Noiseless Measurements Research Articles

Inglés

This paper presents an estimation structure for a continuous stirred-tank reactor, which is comprised of a sliding mode observer-based estimator coupled with a high-order sliding-mode observer. The whole scheme allows the robust estimation of the state and some parameters, specifically the concentration of the reactive mass, the heat of reaction and the global coefficient of heat transfer, by measuring the temperature inside the reactor and the temperature inside the jacket. In order to verify the results, the convergence proof of the proposed structure is done, and numerical simulations are presented with noiseless and noisy measurements, suggesting the applicability of the posed approach.

Time reversal method with stabilizing boundary conditions for Photoacoustic tomography

We study an inverse initial source problem that models photoacoustic tomography measurements with array detectors, and introduce a method that can be viewed as a modification of the so called back and forth nudging method. We show that the method converges at an exponential rate under a natural visibility condition, with data given only on a part of the boundary of the domain of wave propagation. In this paper we consider the case of noiseless measurements.

A brief introduction to distributed compressed sensing and its typical reconstruction limits

A brief introduction to compressed sensing and a discussion of its reconstruction limit analysis are presented. In addition, we briefly introduce the replica method, a technique in statistical mechanics, to show its effectiveness for typical performance analysis on signal processing problems. In this presentation, we especially focus on a signal model called joint sparse model 2 (JSM-2) or the multiple measurement vector problem, in which all sparse signals share their support. The signal model JSM-2 is important for dealing with practical processing problems. We investigate the typical performance of l2,1-norm regularized minimization and the Bayesian optimal reconstruction schemes in terms of mean square error for noiseless and noisy measurement JSM- 2 problems. Employing the replica method, we show that these schemes, which exploit the knowledge that the signal support is shared, can recover the signals more precisely as the number of channels increases. The main focus of our presentation is theoretical analysis; however, we will introduce applications of the signal model JSM-2 for acoustic problems. Most of our presentation is based on papers J. Stat. Mech. (2015) P05029 and J. Stat. Mech. (2016) 063304.

An experimental test of noncontextuality without unphysical idealizations.

To make precise the sense in which nature fails to respect classical physics, one requires a formal notion of classicality. Ideally, such a notion should be defined operationally, so that it can be subject to direct experimental test, and it should be applicable in a wide variety of experimental scenarios so that it can cover the breadth of phenomena thought to defy classical understanding. Bell's notion of local causality fulfils the first criterion but not the second. The notion of noncontextuality fulfils the second criterion, but it is a long-standing question whether it can be made to fulfil the first. Previous attempts to test noncontextuality have all assumed idealizations that real experiments cannot achieve, namely noiseless measurements and exact operational equivalences. Here we show how to devise tests that are free of these idealizations. We perform a photonic implementation of one such test, ruling out noncontextual models with high confidence.

Real-time through-the-wall radar imaging under unknown wall characteristics using the least-squares support vector machines based method

To solve the real-time through-the-wall imaging problem in the presence of wall ambiguities, an approach based on the least-squares support vector machines (LS-SVMs) is proposed. This technique converts the through-the-wall problem into the establishment and use of a mapping between the backscattered data and the target properties. The wall parameters and the propagation effects caused by the walls are both included in the mapping and can be regressed after the LS-SVM training process. The target properties are estimated using LS-SVM. Noiseless and noisy measurements are performed to demonstrate that the approach can provide comparable performance in terms of robustness and efficacy, as well as improved performance in terms of accuracy and convenience, in comparison with the approach based on the support vector machine (SVM). The influence of the radius of the target on the estimation problem is discussed, and the estimated results show that both the LS-SVM and the SVM have good performances in terms of generalization.

Generalized Nested Sampling for Compressing Low Rank Toeplitz Matrices

This paper considers the problem of compressively sampling wide sense stationary random vectors with a low rank Toeplitz correlation matrix. A new structured deterministic sampling method known as the “Generalized Nested Sampling” (GNS) is used to fully exploit the inherent redundancy of low rank Toeplitz matrices. For a Toeplitz matrix of size $N \times N$ with rank $r$ , this sampling scheme uses only $O(\sqrt r)$ measurements and allows exact recovery from noiseless measurements. This compression factor is independent of $N$ and is shown to be larger than that achieved by existing random sampling based techniques for compressing Toeplitz matrices. The recovery procedure exploits the connection between Toeplitz matrices and linear prediction.

Promoting Truthful Behavior in Participatory-Sensing Mechanisms

In this letter, the interplay between a class of nonlinear estimators and strategic sensors is studied in several participatory-sensing scenarios. It is shown that for the class of estimators, if the strategic sensors have access to noiseless measurements of the to-be-estimated-variable, truth-telling is an equilibrium of the game that models the interplay between the sensors and the estimator. Furthermore, performance of the proposed estimators is examined in the case that the strategic sensors form coalitions and in the presence of noise.

Non-uniform spline recovery from small degree polynomial approximation

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm regularization procedure to localize the support and estimate the weights of a target discrete measure in this frame. Furthermore, we derive quantitative bounds on the support recovery and the amplitude errors under a Chebyshev-type minimal separation condition on its support. Incidentally, we study the localization of the knots of non-uniform splines when a Gaussian perturbation of their inner-products with a known polynomial basis is observed (i.e. a small degree polynomial approximation is known) and the boundary conditions are known. We prove that the knots can be recovered in a grid-free manner using semidefinite programming.

Dynamic-Time-Warping-Based Measurement Data Alignment Model for Condition-Based Railroad Track Maintenance

Condition-based maintenance is believed to be a cost-effective and safety-assured strategy for railroad track management. Implementation of the strategy strongly relies on reliable and complete track condition data, reliable track deterioration models, and efficient and solvable mathematical models for optimal track maintenance scheduling. In practice, reliability of track condition inspection data is often in question; therefore, collected inspection data need to be preprocessed before it is used to implement a condition-based maintenance strategy. Reliable track condition inspection data means accurate positioning data and noiseless condition parameter measurements. Based on dynamic time warping, which is a widely used technique in the area of speech signal processing and biomedical engineering, this paper presents a robust optimization model for correcting positional errors of inspection data from a track geometry car, which is a kind of specialized instrument that is extensively used to measure the condition of tracks under wheel loadings. An efficient solution algorithm for the model is proposed as well. Applications of the model to inspection data from the track geometry car show that positional errors are almost removed from the inspection data, regardless of noises in condition parameter measurements and track maintenance interventions, and the model takes 1.5004 s, on average, to complete the positional error correction for a 1-km-long track segment. The presented model is adjustable to alignment of data sequences in many other areas, e.g., railroad inspection by track geometry trolley, highway roughness inspection by Light Detection and Ranging (LiDAR) vehicles, and railroad catenary wire geometry inspection.

Identification of Linear Time-Varying Systems Through Waveform Diversity

Linear, time-varying (LTV) systems composed of time shifts, frequency shifts, and complex amplitude scalings are operators that act on continuous finite-energy waveforms. This paper presents a novel, resource-efficient method for identifying the parametric description of such systems, i.e., the time shifts, frequency shifts, and scalings, from the sampled response to linear frequency modulated (LFM) waveforms, with emphasis on the application to radar processing. If the LTV operator is probed with a sufficiently diverse set of LFM waveforms, then the system can be identified with high accuracy. In the case of noiseless measurements, the identification is perfect, while in the case of noisy measurements, the accuracy is inversely proportional to the noise level. The use of parametric estimation techniques with recently proposed denoising algorithms allows the estimation of the parameters with high accuracy.

Application of Support Vector Machines for Estimating Wall Parameters in Through-Wall Radar Imaging

In through-wall radar imaging (TWRI), ambiguities in wall characteristics including the thickness and the relative permittivity will distort the image and shift the imaged target position. To quickly and accurately estimate the wall parameters, an approach based on a support vector machine (SVM) is proposed. In TWRI problem, the nonlinearity is embodied in the relationship between backscatter data and the wall parameters, which can be obtained through the SVM training process. Measurement results reveal that once the training phase is completed, the technique only needs no more than one second to estimate wall parameters with acceptable errors. Then through-wall images are reconstructed using a back-projection (BP) algorithm by a finite-difference time-domain (FDTD) simulation. Noiseless and noisy measurements are discussed; the simulation results demonstrate that noisy contamination has little influence on the imaging quality. Furthermore, the feasibility and the validity are tested by a more realistic situation. The results show that high-quality and focused images are obtained regardless of the errors in the wall parameter estimates.

Exact Phase Retrieval for a Class of 2-D Parametric Signals

We address the problem of two-dimensional (2-D) phase retrieval from magnitude of the Fourier spectrum. We consider 2-D signals that are characterized by first-order difference equations, which have a parametric representation in the Fourier domain. We show that, under appropriate stability conditions, such signals can be reconstructed uniquely from the Fourier transform magnitude. We formulate the phase retrieval problem as one of computing the parameters that uniquely determine the signal. We show that the problem can be solved by employing the annihilating filter method, particularly for the case when the parameters are distinct. For the more general case of the repeating parameters, the annihilating filter method is not applicable. We circumvent the problem by employing the algebraically coupled matrix pencil (ACMP) method. In the noiseless measurement setup, exact phase retrieval is possible. We also establish a link between the proposed analysis and 2-D cepstrum. In the noisy case, we derive Cramer–Rao lower bounds (CRLBs) on the estimates of the parameters and present Monte Carlo performance analysis as a function of the noise level. Comparisons with state-of-the-art techniques in terms of signal reconstruction accuracy show that the proposed technique outperforms the Fienup and relaxed averaged alternating reflections (RAAR) algorithms in the presence of noise.

Robust, Distributed Estimation of Internal Wave Parameters via Inter-Drogue Measurements

Internal waves are important to oceanographers because, as they travel, they are capable of displacing mass, such as plankton and small fish. This paper considers a group of drogues estimating the physical parameters that determine the dynamics of an ocean linear internal wave. While underwater, individual drogues do not have access to absolute position information and can only rely on inter-drogue measurements. Building on this data and the knowledge of the drogue dynamics under the flow induced by the internal wave, we propose the Vanishing Distance Derivative Detection Strategy to allow individual drogues to determine the wave parameters. We analyze the correctness and robustness of this strategy under noiseless and noisy measurements, respectively. We also introduce a general methodology, termed pth-Order Parameter Fusion, for combining the parameter estimates obtained at different times and characterize its error. Simulations illustrate our results.

Non-Adaptive Group Testing: Explicit Bounds and Novel Algorithms

We consider some computationally efficient and provably correct algorithms with near-optimal sample complexity for the problem of noisy nonadaptive group testing. Group testing involves grouping arbitrary subsets of items into pools. Each pool is then tested to identify the defective items, which are usually assumed to be sparse. We consider nonadaptive randomly pooling measurements, where pools are selected randomly and independently of the test outcomes. We also consider a model where noisy measurements allow for both some false negative and some false positive test outcomes (and also allow for asymmetric noise, and activation noise). We consider three classes of algorithms for the group testing problem (we call them specifically the coupon collector algorithm, the column matching algorithms, and the LP decoding algorithms-the last two classes of algorithms (versions of some of which had been considered before in the literature) were inspired by corresponding algorithms in the compressive sensing literature. The second and third of these algorithms have several flavors, dealing separately with the noiseless and noisy measurement scenarios. Our contribution is novel analysis to derive explicit sample-complexity bounds-with all constants expressly computed-for these algorithms as a function of the desired error probability, the noise parameters, the number of items, and the size of the defective set (or an upper bound on it). We also compare the bounds to information-theoretic lower bounds for sample complexity based on Fano's inequality and show that the upper and lower bounds are equal up to an explicitly computable universal constant factor (independent of problem parameters).

On the appropriate filtering of PIV measurements of turbulent shear flows

The three-dimensional spatial filtering and measurement noise associated with experimental planar and three-dimensional (3D) particle image velocimetry (PIV) measurements is investigated using a combination of direct numerical simulations (DNS) and experimental databases. Spatial filtering velocity fields from a DNS of a zero-pressure-gradient turbulent boundary layer (TBL) at resolutions typical of PIV experiments are shown to underestimate Reynolds stresses by as much as 50 %. Comparison of experimental PIV measurement of a turbulent channel flow and 3D tomographic PIV measurements of a TBL with higher-resolution simulations and hot-wire anemometry measurements show that in real experiments, measurement noise acts to offset this effect. This is shown to produce measurements that appear to provide a good estimate of the turbulent fluctuations in the flow, when in reality the flow is spatially under-resolved and partially contaminated by noise. Means of identifying this noise are demonstrated using the one-dimensional (1D) velocity power spectra and the 1D transfer function between the power spectra of the unfiltered velocity field and the power spectra calculated from the filtered experimental measurement. This 1D transfer function differs from the commonly used sinc transfer function of PIV owing to the integrated effect of filtering in multiple directions. Failure to incorporate this difference is shown to overestimate the maximum resolved wave number in the 3D spectra of the planar PIV by close to 10 %, while conversely underestimating the maximum resolved wave number in the 3D PIV by 50 %. Appropriate spatial filtering of the experimental data is shown to remove the noise-dominated small-scale fluctuations and bring the data inline with that which should be obtained for a noiseless PIV measurement at the corresponding spatial resolution.

Simultaneous estimation of temperature-dependent volumetric heat capacity and thermal conductivity functions via neural networks

An artificial neural network based solution of the inverse heat conduction problem of simultaneous identification of the temperature-dependent volumetric heat capacity and thermal conductivity function of a solid material is presented in this paper. The inverse problem was defined according to the evaluation of the BICOND thermophysical property measurement method. The volumetric heat capacity and thermal conductivity vs. temperature functions are to be determined using the measured transient temperature histories of two sensors. In this study noiseless and noisy artificial measurements were generated by the numerical solution of the corresponding direct heat conduction problem. The inverse problem was solved by multi-layer feed-forward neural network trained by back-propagation algorithm (BP) and radial basis function (RBF) type neural network applying the whole history mapping approach. As suggested by Czél et al. [1], a novel (time vs. temperature) representation of the input data was applied. Numerical tests were performed to analyze the accuracy of the two network types with noiseless and noisy inputs. Moreover, it is not necessary to retrain the network when the temperature range of the measurement is changed. Based on the presented results it can be stated that feed-forward neural networks are powerful tools in non-iterative solution of function estimation inverse heat conduction problems and they are likely to be very effective in evaluation of real measured temperature histories to simultaneously determine the volumetric heat capacity and thermal conductivity as an arbitrary function of temperature.

Measurement Bounds for Sparse Signal Ensembles via Graphical Models

In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models, allowing a correlated ensemble of sparse signals to be jointly recovered from a collection of separately acquired compressive measurements. In this paper, we introduce a framework for modeling sparse signal ensembles that quantifies the intra- and inter-signal dependencies within and among the signals. This framework is based on a novel bipartite graph representation that links the sparse signal coefficients with the measurements obtained for each signal. Using our framework, we provide fundamental bounds on the number of noiseless measurements that each sensor must collect to ensure that the signals are jointly recoverable.

Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors

The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each measurement to a finite number of bits; moreover, there is an inverse relationship between the achievable sampling rate and the bit depth. In this paper, we investigate an alternative CS approach that shifts the emphasis from the sampling rate to the number of bits per measurement. In particular, we explore the extreme case of 1-bit CS measurements, which capture just their sign. Our results come in two flavors. First, we consider ideal reconstruction from noiseless 1-bit measurements and provide a lower bound on the best achievable reconstruction error. We also demonstrate that i.i.d. random Gaussian matrices provide measurement mappings that, with overwhelming probability, achieve nearly optimal error decay. Next, we consider reconstruction robustness to measurement errors and noise and introduce the binary e-stable embedding property, which characterizes the robustness of the measurement process to sign changes. We show that the same class of matrices that provide almost optimal noiseless performance also enable such a robust mapping. On the practical side, we introduce the binary iterative hard thresholding algorithm for signal reconstruction from 1-bit measurements that offers state-of-the-art performance.

Performance of the Delsarte-Goethals Frame on Clustered Sparse Vectors

The Delsarte-Goethals frame (DGF) has been proposed for deterministic compressive sensing of sparse and compressible signals. Results in compressive sensing theory show that the DGF enables successful recovery of an overwhelming majority of sufficiently sparse signals. However, these results do not give a characterization of the sparse vectors for which the recovery procedure fails. In this paper, we present a formal analysis of the DGF that highlights the presence of clustered sparse vectors within its null space. This in turn implies that sparse recovery performance is diminished for sparse vectors that have their nonzero entries clustered together. Such clustered structure is present in compressive imaging applications, where commonly-used raster scannings of 2-D discrete wavelet transform representations yield clustered sparse representations for natural images. Prior work leverages this structure by proposing specially tailored sparse recovery algorithms that partition the recovery of the input vector into known clustered and unclustered portions. Alternatively, we propose new randomized and deterministic raster scannings for clustered coefficient vectors that improve recovery performance. Experimental results verify the aforementioned analysis and confirm the predicted improvements for both noiseless and noisy measurement regimes.

Inverse Identification of Temperature-Dependent Volumetric Heat Capacity by Neural Networks

An artificial neural network (NN)-based solution of the inverse heat conduction problem of identifying the temperature-dependent volumetric heat capacity function of a solid material is presented in this paper. The inverse problem was defined according to the evaluation of the BICOND thermophysical property measurement method. The volumetric heat capacity versus temperature function is to be determined using the measured transient temperature history of a single sensor. In this study, noiseless and noisy artificial measurements were generated by the numerical solution of the corresponding direct heat conduction problem. The inverse problem was solved by back-propagation and radial basis function type neural networks applying the whole history mapping approach. The numerical tests included the comparison of two different data representations of the network inputs (i.e., temperature vs. time and time vs. temperature) and accuracy analysis of the two network types with noiseless and noisy inputs. Based on the results presented, it can be stated that feed-forward NNs are powerful tools in a non-iterative solution of function estimation inverse heat conduction problems and they are likely to be very effective in evaluation of real measured temperature histories to determine the volumetric heat capacity as an arbitrary function of temperature.