For compressed sensing, to address problems which do not involve reconstruction, a correlation analysis between measurements and the transform coefficients is proposed. It is shown that there is a linear relationship between them, which indicates that we can abstract the inner property of images directly in the measurement domain.

Much attention has recently been paid to direction of arrival (DOA) estimation using compressed sensing (CS) techniques, which are sparse signal reconstruction methods. In our previous study, we developed a method for estimating the DOAs of multi-band signals that uses CS processing and that is based on the assumption that incident signals have the same complex amplitudes in all the bands. That method has a higher probability of correct estimation than a single-band DOA estimation method using CS. In this paper, we propose novel DOA estimation methods for multi-band signals with frequency characteristics using the Khatri-Rao product. First, we formulate a method that can estimate DOAs of multi-band signals whose phases alone have frequency dependence. Second, we extend the scheme in such a way that we can estimate DOAs of multi-band signals whose amplitudes and phases both depend on frequency. Finally, we evaluate the performance of the proposed methods through computer simulations and reveal the improvement in estimation performance.

In recent years, ray space (or light field in other literatures) photography has become popular in the area of computer vision and image processing, and the capture of a ray space has become more significant to these practical applications. In order to handle the huge data problem in the acquisition stage, original data are compressively sampled in the first place and completely reconstructed later. In this paper, in order to achieve better reconstruction quality and faster reconstruction speed, we propose a statistically weighted model in the reconstruction of compressively sampled ray space. This model can explore the structure of ray space data in an orthogonal basis, and integrate this structure into the reconstruction of ray space. In the experiment, the proposed model can achieve much better reconstruction quality for both 2D image patch and 3D image cube cases. Especially in a relatively low sensing ratio, about 10%, the proposed method can still recover most of the low frequency components which are of more significance for representation of ray space data. Besides, the proposed method is almost as good as the state-of-art technique, dictionary learning based method, in terms of reconstruction quality, and the reconstruction speed of our method is much faster. Therefore, our proposed method achieves better trade-off between reconstruction quality and reconstruction time, and is more suitable in the practical applications.

Millimeter-wave synthetic aperture imaging radiometer (SAIR) is a powerful sensor for near-field high-resolution observations. However, the large receiver number and system complexity affect the application of SAIR. To overcome this shortage (receiver number), an accurate imaging algorithm based on compressed sensing (CS) theory is proposed in this paper. For reconstructing the brightness temperature images accurately from the sparse SAIR with fewer receivers, the proposed CS-based imaging algorithm is used to accomplish the sparse reconstruction with fewer visibility samples. The reconstruction is performed by minimizing the $l_{1}$ norm of the transformed image. Compared to the FFT-based methods based on Fourier transform, the required receiver number can be further reduced by this method. The simulation results demonstrate that the proposed CS-based method has higher reconstruction accuracy for the sparse SAIR.

There have been many matching pursuit algorithms (MPAs) which handle the sparse signal recovery problem, called compressed sensing (CS). In the MPAs, the correlation step makes a dominant computational complexity. In this paper, we propose a new fast correlation method for the MPA when we use partial Fourier sensing matrices and partial Hadamard sensing matrices which are widely used as the sensing matrix in CS. The proposed correlation method can be applied to almost all MPAs without causing any degradation of their recovery performance. Also, the proposed correlation method can reduce the computational complexity of the MPAs well even though there are restrictions depending on a used MPA and parameters.

In compressed sensing, the design of the measurement matrix is a key work. In order to achieve a more precise reconstruction result, the columns of the measurement matrix should have better orthogonality or linear incoherence. A random matrix, like a Gaussian random matrix (GRM), is commonly adopted as the measurement matrix currently. However, the columns of the random matrix are only statistically-orthogonal. By substituting an orthogonal basis into the random matrix to construct a semi-random measurement matrix and by optimizing the mutual coherence between dictionary columns to approach a theoretical lower bound, the linear incoherence of the measurement matrix can be greatly improved. With this optimization measurement matrix, the signal can be reconstructed from its measures more precisely.

We propose a cooperative compressed spectrum sensing scheme for correlated signals in wideband cognitive radio networks. In order to design a reconstruction algorithm which accurately recover the wideband signals from the compressed samples in low SNR (Signal-to-Noise Ratio) environments, we consider the multiple measurement vector model exploiting a sequence of input signals and propose a cooperative sparse Bayesian learning algorithm which models the temporal correlation of the input signals. Simulation results show that the proposed scheme outperforms existing compressed sensing algorithms for low SNRs.

Presented is a new measuring and reconstruction framework of Compressed Sensing (CS), aiming at reducing the measurements required to ensure faithful reconstruction. A sparse vector is segmented into sparser vectors. These new ones are then randomly sensed. For recovery, we reconstruct these vectors individually and assemble them to obtain the original signal. We show that the proposed scheme, referred to as SegOMP, yields higher probability of exact recovery in theory. It is finished with much smaller number of measurements to achieve a same reconstruction quality when compared to the canonical greedy algorithms. Extensive experiments verify the validity of the SegOMP and demonstrate its potentials.

This letter deals with a sparse signal recovery problem and proposes a new algorithm based on the iterative reweighted least squares (IRLS) algorithm. We assume that the non-zero values of a sparse signal is always greater than a given constant and modify the IRLS algorithm to satisfy this assumption. Numerical results show that the proposed algorithm recovers a sparse vector efficiently.

Packet loss and energy dissipation are two major challenges of designing large-scale wireless sensor networks. Since sensing data is spatially correlated, compressed sensing (CS) is a promising reconstruction scheme to provide low-cost packet error correction and load balancing. In this letter, assuming a multi-hop network topology, we present a CS-oriented data aggregation scheme with a new measurement matrix which balances energy consumption of the nodes and allows for recovery of lost packets at fusion center without additional transmissions. Comparisons with existing methods show that the proposed scheme offers higher recovery precision and less energy consumption on TinyOS.

The main target of compressed sensing is recovery of one-dimensional signals, because signals more than two-dimension can also be treated as one-dimensional ones by raster scan, which makes the sensing matrix huge. This is unavoidable for general sensing processes. In separable cases like discrete Fourier transform (DFT) or standard wavelet transforms, however, the corresponding sensing process can be formulated using two matrices which are multiplied from both sides of the target two-dimensional signals. We propose an approximate message passing (AMP) algorithm for the separable sensing process. Typically, we suppose DFT for the sensing process, in which the measurements are complex numbers. Therefore, the formulation includes cases in which both target signal and measurements are complex. We show the effectiveness of the proposed algorithm by computer simulations.

In this letter, parallel orthogonal matching pursuit (POMP) is proposed to supplement orthogonal matching pursuit (OMP) which has been widely used as a greedy algorithm for sparse signal recovery. Empirical simulations show that POMP outperforms the existing sparse signal recovery algorithms including OMP, compressive sampling matching pursuit (CoSaMP), and linear programming (LP) in terms of the exact recovery ratio (ERR) for the sparse pattern and the mean-squared error (MSE) between the estimated signal and the original signal.

Network tomography is a technique for estimating internal network characteristics from end-to-end measurements. In this paper, we focus on loss tomography, which is a network tomography problem for estimating link loss rates. We study a loss tomography problem to detect links with high link loss rates in network environments with dynamically changing link loss rates, and propose a window-based sequential loss tomography scheme. The loss tomography problem is formulated as an underdetermined linear inverse problem, where there are infinitely many candidates of the solution. In the proposed scheme, we use compressed sensing, which can solve the problem with a prior information that the solution is a sparse vector. Measurement nodes transmit probe packets on measurement paths established between them, and calculate packet loss rates of measurement paths (path loss rates) from probe packets received within a window. Measurement paths are classified into normal quality and low quality states according to the path loss rates. When a measurement node finds measurement paths in the low quality states, link loss rates are estimated by compressed sensing. Using simulation scenarios with a few link states changing dynamically from low to high link loss rates, we evaluate the performance of the proposed scheme.

In this paper, we consider the optimization of measurement matrix in Compressed Sensing (CS) framework. Based on the boundary constraint, we propose a novel algorithm to make the “mutual coherence” approach a lower bound. This algorithm is implemented by using an iterative strategy. In each iteration, a neighborhood interval of the maximal off-diagonal entry in the Gram matrix is scaled down with the same shrinkage factor, and then a lower mutual coherence between the measurement matrix and sparsifying matrix is obtained. After many iterations, the magnitudes of most of off-diagonal entries approach the lower bound. The proposed optimization algorithm demonstrates better performance compared with other typical optimization methods, such as t-averaged mutual coherence. In addition, the effectiveness of CS can be used for the compression of complex synthetic aperture radar (SAR) image is verified, and experimental results using simulated data and real field data corroborate this claim.

This survey provides a brief introduction to compressed sensing as well as several major algorithms to solve it and its various applications to communications systems. We firstly review linear simultaneous equations as ill-posed inverse problems, since the idea of compressed sensing could be best understood in the context of the linear equations. Then, we consider the problem of compressed sensing as an underdetermined linear system with a prior information that the true solution is sparse, and explain the sparse signal recovery based on 1 optimization, which plays the central role in compressed sensing, with some intuitive explanations on the optimization problem. Moreover, we introduce some important properties of the sensing matrix in order to establish the guarantee of the exact recovery of sparse signals from the underdetermined system. After summarizing several major algorithms to obtain a sparse solution focusing on the 1 optimization and the greedy approaches, we introduce applications of compressed sensing to communications systems, such as wireless channel estimation, wireless sensor network, network tomography, cognitive radio, array signal processing, multiple access scheme, and networked control.

This letter deals with a system identification problem with unknown model order, which can be formulated as the matrix rank minimization problem by applying the subspace identification method. A sequential rank minimization algorithm is provided by modifying the null space based alternating optimization (NSAO) algorithm, and a model order identification algorithm is proposed. Numerical examples show that the proposed sequential algorithm can adaptively identify the model order of switched systems whose model order changes.

In this letter, a new method is proposed to solve the direction-of-arrivals (DOAs) estimation problem of coherently distributed sources based on the block-sparse signal model of compressed sensing (CS) and the convex optimization theory. We make use of a certain number of point sources and the CS array architecture to establish the compressive version of the discrete model of coherently distributed sources. The central DOA and the angular spread can be estimated simultaneously by solving a convex optimization problem which employs a joint norm constraint. As a result we can avoid the two-dimensional search used in conventional algorithms. Furthermore, the multiple-measurement-vectors (MMV) scenario is also considered to achieve robust estimation. The effectiveness of our method is confirmed by simulation results.

In remote control, efficient compression or representation of control signals is essential to send them through rate-limited channels. For this purpose, we propose an approach of sparse control signal representation using the compressive sampling technique. The problem of obtaining sparse representation is formulated by cardinality-constrained 2 optimization of the control performance, which is reducible to 1-2 optimization. The low rate random sampling employed in the proposed method based on the compressive sampling, in addition to the fact that the 1-2 optimization can be effectively solved by a fast iteration method, enables us to generate the sparse control signal with reduced computational complexity, which is preferable in remote control systems where computation delays seriously degrade the performance. We give a theoretical result for control performance analysis based on the notion of restricted isometry property (RIP). An example is shown to illustrate the effectiveness of the proposed approach via numerical experiments.

In this paper, a novel algorithm, Cross Low-dimension Pursuit, based on a new structured sparse matrix, Permuted Block Diagonal (PBD) matrix, is proposed in order to recover sparse signals from incomplete linear measurements. The main idea of the proposed method is using the PBD matrix to convert a high-dimension sparse recovery problem into two (or more) groups of highly low-dimension problems and crossly recover the entries of the original signal from them in an iterative way. By sampling a sufficiently sparse signal with a PBD matrix, the proposed algorithm can recover it efficiently. It has the following advantages over conventional algorithms: (1) low complexity, i.e., the algorithm has linear complexity, which is much lower than that of existing algorithms including greedy algorithms such as Orthogonal Matching Pursuit and (2) high recovery ability, i.e., the proposed algorithm can recover much less sparse signals than even 1-norm minimization algorithms. Moreover, we demonstrate both theoretically and empirically that the proposed algorithm can reliably recover a sparse signal from highly incomplete measurements.

To satisfy the requirement of a unified platform which can flexibly deal with various wireless radio systems, we proposed and implemented a heterogeneous network system composed of distributed flexible access points and a protocol-free signal processing unit. Distributed flexible access points are remote RF devices which perform the reception of multiple types of radio wave data and transfer the received data to the protocol-free signal processing unit through wired access network. The protocol-free signal processing unit performs multiple types of signal analysis by software. To realize a highly flexible and efficient radio wave data reception and transfer, we employ the recently developed compressed sensing technology. Moreover, we propose a combined Nyquist and compressed sampling method for the decoding signals to be sampled at the Nyquist rate and for the sensing signals to be sampled at the compressed rate. For this purpose, the decoding signals and the sensing signals are converted into the intermediate band frequency (IF) and mixed. In the IF band, the decoding signals are set at lower center frequencies than those of the sensing signals. The down converted signals are sampled at the rate of four times of the whole bandwidth of the decoding signals plus two times of the whole bandwidth of the sensing signals. The purpose of above setting is to simultaneously conduct Nyquist rate and compressed rate sampling in a single ADC. Then, all of odd (or even) samples are preserved and some of even (or odd) samples are randomly discarded. This method reduces the data transfer burden in dealing with the sensing signals while guaranteeing the realization of Nyquist-rate decoding performance. Simulation and experiment results validate the efficiency of the proposed method.