Compressive Sensing Research Papers - Academia.edu (original) (raw)

Compressive Sensing has attracted significant interests since it enables sampling signal at lower rate than Shannon - Nyquist theorem. Block based compressive sensing (BCS) is preferred due to its advantage of low complexity random... more

Compressive Sensing has attracted significant interests
since it enables sampling signal at lower rate than Shannon
- Nyquist theorem. Block based compressive sensing (BCS)
is preferred due to its advantage of low complexity random
projection and reconstruction. Its sampling efficiency has
further improved with various adaptive sampling schemes.
In this work, we study relationship between several block
characteristics and performance indexes. We solve problem
of adaptive block based compressive sensing (ABCS) in
more a complete approach – joint evaluate sampling and
reconstruction. An efficient ABCS simulation model is
proposed to validate the proposed method.

This book is a result of author's thirty-three years of experience in teaching and research in signal processing.The book will guide you from a review of continuous-time signals and systems, through the world of digital signal processing,... more

This book is a result of author's thirty-three years of experience in teaching and research in signal processing.The book will guide you from a review of continuous-time signals and systems, through the world of digital signal processing, up to some of the most advanced theory and techniques in adaptive systems, time-frequency analysis, and sparse signal processing. It provides simple examples and explanations for each, including the most complex transform, method, algorithm or approach presented in the book. The most sophisticated results in signal processing theory are illustrated on simple numerical examples. The book is written for students learning digital signal processing and for engineers and researchers refreshing their knowledge in this area. The selected topics are intended for advanced courses and for preparing the reader to solve problems in some of the state of art areas in signal processing.

We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for... more

We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided algorithmically simple proofs of the Johnson–Lindenstrauss lemma; and (ii) covering numbers for finite-dimensional balls in Euclidean space. This leads to an elementary proof of the Restricted Isometry Property and brings out connections between Compressed Sensing and the Johnson–Lindenstrauss lemma. As a result, we obtain simple and direct proofs of Kashin’s theorems on widths of finite balls in Euclidean space (and their improvements due to Gluskin) and proofs of the existence of optimal Compressed Sensing measurement matrices. In the process, we also prove that these measurements have a certain universality with respect to the sparsity-inducing basis.

Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using... more

Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuous-time signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.

Orthogonal matching pursuit (OMP) is the canonical greedy algorithm for sparse approximation. In this paper we demonstrate that the restricted isometry property (RIP) can be used for a very straightforward analysis of OMP. Our main... more

Orthogonal matching pursuit (OMP) is the canonical greedy algorithm for sparse approximation. In this paper we demonstrate that the restricted isometry property (RIP) can be used for a very straightforward analysis of OMP. Our main conclusion is that the RIP of order K+1 (with isometry constant δ 1 / (3 K^(1/2))) is sufficient for OMP to exactly recover any K-sparse signal. The analysis relies on simple and intuitive observations about OMP and matrices which satisfy the RIP. For restricted classes of K-sparse signals (those that are highly compressible), a relaxed bound on the isometry constant is also established. A deeper understanding of OMP may benefit the analysis of greedy algorithms in general. To demonstrate this, we also briefly revisit the analysis of the regularized OMP (ROMP) algorithm.

When dealing with an elevated sensor number we may have to reduce our sampling time or the sensing features in order to achieve real time sensing. In this paper we propose a make use of the recently developed theory of Compressive... more

When dealing with an elevated sensor number we may
have to reduce our sampling time or the sensing features in order to achieve real time sensing. In this paper we propose a make use of the recently developed theory of Compressive Sensing to try and reduce the number of sensing as well as the sample size without loosing quality in our sampling for doing a good feature recognition.

Sparse Bayesian learning (SBL) is an important family of algorithms for sparse signal recovery and compressed sensing. It has shown superior recovery performance in challenging practical problems, such as highly underdetermined inverse... more

Sparse Bayesian learning (SBL) is an important family of algorithms for sparse signal recovery and compressed sensing. It has shown superior recovery performance in challenging practical problems, such as highly underdetermined inverse problems, recovering signals with less sparsity, recovering signals based on highly coherent measuring/sensing/dictionary matrices, and recovering signals with rich structure. However, its advantages are smeared in current literature due to some misunderstandings on the parameters of SBL and incorrect parameter settings in algorithm comparison and practical use. This work clarifies some important issues, and serves as guidance for correctly using SBL.

A noise map facilitates monitoring of environmental noise pollution in urban areas. It can raise citizen awareness of noise pollution levels, and aid in the development of mitigation strategies to cope with the adverse effects. However,... more

A noise map facilitates monitoring of environmental noise pollution in urban areas. It can raise citizen awareness of noise pollution levels, and aid in the development of mitigation strategies to cope with the adverse effects. However, state-of-the-art techniques for rendering noise maps in urban areas are expensive and rarely updated (months or even years), as they rely on population and traffic models rather than on real data. Participatory urban sensing can be leveraged to create an open and inexpensive platform for rendering up-to-date noise maps. In this paper, we present the design, implementation and performance eval- uation of an end-to-end participatory urban noise mapping system called Ear- Phone. Ear-Phone, for the first time, leverages Compressive Sensing to ad- dress the fundamental problem of recovering the noise map from incomplete and random samples obtained by crowdsourcing data collection. Ear-Phone, implemented on Nokia N95 and HP iPAQ mobile devices, also addres...

In this paper, wavelets and fuzzy support vector machines are used to automated detect and classify power quality (PQ) disturbances. Electric power quality is an aspect of power engineering that has been with us since the inception of... more

In this paper, wavelets and fuzzy support vector machines are used to automated detect and classify power quality (PQ) disturbances. Electric power quality is an aspect of power engineering that has been with us since the inception of power systems. The types of concerned disturbances include voltage sags, swells, interruptions, switching transients, impulses, flickers, harmonics, and notches. Fourier transform and wavelet analysis are utilized to denoise the digital signals, to decompose the signals and then to obtain eight common features for the sampling PQ disturbance signals. A fuzzy support vector machines is designed and trained by 8-dimension feature space points for making a decision regarding the type of the disturbance. Simulation cases illustrate the effectiveness.

Energy consumption is an important issue in continuous wireless telemonitoring of physiological signals. Compressed sensing (CS) is a promising framework to address it, due to its energy-efficient data compression procedure. However, most... more

Energy consumption is an important issue in continuous wireless telemonitoring of physiological signals. Compressed sensing (CS) is a promising framework to address it, due to its energy-efficient data compression procedure. However, most CS algorithms have difficulty in data recovery due to nonsparsity characteristic of many physiological signals. Block sparse Bayesian learning (BSBL) is an effective approach to recover such signals with satisfactory recovery quality. However, it is time-consuming in recovering multichannel signals, since its computational load almost linearly increases with the number of channels. This work proposes a spatiotemporal sparse Bayesian learning algorithm to recover multichannel signals simultaneously. It not only exploits temporal correlation within each channel signal, but also exploits inter-channel correlation among different channel signals. Furthermore, its computational load is not significantly affected by the number of channels. The proposed algorithm was applied to brain computer interface (BCI) and EEG-based driver’s drowsiness estimation. Results showed that the algorithm had both better recovery performance and much higher speed than BSBL. Particularly, the proposed algorithm ensured that the BCI classification and the drowsiness estimation had little degradation even when data were compressed by 80%, making it very suitable for continuous wireless telemonitoring of multichannel signals.

Underwater wireless communication networks (UWCNs) are constituted by sensors and autonomous underwater vehicles (AUVs) that interact to perform specific applications inside water. Commonly used Electromagnetic waves are not suitable as... more

Underwater wireless communication networks (UWCNs) are constituted by sensors and autonomous underwater
vehicles (AUVs) that interact to perform specific applications inside water. Commonly used Electromagnetic waves are not
suitable as the physical layer technology for UWCNs due to high path losses and larger antenna size. Most widely accepted
physical layer technology for UWCNs is acoustic waves. But they are adversely affected by ambient noise, multipath
propagation, and fading. In order to overcome these difficulties a new alternative technology for physical layer is needed.
Magnetic induction (MI) is a promising technique for UWCNs that is not affected by large propagation delays, multipath
propagation, and fading. The transmitter and receiver can be implemented by simple coils of wire. The transmission of
information is done through alternating magnetic field generated by the coils. MI have less path loss and Bit Error Rate
compared to other technique up to a particular transmission range. By using sufficient number of relay coils or repeaters in
between the transmitter and the receiver the transmission range can be increased. The power consumption and size of MI
transceiver are very small compared to other technologies. Magnetic induction techniques provide smooth transmission
through air water interface. So Communication between AUVs and docking stations, or control of AUVs from surface vessels
and shore is helpful in environmental and military applications. MI is strongly recommended as a physical transmission
technology for UWCN in both fresh water and sea water.

The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the... more

The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.

The vision of some particular applications such as robot-guided remote surgery where the image of a patient body will need to be captured by the smart visual sensor and to be sent on a real-time basis through a network of high bandwidth... more

The vision of some particular applications such as robot-guided remote surgery where the image of a patient body will need to be captured by the smart visual sensor and to be sent on a real-time basis through a network of high bandwidth but yet limited. The particular problem considered for the study is to develop a mechanism of a hybrid approach of compression where the Region-ofInterest (ROI) should be compressed with lossless compression techniques and Non-ROI should be compressed with Compressive Sensing (CS) techniques. So the challengem is gaining equal image quality for both ROI and Non-ROI while overcoming optimized dimension reduction by sparsity into Non-ROI. It is essential to retain acceptable visual quality to Non-ROI compressed region to obtain a better reconstructed image. This step could bridge the trade-off between image quality and traffic load. The study outcomes were compared with traditional hybrid compression methods to find that proposed method achieves better compression performance as compared to conventional hybrid compression techniques on the performances parameters e.g. PSNR, MSE, and Compression Ratio.

Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap... more

Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap between the discrete, finite-dimensional CS framework and the problem of acquiring a continuous-time signal. In this paper, we attempt to bridge this gap by exploiting the Discrete Prolate Spheroidal Sequences (DPSS's), a collection of functions that trace back to the seminal work by Slepian, Landau, and Pollack on the eff ects of time-limiting and bandlimiting operations. DPSS's form a highly efficient basis for sampled bandlimited functions; by modulating and merging DPSS bases, we obtain a dictionary that o ffers high-quality sparse approximations for most sampled multiband signals. This multiband modulated DPSS dictionary can be readily incorporated into the CS framework. We provide theoretical guarantees and practical insight into the use of this dictionary for recovery of sampled multiband signals from compressive measurements.

Human action recognition is an integral part of smart health monitoring, where intelligence behind the services is obtained and improves through sensor information. It poses tremendous challenges due to huge diversities of human actions... more

Human action recognition is an integral part of smart health monitoring, where intelligence behind the services is obtained and improves through sensor information. It poses tremendous challenges due to huge diversities of human actions and also a large variation in how a particular action can be performed. This problem has been intensified more with the emergence of Internet of Things (IoT), which has resulted in larger datasets acquired by a massive number of sensors. The big data based machine learning is the best candidate to deal with this grand challenge. However, one of the biggest challenges in using large datasets in machine learning is to label sufficient data to train a model accurately .Instead of using expensive supervised learning, we propose a semi-supervised classifier for time-series data. The proposed framework is the joint design of variational auto-encoder (VAE) and convolutional neural network (CNN). In particular, the VAE intends to extract the salient characteristics of human activity data and to provide the useful criteria for the compressed sensing reconstruction, while the CNN aims for extracting the discriminative features and for producing the low-dimension latent codes. Given a combination of labeled and raw time-series data, our architecture utilizes compressed samples from the latent vector in a deconvolutional decoder to reconstruct the input time-series. We intend to train the classifier to detect human actions for smart health systems.

Due to increasing number of wireless services spectrum congestion is a major concern in both military and commercial wireless networks. To support growing demand for omnipresent spectrum usage, Cognitive Radio is a new epitome in wireless... more

Due to increasing number of wireless services spectrum congestion is a major concern in both military and commercial wireless networks. To support growing demand for omnipresent spectrum usage, Cognitive Radio is a new epitome in wireless communication that can be used to exploit unused part of the spectrum by dynamically adjusting its operating parameters. While cognitive radio technology is a promising solution to the spectral congestion problem, efficient methods for detecting white spaces in wideband radio spectrum remain a challenge in which secondary users reliably detect spectral opportunities across a wide frequency range. Conventional methods of detection are forced to use the high sampling rate requirement of Nyquist criterion. These are limited in their operational bandwidth by existing hardware devices, much of the extensive theoretical work on spectrum sensing is impossible to realize in practice over a wide frequency band. To lessen the sampling bottleneck, some researchers have begun to use a technique called Compressive Sensing (CS), which allows for the acquisition of sparse signals at sub-Nyquist rates, in conjunction with CRs. In this paper, various wideband spectrum sensing algorithms are discussed along with their merits and limitations and future challenges. Specially, the sub-Nyquist techniques, like compressive sensing and multi-channel sub-Nyquist sampling techniques are concentrated upon.

—Conventional approaches to sampling images use Shannon theorem, which requires signals to be sampled at a rate twice the maximum frequency. This criterion leads to larger storage and bandwidth requirements. Compressive Sensing (CS) is a... more

—Conventional approaches to sampling images use Shannon theorem, which requires signals to be sampled at a rate twice the maximum frequency. This criterion leads to larger storage and bandwidth requirements. Compressive Sensing (CS) is a novel sampling technique that removes the bottleneck imposed by Shannon's theorem. This theory utilizes sparsity present in the images to recover it from fewer observations than the traditional methods. It joins the sampling and compression steps and enables to reconstruct with the only fewer number of observations. This property of compressive Sensing provides evident advantages over Nyquist-Shannon theorem. The image reconstruction algorithms with CS increase the efficiency of the overall algorithm in reconstructing the sparse signal. There are various algorithms available for recovery. These algorithms include convex minimization class, greedy pursuit algorithms. Numerous algorithms come under these classes of recovery techniques. This paper discusses the origin, purpose, scope and implementation of CS in image reconstruction. It also depicts various reconstruction algorithms and compares their complexity, PSNR and running time. It concludes with the discussion of the various versions of these reconstruction algorithms and future direction of CS-based image reconstruction algorithms.

In order to reduce the quantity of mixing water used and to improve the physical properties and mechanical performance of concrete, we have incorporated an additive of super plasticizer of a high water reducer and accelerator of setting... more

In order to reduce the quantity of mixing water used and to improve the physical properties and mechanical performance of concrete, we have incorporated an additive of super plasticizer of a high water reducer and accelerator of setting 'HRWRASP103' in the formulation matrix of concrete at various percentages ranging from 0.5 to 4% by weight of cement with a step of 0.5%. The influence of the incorporation of HRWRASP103 in a cement matrix on the physical properties of fresh cement paste and on the mechanical performance of mortar and/or concrete in the hardened state has been studied on the other hand. The obtained results from various formulation elaborated shows that the dosage between 0.5% and 2.5% of HRWRASP103 by weight of cement in our formulations reduces the amount of mixing water used. We have distinguished that the setting time decreases. Similarly, the porosity, the capillary absorption and the absorption by immersion in water have been decreased on one hand. On the other hand, we observed that the compressive strengths at the young age (2 days), median age (7 days) and long-term (28 days) were improved. The addition of HRWRASP103 in the formulation of cement also allowed us to produce a durable concrete.

The recently introduced theory of compressive sensing (CS) enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be... more

The recently introduced theory of compressive sensing (CS) enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be significantly smaller than the ambient dimension of the signal and yet preserve the significant signal information. Interestingly, it can be shown that random measurement schemes provide a near-optimal encoding in terms of the required number of measurements. In this report, we explore another relatively unexplored, though often alluded to, advantage of using random matrices to acquire CS measurements. Specifically, we show that random matrices are democratic, meaning that each measurement carries roughly the same amount of signal information. We demonstrate that by slightly increasing the number of measurements, the system is robust to the loss of a small number of arbitrary measurements. In addition, we draw connections to oversampling and demonstrate stability from the loss of significantly more measurements.

1 adsetiawan@students.itb.ac.id, 2 suksmono@stei.itb.ac.id, 3 hgunawan@math.itb.ac.id, 4 tmengko@itb.ac.id Abstrak Teknologi multimedia berkembang terus dan semakin banyak digunakan dalam konten komunikasi. Konten multimedia memungkinkan interaksi yang lebih kaya jika diandingkan dengan konten tekstual. Citra merupakan komponen komunikasi yang banyak digunakan. Pertumbuhan penggunaan citra sebagai konten komunikasi menyebabkan meningkatnya kebutuhan infrastruktur telekomunikasi pita lebar. Pengembangan algoritma pemampatan citra dapat dimanfaatkan untuk mengifisienkan penggunaan lebar pita telekomunikasi. Algoritma pemampatan merugi (lossy) memberikan rasio pemampatan yang lebih tinggi dibandingkan algoritma pemampatan tak merugi (lossless). Algoritma pemampatan merugi memanfaatkan sifat sparsitas dari citra. Citra akan ditransformasikan ke domain basis tertentu yang merepresentasikan citra tersebut lebih sparse (kompresif). Basis yang diusulkan dalam penelitian ini adalah basis latih K-SVD. Penggunaan basis latih ini dapat mentransformasikan citra ke domain yang lebih kompresif. Hal ini disebabkan karena penggunaan pustaka latih lebih mengeksplorasi sifat-sifat dari citra. Metoda pemampatan yang dikembangkan merupakan pengembangan dari kuantisasi vektor yang diperumum, sehingga memungkinkan representasi citra dari kombinasi linear beberapa fungsi basis dengan jumlah basis yang tetap (sparsitas tetap). Metoda sparsitas tetap yang diusulkan akan dibandingkan dengan kuantisasi vektor fuzzy (Scalable Fuzzy Vektor Quantization) dan JPEG pada laju bit yang rendah untuk mengefisienkan penggunaan lebar pita telekomunikasi. Kata kunci : representasi sparse, K-SVD, kuantisasi vektor, laju bit rendah Abstract Multimedia technology continues to evolve and is increasingly used in the content of communication. Multimedia content enables richer interaction compared to textual content. The image is a component of widely used communications. The growth of image usage as communication content led to a growing need for broadband telecommunications infrastructure. The development of image compression algorithms can be used to optimize telecommunications bandwidth usage more efficiently. Lossy compression algorithm gives higher compression ratio than a lossless one. Lossy compression algorithm exploits the nature of image sparsity. The image will be transformed into certain basis domain to represent the image more sparsely. The proposed basis are trained-basis based on K-SVD. The proposed trained-basis capable of transforming the image into a more compressible domain. The reason is that the trained-basis dictionary explore the prior of the image. The developed compression method is based on generalized vector quantization, allowing the representation of image over a linear combination of some basis functions. The proposed method is compared with fuzzy vector quantization (Scalable Fuzzy Vector Quantization) and JPEG at low bit rate to make efficient use of telecommunications bandwidth.

Compressive sensing (CS) has recently attracted considerable attention for its capability of simultaneous sampling and compression. CS produce high reconstruction performance based on the sparsity of signal in selected transform domain.... more

Compressive sensing (CS) has recently attracted considerable attention for its capability of simultaneous sampling and compression. CS produce high reconstruction performance based on the sparsity of signal in selected transform domain. However, CS still has challenges in low performance and
computational complexity of reconstruction. Motivated by nonlocal structure of natural image and based on the cartoon texture image decomposition technique, this thesis proposes an efficient edges/textures preserving total variation based reconstruction algorithm. A fast implementation of the proposed
method is presented using split Bregman method.
Toward more efficient sensing scheme, we study hybrid sensing matrix with combination of deterministic DCT and Gaussian random matrices which efficient sample the similarity and difference of image but broke democracy property of
CS. In order to overcome this drawback and provide fast reconstruction, we further develop a novel multi-resolution KCS sensing matrix which not only provides multi-resolution measurement, reduces reconstruction running time but
also improves the final reconstruction performance. The proposed scheme are evaluated via convincing numerical experiments which shows significant improvement over the conventional scheme and competitive performance with other state of the art algorithms in terms of objective and subjective quality

Compressive sensing (CS) exploits the sparsity present in many signal environments to reduce the number of measurements needed for digital acquisition and processing. We have previously introduced the concept and feasibility of using CS... more

Compressive sensing (CS) exploits the sparsity present in many signal environments to reduce the number of measurements needed for digital acquisition and processing. We have previously introduced the concept and feasibility of using CS techniques to build a wideband signal acquisition systems. This paper extends that work to examine such a receiver’s performance as a function of several key design parameters. In particular we show that that the system noise figure is predictably degraded as the subsampling implicit in CS is made more aggressive. Conversely we show that the dynamic range of a CS-based system can be substantially improved as the subsampling factor grows. The ability to control these aspects of performance provides an engineer new degrees of freedom in the design of wideband acquisition systems. A specific practical example, a multi-collector emitter geolocation system, is included to illustrate that point.

Roadside units (RSUs) are public and personal wireless access points that can provide communications with infrastructure in ad hoc vehicular networks. We present CLOCS (Counting and Localization using Online Compressive Sensing), a novel... more

Roadside units (RSUs) are public and personal wireless access points that can provide communications with infrastructure in ad hoc vehicular networks. We present CLOCS (Counting and Localization using Online Compressive Sensing), a novel system to retrieve both the number and locations of RSUs through wardriving. CLOCS employs online compressive sensing (CS), where received signal strength (RSS) values are recorded at runtime, and the number and location of RSUs are recovered immediately based on limited RSS readings. CLOCS also uses fine retrieval based on an expectation maximization method along the driving route. Extensive simulation results and experiments in a real testbed deployed in the campus of the University of California, Irvine confirm that CLOCS can successfully reduce the number of measurements for RSU recovery, while maintaining satisfactory counting and localization accuracy. In addition, data dissemination, time cost, and effects of different mobile scenarios using CLOCS are analyzed, and the impact of CLOCS on network connectivity is studied using Microsoft VanLan traces.

This paper is concerned with aircraft aeroelastic interactions and the propagation of parametric uncertainties in numerical simulations using high-fidelity fluid flow solvers. More specifically, the influence of variable operational and... more

This paper is concerned with aircraft aeroelastic interactions and the propagation of parametric uncertainties in numerical simulations using high-fidelity fluid flow solvers. More specifically, the influence of variable operational and structural parameters (random inputs) on the drag performance and deformation (outputs) of a flexible wing in transonic regime, is assessed. Because of the complexity of fluid flow solvers, non-intrusive uncertainty quantifica-tion techniques are favored. Polynomial surrogate models based on homogeneous chaos expansions in the random inputs are commonly considered in this respect. The polynomial expansion coefficients are constructed using either structured sampling sets of the input parameters, as Gauss quadrature nodes, or unstructured sampling sets, as in Monte-Carlo methods. In complex systems such as the advanced aeroelastic test case studied here, the output quantities of interest generally depend only weakly on the multiple cross-interactions between the random inputs. Consequently, only low-order polynomials significantly contribute to their surrogates, which thus have a sparse structure in the underlying polynomial bases. This feature prompts to use compressed sensing, or compressive sampling theory for the construction of the polynomial surrogates. The proposed methodology is non-adapted and considers unstructured sampling sets orders of magnitude smaller than the ones required by the usual techniques with structured sampling sets. It is illustrated in the present work for a moderately to high dimensional parametric space.

In this paper we study aircraft aeroelastic interactions and the propagation of parametric uncertainties in numerical simulations using high-fidelity fluid flow solvers. We more particularly address the influence of variable operational... more

In this paper we study aircraft aeroelastic interactions and the propagation of parametric uncertainties in numerical simulations using high-fidelity fluid flow solvers. We more particularly address the influence of variable operational and structural parameters (random inputs) on the drag performance and shape (outputs) of a flexible wing in transonic regime. Polynomial surrogate models based on homogeneous chaos expansions in the random inputs are considered in this respect. The polynomial expansion coefficients are usually constructed by projection using either structured sampling sets of the input parameters, as Gauss quadrature nodes, or unstructured sampling sets, as in Monte-Carlo methods. However, in complex systems such as the advanced aeroelastic test case studied here, the output quantities of interest generally depend only weekly on the multiple cross-interactions between the random inputs. Consequently, only low-order polynomials significantly contribute to their surrogates, which thus have a sparse structure in the underlying polynomial bases. This feature prompts the use of compressed sensing for the construction of the polynomial surrogates by regression. This alternative methodology is non-adapted and considers unstructured sampling sets orders of magnitude smaller than the structured or unstructured sampling sets required in projection methods. It is illustrated in the present work for a moderately to high dimensional parametric space and an aeroelastic test case of industrial relevance.

The recently introduced theory of compressed sensing enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller... more

The recently introduced theory of compressed sensing enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist rate samples. Interestingly, it has been shown that random projections are a satisfactory measurement scheme. This has inspired the design of physical systems that directly implement similar measurement schemes. However, despite the intense focus on the reconstruction of signals, many (if not most) signal processing problems do not require a full reconstruction of the signal—we are often interested only in solving some sort of detection problem or in the estimation of some function of the data. In this report, we show that the compressed sensing framework is useful for a wide range of statistical inference tasks. In particular, we demonstrate how to solve a variety of signal detection and estimation problems given the measurements without ever reconstructing the signals themselves. We provide theoretical bounds along with experimental results.