Event-triggered Sampling and Reconstruction of Sparse Real-valued Trigonometric Polynomials

We propose data acquisition from continuous-time signals belonging to the class of real-valued trigonometric polynomials using an event-triggered sampling paradigm. The sampling schemes proposed are: level crossing (LC), close to extrema LC, and extrema sampling. Analysis of robustness of these schemes to jitter, and bandpass additive gaussian noise is presented. In general these sampling schemes will result in non-uniformly spaced sample instants. We address the issue of signal reconstruction from the acquired data-set by imposing structure of sparsity on the signal model to circumvent the problem of gap and density constraints. The recovery performance is contrasted amongst the various schemes and with random sampling scheme. In the proposed approach, both sampling and reconstruction are non-linear operations, and in contrast to random sampling methodologies proposed in compressive sensing these techniques may be implemented in practice with low-power circuitry.

Ellipse Fitting Using the Finite Rate of Innovation Sampling Principle

Standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse. When the data are noisy and come from a partial ellipse, the state-of-the-art methods tend to produce biased ellipses. We rely on the sampling structure of the underlying signal and show that the x- and y-coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals, and that their parameters are estimable from partial data. We consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude-modulated complex exponentials. A low-pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials. The annihilating filter used in FRI approaches is applied to estimate the sampling interval in the closed form. We perform experiments on simulated and real data, and assess both objective and subjective performances in comparison with the state-of-the-art ellipse fitting methods. The proposed method produces ellipses with lesser bias. Furthermore, the mean-squared error is lesser by about 2 to 10 dB. We show the applications of ellipse fitting in iris images starting from partial edge contours, and to free-hand ellipses drawn on a touch-screen tablet.

Empirical Analysis of Sampling Based Estimators for Evaluating RBMs

The Restricted Boltzmann Machines (RBM) can be used either as classifiers or as generative models. The quality of the generative RBM is measured through the average log-likelihood on test data. Due to the high computational complexity of evaluating the partition function, exact calculation of test log-likelihood is very difficult. In recent years some estimation methods are suggested for approximate computation of test log-likelihood. In this paper we present an empirical comparison of the main estimation methods, namely, the AIS algorithm for estimating the partition function, the CSL method for directly estimating the log-likelihood, and the RAISE algorithm that combines these two ideas.

Time-Instant Sampling Based Encoding of Time-Varying Acoustic Spectrum

The inner ear has been shown to characterize an acoustic stimuli by transducing fluid motion in the inner ear to mechanical bending of stereocilia on the inner hair cells (IHCs). The excitation motion/energy transferred to an IHC is dependent on the frequency spectrum of the acoustic stimuli, and the spatial location of the IHC along the length of the basilar membrane (BM). Subsequently, the afferent auditory nerve fiber (ANF) bundle samples the encoded waveform in the IHCs by synapsing with them. In this work we focus on sampling of information by afferent ANFs from the IHCs, and show computationally that sampling at specific time instants is sufficient for decoding of time-varying acoustic spectrum embedded in the acoustic stimuli. The approach is based on sampling the signal at its zero-crossings and higher-order derivative zero-crossings. We show results of the approach on time-varying acoustic spectrum estimation from cricket call signal recording. The framework gives a time-domain and non-spatial processing perspective to auditory signal processing. The approach works on the full band signal, and is devoid of modeling any bandpass filtering mimicking the BM action. Instead, we motivate the approach from the perspective of event-triggered sampling by afferent ANFs on the stimuli encoded in the IHCs. Though the approach gives acoustic spectrum estimation but it is shallow on its complete understanding for plausible bio-mechanical replication with current mammalian auditory mechanics insights.

Hierarchy of structure functions for passive scalars advected by turbulent flows

A hierarchical model is proposed for the joint moments of the passive scalar dissipation and the velocity dissipation in fluid turbulence. This model predicts that the joint probability density function (PDF) of the dissipations is a bivariate log-Poisson. An analytical calculation of the scaling exponents of structure functions of the passive scalar is carried out for this hierarchical model, showing a good agreement with the results of direct numerical simulations and experiments.

Direct Numerical Simulation of Passive Scalar in Decaying Compressible Turbulence

The passive scalars in the decaying compressible turbulence with the initial Reynolds number (defined by Taylor scale and RMS velocity) Re=72, the initial turbulent Mach numbers (defined by RMS velocity and mean sound speed) Mt=0.2-0.9, and the Schmidt numbers of passive scalar Sc=2-10 are numerically simulated by using a 7th order upwind difference scheme and 8th order group velocity control scheme. The computed results are validated with different numerical methods and different mesh sizes. The Batchelor scaling with k(-1) range is found in scalar spectra. The passive scalar spectra decay faster with the increasing turbulent Mach number. The extended self-similarity (ESS) is found in the passive scalar of compressible turbulence.

Elliptical slice sampling

Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with multivariate Gaussian priors. Its key properties are: 1) it has simple, generic code applicable to many models, 2) it has no free parameters, 3) it works well for a variety of Gaussian process based models. These properties make our method ideal for use while model building, removing the need to spend time deriving and tuning updates for more complex algorithms.

Latin hypercube sampling used in the calculation of the fracture probability

The paper proposes Latin hypercube sampling combined with the stratified sampling of variance reduction technique to calculate accurate fracture probability. In the compound sampling, the number of simulations is relatively small and the calculation error is satisfactory.

Fixed-lag blind equalization and sequence estimation in digital communications systems using sequential importance sampling

We present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) on a discrete non-linear, non-Gaussian state space system with unknown parameters. Our particular application is in the field of digital communication systems. Each input data point is taken from a finite set of symbols. We represent transmission media as a fixed filter with a finite impulse response (FIR), hence a discrete state-space system is formed. Conventional Markov chain Monte Carlo (MCMC) techniques such as the Gibbs sampler are unsuitable for this task because they can only perform processing on a batch of data. Data arrives sequentially, so it would seem sensible to process it in this way. In addition, many communication systems are interactive, so there is a maximum level of latency that can be tolerated before a symbol is decoded. We will demonstrate this method by simulation and compare its performance to existing techniques.

Athermal colourless C-band optical transmitter for passive optical networks

A new control algorithm with reduced mode-hopping is demonstrated for uncooled WDM C-band channel generation from a DS-DBR laser with 100GHz spacing and low thermal drift up to 70°C. 10Gb/s external modulation with transmission over a 25km link is achieved. ©2010 IEEE.