. Tests show that our approach allows a successful performance even when starting from clearly inaccurate camera calibrations, which would ruin conventional approaches.

Temperature Sensor Placement Including Routing Overhead and Sampling Inaccuracies

Dynamic thermal management techniques require a collection of on-chip thermal sensors that imply a significant area and power overhead. Finding the optimum number of temperature monitors and their location on the chip surface to optimize accuracy is an NP-hard problem. In this work we improve the modeling of the problem by including area, power and networking constraints along with the consideration of three inaccuracy terms: spatial errors, sampling rate errors and monitor-inherent errors. The problem is solved by the simulated annealing algorithm. We apply the algorithm to a test case employing three different types of monitors to highlight the importance of the different metrics. Finally we present a case study of the Alpha 21364 processor under two different constraint scenarios.

Almost rejectionless sampling from Nakagami-m distributions (m ≥ 1)

The Nakagami-m distribution is widely used for the simulation of fading channels in wireless communications. A novel, simple and extremely efficient acceptance-rejection algorithm is introduced for the generation of independent Nakagami-m random variables. The proposed method uses another Nakagami density with a half-integer value of the fading parameter, mp ¼ n/2 ≤ m, as proposal function, from which samples can be drawn exactly and easily. This novel rejection technique is able to work with arbitrary values of m ≥ 1, average path energy, V, and provides a higher acceptance rate than all currently available methods. RESUMEN. Método extremadamente eficiente para generar variables aleatorias de Nakagami (utilizadas para modelar el desvanecimiento en canales de comunicaciones móviles) basado en "rejection sampling".

Efficient sampling from truncated bivariate Gaussians via Box-Muller transformation

Many practical simulation tasks demand procedures to draw samples efficiently from multivariate truncated Gaussian distributions. In this work, we introduce a novel rejection approach, based on the Box-Muller transformation, to generate samples from a truncated bivariate Gaussian density with an arbitrary support. Furthermore, for an important class of support regions the new method allows us to achieve exact sampling, thus becoming the most efficient approach possible. RESUMEN. Método específico para generar muestras de manera eficiente de Gaussianas bidimensionales truncadas con cualquier zona de truncamiento basado en la transformación de Box-Muller.

The Kramer sampling theorem revisited

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. Besides, it has been the cornerstone for a significant mathematical literature on the topic of sampling theorems associated with differential and difference problems. In this work we provide, in an unified way, new and old generalizations of this result corresponding to various different settings; all these generalizations are illustrated with examples. All the different situations along the paper share a basic approach: the functions to be sampled are obtaining by duality in a separable Hilbert space H through an H -valued kernel K defined on an appropriate domain.

Generalized sampling in U-invariant subspaces

In this work we carry out some results in sampling theory for U-invariant subspaces of a separable Hilbert space H, also called atomic subspaces. These spaces are a generalization of the well-known shift- invariant subspaces in L2 (R); here the space L2 (R) is replaced by H, and the shift operator by U. Having as data the samples of some related operators, we derive frame expansions allowing the recovery of the elements in Aa. Moreover, we include a frame perturbation-type result whenever the samples are affected with a jitter error.

Independent doubly Adaptive Rejection Metropolis Sampling

Adaptive Rejection Metropolis Sampling (ARMS) is a wellknown MCMC scheme for generating samples from onedimensional target distributions. ARMS is widely used within Gibbs sampling, where automatic and fast samplers are often needed to draw from univariate full-conditional densities. In this work, we propose an alternative adaptive algorithm (IA2RMS) that overcomes the main drawback of ARMS (an uncomplete adaptation of the proposal in some cases), speeding up the convergence of the chain to the target. Numerical results show that IA2RMS outperforms the standard ARMS, providing a correlation among samples close to zero.