TIME VARYING LINEAR PREDICTION USING SPARSITY CONSTRAINTS

Time-varying linear prediction has been studied in the context of speech signals, in which the auto-regressive (AR) coefficients of the system function are modeled as a linear combination of a set of known bases. Traditionally, least squares minimization is used for the estimation of model parameters of the system. Motivated by the sparse nature of the excitation signal for voiced sounds, we explore the time-varying linear prediction modeling of speech signals using sparsity constraints. Parameter estimation is posed as a 0-norm minimization problem. The re-weighted 1-norm minimization technique is used to estimate the model parameters. We show that for sparsely excited time-varying systems, the formulation models the underlying system function better than the least squares error minimization approach. Evaluation with synthetic and real speech examples show that the estimated model parameters track the formant trajectories closer than the least squares approach.

GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

Self-Assembled Discrete Molecules for Sensing Nitroaromatics

Efficient sensing of trace amount nitroaromatic (NAC) explosives has become a major research focus in recent time due to concerns over national security as well as their role as environment pollutants. NO2-containing electron-deficient aromatic compounds, such as picric acid (PA), trinitrotoluene (TNT), and dinitrotoluene (DNT), are the common constituents of many commercially available chemical explosives. In this article, we have summarized our recent developments on the rational design of electron-rich self-assembled discrete molecular sensors and their efficacy in sensing nitroaromatics both in solution as well as in vapor phase. Several p-electron-rich fluorescent metallacycles (squares, rectangles, and tweezers/pincers) and metallacages (trigonal and tetragonal prisms) have been synthesized by means of metal-ligand coordination-bonding interactions, with enough internal space to accommodate electron-deficient nitroaromatics at the molecular level by multiple supramolecular interactions. Such interactions subsequently result in the detectable fluorescence quenching of sensors even in the presence of trace quantities of nitroaromatics. The fascinating sensing characteristics of molecular architectures discussed in this article may enable future development of improved sensors for nitroaromatic explosives.

Modified Greedy Pursuits for Improving Sparse Recovery

Compressive Sensing (CS) theory combines the signal sampling and compression for sparse signals resulting in reduction in sampling rate. In recent years, many recovery algorithms have been proposed to reconstruct the signal efficiently. Subspace Pursuit and Compressive Sampling Matching Pursuit are some of the popular greedy methods. Also, Fusion of Algorithms for Compressed Sensing is a recently proposed method where several CS reconstruction algorithms participate and the final estimate of the underlying sparse signal is determined by fusing the estimates obtained from the participating algorithms. All these methods involve solving a least squares problem which may be ill-conditioned, especially in the low dimension measurement regime. In this paper, we propose a step prior to least squares to ensure the well-conditioning of the least squares problem. Using Monte Carlo simulations, we show that in low dimension measurement scenario, this modification improves the reconstruction capability of the algorithm in clean as well as noisy measurement cases.

Event-triggered sampling using signal extrema for instantaneous amplitude and instantaneous frequency estimation

Event-triggered sampling (ETS) is a new approach towards efficient signal analysis. The goal of ETS need not be only signal reconstruction, but also direct estimation of desired information in the signal by skillful design of event. We show a promise of ETS approach towards better analysis of oscillatory non-stationary signals modeled by a time-varying sinusoid, when compared to existing uniform Nyquist-rate sampling based signal processing. We examine samples drawn using ETS, with events as zero-crossing (ZC), level-crossing (LC), and extrema, for additive in-band noise and jitter in detection instant. We find that extrema samples are robust, and also facilitate instantaneous amplitude (IA), and instantaneous frequency (IF) estimation in a time-varying sinusoid. The estimation is proposed solely using extrema samples, and a local polynomial regression based least-squares fitting approach. The proposed approach shows improvement, for noisy signals, over widely used analytic signal, energy separation, and ZC based approaches (which are based on uniform Nyquist-rate sampling based data-acquisition and processing). Further, extrema based ETS in general gives a sub-sampled representation (relative to Nyquistrate) of a time-varying sinusoid. For the same data-set size captured with extrema based ETS, and uniform sampling, the former gives much better IA and IF estimation. (C) 2015 Elsevier B.V. All rights reserved.

Optimum Parameter Selection in Sparse Reconstruction of Frequency-Domain Optical-Coherence Tomography Signals

For a multilayered specimen, the back-scattered signal in frequency-domain optical-coherence tomography (FDOCT) is expressible as a sum of cosines, each corresponding to a change of refractive index in the specimen. Each of the cosines represent a peak in the reconstructed tomogram. We consider a truncated cosine series representation of the signal, with the constraint that the coefficients in the basis expansion be sparse. An l(2) (sum of squared errors) data error is considered with an l(1) (summation of absolute values) constraint on the coefficients. The optimization problem is solved using Weiszfeld's iteratively reweighted least squares (IRLS) algorithm. On real FDOCT data, improved results are obtained over the standard reconstruction technique with lower levels of background measurement noise and artifacts due to a strong l(1) penalty. The previous sparse tomogram reconstruction techniques in the literature proposed collecting sparse samples, necessitating a change in the data capturing process conventionally used in FDOCT. The IRLS-based method proposed in this paper does not suffer from this drawback.

An Alternating l(p) - l(2) Projections Algorithm (ALPA) for Speech Modeling using Sparsity Constraints

We address the problem of separating a speech signal into its excitation and vocal-tract filter components, which falls within the framework of blind deconvolution. Typically, the excitation in case of voiced speech is assumed to be sparse and the vocal-tract filter stable. We develop an alternating l(p) - l(2) projections algorithm (ALPA) to perform deconvolution taking into account these constraints. The algorithm is iterative, and alternates between two solution spaces. The initialization is based on the standard linear prediction decomposition of a speech signal into an autoregressive filter and prediction residue. In every iteration, a sparse excitation is estimated by optimizing an l(p)-norm-based cost and the vocal-tract filter is derived as a solution to a standard least-squares minimization problem. We validate the algorithm on voiced segments of natural speech signals and show applications to epoch estimation. We also present comparisons with state-of-the-art techniques and show that ALPA gives a sparser impulse-like excitation, where the impulses directly denote the epochs or instants of significant excitation.

Robust Savitzky-Golay Filters

Local polynomial approximation of data is an approach towards signal denoising. Savitzky-Golay (SG) filters are finite-impulse-response kernels, which convolve with the data to result in polynomial approximation for a chosen set of filter parameters. In the case of noise following Gaussian statistics, minimization of mean-squared error (MSE) between noisy signal and its polynomial approximation is optimum in the maximum-likelihood (ML) sense but the MSE criterion is not optimal for non-Gaussian noise conditions. In this paper, we robustify the SG filter for applications involving noise following a heavy-tailed distribution. The optimal filtering criterion is achieved by l(1) norm minimization of error through iteratively reweighted least-squares (IRLS) technique. It is interesting to note that at any stage of the iteration, we solve a weighted SG filter by minimizing l(2) norm but the process converges to l(1) minimized output. The results show consistent improvement over the standard SG filter performance.

Unique Covering Problems with Geometric Sets

The Exact Cover problem takes a universe U of n elements, a family F of m subsets of U and a positive integer k, and decides whether there exists a subfamily(set cover) F' of size at most k such that each element is covered by exactly one set. The Unique Cover problem also takes the same input and decides whether there is a subfamily F' subset of F such that at least k of the elements F' covers are covered uniquely(by exactly one set). Both these problems are known to be NP-complete. In the parameterized setting, when parameterized by k, Exact Cover is W1]-hard. While Unique Cover is FPT under the same parameter, it is known to not admit a polynomial kernel under standard complexity-theoretic assumptions. In this paper, we investigate these two problems under the assumption that every set satisfies a given geometric property Pi. Specifically, we consider the universe to be a set of n points in a real space R-d, d being a positive integer. When d = 2 we consider the problem when. requires all sets to be unit squares or lines. When d > 2, we consider the problem where. requires all sets to be hyperplanes in R-d. These special versions of the problems are also known to be NP-complete. When parameterizing by k, the Unique Cover problem has a polynomial size kernel for all the above geometric versions. The Exact Cover problem turns out to be W1]-hard for squares, but FPT for lines and hyperplanes. Further, we also consider the Unique Set Cover problem, which takes the same input and decides whether there is a set cover which covers at least k elements uniquely. To the best of our knowledge, this is a new problem, and we show that it is NP-complete (even for the case of lines). In fact, the problem turns out to be W1]-hard in the abstract setting, when parameterized by k. However, when we restrict ourselves to the lines and hyperplanes versions, we obtain FPT algorithms.

l(1)-K-SVD: A robust dictionary learning algorithm with simultaneous update

We develop a new dictionary learning algorithm called the l(1)-K-svp, by minimizing the l(1) distortion on the data term. The proposed formulation corresponds to maximum a posteriori estimation assuming a Laplacian prior on the coefficient matrix and additive noise, and is, in general, robust to non-Gaussian noise. The l(1) distortion is minimized by employing the iteratively reweighted least-squares algorithm. The dictionary atoms and the corresponding sparse coefficients are simultaneously estimated in the dictionary update step. Experimental results show that l(1)-K-SVD results in noise-robustness, faster convergence, and higher atom recovery rate than the method of optimal directions, K-SVD, and the robust dictionary learning algorithm (RDL), in Gaussian as well as non-Gaussian noise. For a fixed value of sparsity, number of dictionary atoms, and data dimension, l(1)-K-SVD outperforms K-SVD and RDL on small training sets. We also consider the generalized l(p), 0 < p < 1, data metric to tackle heavy-tailed/impulsive noise. In an image denoising application, l(1)-K-SVD was found to result in higher peak signal-to-noise ratio (PSNR) over K-SVD for Laplacian noise. The structural similarity index increases by 0.1 for low input PSNR, which is significant and demonstrates the efficacy of the proposed method. (C) 2015 Elsevier B.V. All rights reserved.

On Fast Bilateral Filtering Using Fourier Kernels

It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the nonlinear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are obtained by solving a series of least-squares problems. The coefficients can be efficiently computed using a recursive form of the QR decomposition. By controlling the cardinality of the Fourier basis, we can obtain a good tradeoff between the run-time and the filtering accuracy. In particular, we are able to guarantee subpixel accuracy for the overall filtering, which is not provided by the most existing methods for fast bilateral filtering. We present simulation results to demonstrate the speed and accuracy of the proposed algorithm.

Wireless Network-Coded Accumulate-Compute-and-Forward Two-Way Relaying

For the physical-layer network-coded wireless two-way relaying, it was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to channel conditions greatly reduces the impact of multiple-access interference, which occurs at the relay, and all these network coding maps should satisfy a requirement called exclusive law. We extend this approach to an accumulate-compute-and-forward protocol, which employs two phases: a multiple access (MA) phase consisting of two channel uses with independent messages in each channel use and a broadcast (BC) phase having one channel use. Assuming that the two users transmit points from the same 4-phase-shift keying (PSK) constellation, every such network coding map that satisfies the exclusive law can be represented by a Latin square of side 16, and conversely, this relationship can be used to get the network coding maps satisfying the exclusive law. Two methods of obtaining this network coding map to be used at the relay are discussed. Using the structural properties of the Latin squares for a given set of parameters, the problem of finding all the required maps is reduced to finding a small set of maps for the case. Having obtained all the Latin squares, a criterion is provided to select a Latin square for a given realization of fade state. This criterion turns out to be the same as the one used byMuralidharan et al. for two-stage bidirectional relaying.

Monte Carlo Valuation of natural gas investments

This paper deals with the valuation of energy assets related to natural gas. In particular, we evaluate a baseload Natural Gas Combined Cycle (NGCC) power plant and an ancillary instalation, namely a Liquefied Natural Gas (LNG) facility, in a realistic setting; specifically, these investments enjoy a long useful life but require some non-negligible time to build. Then we focus on the valuation of several investment options again in a realistic setting. These include the option to invest in the power plant when there is uncertainty concerning the initial outlay, or the option's time to maturity, or the cost of CO2 emission permits, or when there is a chance to double the plant size in the future. Our model comprises three sources of risk. We consider uncertain gas prices with regard to both the current level and the long-run equilibrium level; the current electricity price is also uncertain. They all are assumed to show mean reversion. The two-factor model for natural gas price is calibrated using data from NYMEX NG futures contracts. Also, we calibrate the one-factor model for electricity price using data from the Spanish wholesale electricity market, respectively. Then we use the estimated parameter values alongside actual physical parameters from a case study to value natural gas plants. Finally, the calibrated parameters are also used in a Monte Carlo simulation framework to evaluate several American-type options to invest in these energy assets. We accomplish this by following the least squares MC approach.

Confianza como consecuencia del compromiso percibido: Implicaciones sobre el aprendizaje y la innovación

En este trabajo pretendemos alcanzar un doble objetivo. En primer lugar, estudiamos la influencia del compromiso afectivo de los empleados percibido por el directivo, tanto sobre su nivel de confianza, como sobre la capacidad de aprendizaje organizativo (CAO). Igualmente, analizamos cómo influye sobre la CAO esta predisposición del directivo a confiar en sus empleados. En segundo lugar, examinamos si el compromiso afectivo de los empleados percibido por el directivo, la confianza del directivo y la CAO favorecen la innovación en producto. Aplicando modelos de ecuaciones estructurales (Partial Least Squares -PLS-) sobre una muestra de 92 empresas pertenecientes a sectores innovadores españoles se concluye que el compromiso afectivo que el directivo percibe en los empleados determina su nivel de confianza en aquellos. Asimismo, ambas variables (compromiso afectivo de los empleados percibido por el directivo y confianza del directivo) explican la CAO. Finalmente, se comprueba que los dos factores considerados (compromiso afectivo percibido y confianza) influyen sobre la innovación en producto a través de la CAO.

Relationship between fish size and otolith length for 63 species of fishes from the Eastern North Pacific Ocean

Otoliths commonly are used to determine the taxon, age, and size of fishes. This information is useful for population management, predator-prey studies, and archaeological research. The relationship between the length of a fish and the length of its otoliths remains unknown for many species of marine fishes in the Pacific Ocean. Therefore, the relationships between fish length and fish weight, and between otolith length and fish length, were developed for 63 species of fishes caught in the eastern North Pacific Ocean. We also summarized similar relationships for 46 eastern North Pacific fish species reported in the literature. The relationship between fish length and otolith length was linear, and most of the variability was explained by a simple least-squares regression (r 2 > 0.700 for 45 of 63 species). The relationship between otolith length and fish length was not significantly different between left and right otoliths for all but one fish species. Images of otoliths from 77 taxa are included to assist in the identification of species. (PDF file contains 38 pages.)