Integration of CS into MoM for Efficiently Solving of Bistatic Scattering Problems

The analysis of the target’s broadband electromagnetic scattering characteristics plays an important role in radar stealth and recognition areas. The traditional method of moments (MoM) needs to calculate the currents at each frequency point when analyzing the target. With the increase of the target electrical size and complexity, the radar cross section (RCS) of the target changes drastically with frequency, it is necessary to calculate the accurate frequency response with a small frequency interval, which is very time-consuming in calculation and not feasible. This paper proposes to combine the subdomain method of moments (SMoM) with the Chebyshev approximation technique (CAT) to efficiently analyze the electromagnetic scattering of arbitrary shaped objects over a broad frequency band. In the SMoM technique, the whole object can be divided into several regions, each of which can be independently solved by the method of moments (MoM). The CAT technique is employed to expand the unknown current coefficients into a Chebyshev series for achieving fast frequency sweeping. Instead of direct point-by-point simulations, it is only necessary to calculate the currents by SMoM at several Chebyshev-Gauss frequency sample points. Furthermore, the Chebyshev series are matched via the Maehly approximation to a rational function to improve the accuracy. Numerical examples show that the hybrid technique can greatly reduce the computation time without loss of accuracy.

A novel solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number

Compressive sensing relies on the sparse prior imposed on the signal of interest to solve the ill-posed recovery problem in an under-determined linear system. The objective function used to enforce the sparse prior information should be both effective and easily optimizable. Motivated by the entropy concept from information theory, in this paper we propose the generalized Shannon entropy function and R\'{e}nyi entropy function of the signal as the sparsity promoting regularizers. Both entropy functions are nonconvex, non-separable. Their local minimums only occur on the boundaries of the orthants in the Euclidean space. Compared to other popular objective functions, minimizing the generalized entropy functions adaptively promotes multiple high-energy coefficients while suppressing the rest low-energy coefficients. The corresponding optimization problems can be recasted into a series of reweighted $l_1$-norm minimization problems and then solved efficiently by adapting the FISTA. Sparse signal recovery experiments on both the simulated and real data show the proposed entropy functions minimization approaches perform better than other popular approaches and achieve state-of-the-art performances.

Reconstruction of unknown objects requires efficient inversion for measured electromagnetic scattering data. In frequency-domain integral equation method for reconstructing dielectric objects, the volume integral equations (VIEs) are involved because the imaging domain with both true unknown objects and part of background is inhomogeneous. When solving the forward scattering integral equation (FSIE), the Nyström method is used since the traditional method of moments (MoM) with the Schaubert-Wilton-Glisson (SWG) basis function may not be convenient due to the inhomogeneity of the imaging domain. The benefits of the Nyström method include the simple implementation without using any basis and testing functions and lower requirement on geometrical discretization, so it is very suitable for inhomogeneous problems. When solving the inverse scattering integral equation (ISIE), the Gauss-Newton minimization approach (GNMA) with a multiplicative regularization method (MRM) is employed. Numerical examples for reconstructing three-dimensional dielectric objects are presented to illustrate the inversion approach.

Computed Tomography (CT) is one of the significant research areas in medical image analysis. One of the main aspects of CT that researchers remain focused, is on reducing the dosage as X-rays are generally harmful to human bodies. In order to reduce radiation dosage, compressed sensing (CS) based methodologies appear to be promising. The basic premise is that medical images have inherent sparsity in some transformation domain. As a result, CS provides the possibility of recovering a high quality image from fewer projection data. In general, the sensing matrix in CT is generated from Radon projections by appropriately sampling the radial and angular parameters. In our work, by restricting the number of such parameters, we generate an under-determined linear system involving projection (Radon) data and a sparse sensing matrix, bringing thereby the problem into CS framework.

A novel method which employs the recently developed theory of compressed sensing (CS) in method of moments (MoM) is presented. With a suitable discrete wavelet transform (DWT), the known impedance matrix, excitation and the unknown solution are localized, so the CS technique is introduced to construct the underdetermined equation that can be efficiently solved by the stagewise orthogonal matching pursuit technique (StOMP) method. Based on the fact of the significant correlation between the localized solution and excitation vector, the underdetermined equation can be constructed systematically and deterministically. Due to the computational complexity of StOMP depends not only on the size of equation, but also on the sparsity of solution, the computa¬tional cost of our method can be saved dramatically. The perfor¬mance of the proposed approach is illustrated by numerical studies of electromagnetic field integral equations.

We propose a variance-component probabilistic model for sparse signal reconstruction and model selection. The measurements follow an underdetermined linear model, where the unknown regression vector (signal) is sparse or approximately sparse and noise covariance matrix is known up to a constant. The signal is composed of two disjoint parts: a part with significant signal elements and the complementary part with insignificant signal elements that have zero or small values. We assign distinct variance components to the candidates for the significant signal elements and a single variance component to the rest of the signal; consequently, the dimension of our model's parameter space is proportional to the assumed sparsity level of the signal. We derive a generalized maximum-likelihood (GML) rule for selecting the most efficient parameter assignment and signal representation that strikes a balance between the accuracy of data fit and compactness of the parameterization. We prove that, under mild conditions, the GML-optimal index set of the distinct variance components coincides with the support set of the sparsest solution to the underlying underdetermined linear system. Finally, we propose an expansion-compression variance-component based method (ExCoV) that aims at maximizing the GML objective function and provides an approximate GML estimate of the significant signal element set and an empirical Bayesian signal estimate. The ExCoV method is automatic and demands no prior knowledge about signal-sparsity or measurement-noise levels. We also develop a computationally and memory efficient approximate ExCoV scheme suitable for large-scale problems, apply the proposed methods to reconstruct one- and two-dimensional signals from compressive samples, and demonstrate their reconstruction performance via numerical simulations. Compared with the competing approaches, our schemes perform particularly well in challenging scenarios where the noise is large or the number of measurements is small.

This study aims at the problem of reconstruction the unknown links in debt networks among enterprises. We use the topological matrix of the enterprise debt network as the object of reconstruction and use the time series data of accounts receivable and payable as input and output information in the debt network to establish an underdetermined linear system about the topological matrix of the debt network. We establish an iteratively reweighted least-squares algorithm, which is an algorithm in compressed sensing. This algorithm uses reweighted ell _2-minimization to approximate ell _1-norm of the target vectors. We solve the ell _1-minimization problem of the underdetermined linear system using the iteratively reweighted least-squares algorithm and obtain the reconstructed topological matrix of the debt network. Simulation experiments show that the topology matrix reconstruction method of enterprise debt networks based on compressed sensing can reconstruct over 70% of the unknown network links, and the error is controlled within 2%.

In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in compressed sensing is known to provide excellent reconstruction accuracy. However, when there is missing data, the theoretical guarantees associated with sparse recovery have not been well studied. Therefore, in this paper, we derive an upper bound on the minimum number of measurements required to ensure faithful recovery of a sparse signal when the generation of missing data is modeled using a Bernoulli erasure channel. We analyze three different network topologies, namely, star, (relay aided-)tree, and serial-star topologies. Our analysis establishes how the minimum required number of measurements for recovery scales with the network parameters, the properties of the measurement matrix, and the recovery algorithm. Finally, through numerical simulations, we show the variation of the minimum required number of measurements with different system parameters and validate our theoretical results.

In this article, we present a novel method that results in efficient minimum norm solution for the rate coordination problem in redundant manipulators. The theory is developed based upon a geometric interpretation that, for minimum norm criterion, vectors orthogonal to constraint space should pass through the origin of the solution space. It is shown that, for any spatial manipulator with 1, 2, or 3 degrees of redundancy, the minimum norm rate solution can be derived in analytic closed form. An example of the analytic formulation is given for a 3R planar case, substantiated with simulation results. The behavior of this algorithm in nonredundant and near singular situations is also discussed. The method offers an equivalent but much more efficient alternative to using the pseudoinverse in redundancy resolution and, in fact, is applicable to any underdetermined linear system. An alternative formulation of pseudoinverse arrived at in the course of the development is also presented. © 1992 John Wiley & Sons, Inc.

The alpha approximation method is known to be effective and simple for soil moisture retrieval from time series of synthetic aperture radar data. However, its accuracy is usually degraded by the scattering from vegetation, and it entails working with an underdetermined linear system when solving the unknown surface parameters. In this work, we study how the availability of fully polarimetric data and a diversity in incidence angles can help this method for soil moisture estimation. Results are obtained using data from the Soil Moisture Active Passive Validation Experiment 2012 campaign acquired by an air-borne L-band radar system. The assessment of the performance is based on in situ measurements over agricultural fields corresponding to five different crop types: bean, soybean, canola, corn, and wheat. The validation shows that, compared with the original method, the retrieval accuracy can be improved when the polarimetric decomposition is included in the approach. The combination of polarimetric decomposition and multi-incidence observations of enriched data provides the best performance, with a decrease in the final root-mean-square error between 0.4% and 5% with respect to single-pol and single-incidence data. Compared with HH, the results obtained for VV data present a higher accuracy for the overall crop types. The most noticeable improvement is achieved for corn, soybean and wheat, demonstrating the contribution of this extension of the original approach.

This paper addresses the problem of feature selection for the classification of ground penetrating radar signals. We propose a new classification approach based on time-frequency analysis and sparse kernel feature selection. In the proposed approach, a time-frequency or a time-scale transform is first applied to the one-dimensional radar trace. Sparse kernel feature selection is then employed to extract an optimum set of features for classification. The sparse kernel method is formulated as an underdetermined linear system in a high-dimensional space, and the category labels of the training samples are used as measurements to select the most informative features. The proposed approach is evaluated through an industrial application of assessing railway ballast fouling conditions. Experimental results show that the proposed combination of sparse kernel feature selection and support vector machine classification yields very high classification rates using only a small number of features.

Compressive sensing (CS) has been shown to be a useful tool for subsurface or through-the-wall imaging (TWI) using ground penetrating radar (GPR). It has been used to decrease both time/frequency or spatial measurements and generate high-resolution images. Although current works apply CS directly to TWI, questions on the required number of measurements for a sparsity level, measurement strategy to subsample in frequency and space, or imaging performance in varying noise levels and limits on CS range resolution performance still needs to be answered. In addition current CS-based imaging methods are based on two basic assumptions; targets are point like and positioned at only discrete grid locations and wall thickness and its dielectric constant are perfectly known. However, these assumptions are not usually valid in most TWI applications. This work extends the theory of CS-based radar imaging developed for subsurface imaging to TWI and outlines the performance of the proposed imaging for the above-mentioned questions using numerical simulations. The effect of unknown parameters on the imaging performance is analyzed, and it is observed that off-the-grid point targets and big modeling errors decreases the performance of CS imaging.

Compressive sensing sectional imaging for single-shot in-line self-interference incoherent holography

As an alternative paradigm to the Shannon-Nyquist sampling theorem, compressive sensing enables sparse signals to be acquired by sub-Nyquist analog-to-digital converters thus may launch a revolution in signal collection, transmission and processing. In the practical compressive sensing applications, the sparse signal is always affected by noise and interference, and therefore the recovery performance reduces based on the conventional compressive sensing, especially in the low signal-to-noise scene, the sparse recovery is usually unavailable. In this paper, the influence of noise on recovery performance is analyzed, so as to provide the theoretical basis for the noise folding phenomenon in compressive sensing. From the analysis, we find that the expected noise gain in the random measure process is closely related to the row and column of the measurement matrix. However, only those columns corresponding to the support for the sparse signal contribute to the sparse vector. In the traditional Shannon-Nyquist sampling system, an antialiasing filter is applied before the sampling process, so as to filter the noise beyond the passband of interest. Inspired by the necessity of antialiasing filtering in bandpass signal sampling, we propose a selective measurement scheme, namely adapted compressive sensing, whose measurement matrix can be updated according to the noise information fed back by the processing center. The measurement matrix is specially designed, and the sensing matrix has directivity so that the signal noise can be suppressed. The measurement matrix senses only the spectrum of interest, where the sparse spectrum is most likely to lie. Moreover, we compare the recovery performance of the proposed adaptive scheme with those of the non-adaptive orthogonal matching pursuit algorithm, FOCal underdetermined system solver algorithm, and sarse Bayesian learning algorithm. Extensive numerical experiments show that the proposed scheme has a better improvement in the performance of the sparse signal recovery. From the viewpoint of implementation, the measurement noise should be taken into consideration in the system, and more efficient algorithms will be developed for source pre-estimation at lower signal-to-noise ratio.