A light field (LF), which is represented as a set of dense, multi-view images, has been used in various 3D applications. To make LF acquisition more efficient, researchers have investigated compressive sensing methods by incorporating certain coding functionalities into a camera. In this paper, we focus on a challenging case called snapshot compressive LF imaging, in which an entire LF is reconstructed from only a single acquired image. To embed a large amount of LF information in a single image, we consider two promising methods based on rapid optical control during a single exposure: time-multiplexed coded aperture (TMCA) and coded focal stack (CFS), which were proposed individually in previous works. Both TMCA and CFS can be interpreted in a unified manner as extensions of the coded aperture (CA) and focal stack (FS) methods, respectively. By developing a unified algorithm pipeline for TMCA and CFS, based on deep neural networks, we evaluated their performance with respect to other possible imaging methods. We found that both TMCA and CFS can achieve better reconstruction quality than the other snapshot methods, and they also perform reasonably well compared to methods using multiple acquired images. To our knowledge, we are the first to present an overall discussion of TMCA and CFS and to compare and validate their effectiveness in the context of compressive LF imaging.

Deep learning is playing an increasingly important role in signal processing field due to its excellent performance on many inference problems. Parametric bilinear generalized approximate message passing (P-BiG-AMP) is a new approximate message passing based approach to a general class of structure-matrix bilinear estimation problems. In this letter, we propose a novel feed-forward neural network architecture to realize P-BiG-AMP methodology with deep learning for the inference problem of compressive sensing under matrix uncertainty. Linear transforms utilized in the recovery process and parameters involved in the input and output channels of measurement are jointly learned from training data. Simulation results show that the trained P-BiG-AMP network can achieve higher reconstruction performance than the P-BiG-AMP algorithm with parameters tuned via the expectation-maximization method.

In cognitive radio (CR) networks, spectrum sensing is an essential task for enabling dynamic spectrum sharing. However, the problem becomes quite challenging in wideband spectrum sensing due to high sampling pressure, limited power and computing resources, and serious channel fading. To overcome these challenges, this paper proposes a distributed collaborative spectrum sensing scheme based on 1-bit compressive sensing (CS). Each secondary user (SU) performs local 1-bit CS and obtains support estimate information from the signal reconstruction. To utilize joint sparsity and achieve spatial diversity, the support estimate information among the network is fused via the average consensus technique based on distributed computation and one-hop communications. Then the fused result on support estimate is used as priori information to guide the next local signal reconstruction, which is implemented via our proposed weighted binary iterative hard thresholding (BIHT) algorithm. The local signal reconstruction and the distributed fusion of support information are alternately carried out until reliable spectrum detection is achieved. Simulations testify the effectiveness of our proposed scheme in distributed CR networks.

We research device-free (DF) multi-target tracking scheme in this paper. The existing localization and tracking algorithms are always pay attention to the single target and need to collect a large amount of localization information. In this paper, we exploit the sparse property of multiple target locations to achieve target trace accurately with much less sampling both in the wireless links and the time slots. The proposed approach mainly includes the target localization part and target trace recovery part. In target localization part, by exploiting the inherent sparsity of the target number, Compressive Sensing (CS) is utilized to reduce the wireless links distributed. In the target trace recovery part, we exploit the compressive property of target trace, as well as designing the measurement matrix and the sparse matrix, to reduce the samplings in time domain. Additionally, Kronecker Compressive Sensing (KCS) theory is used to simultaneously recover the multiple traces both of the X label and the Y Label. Finally, simulations show that the proposed approach holds an effective recovery performance.

In compressive sensing theory (CS), the restricted isometry property (RIP) is commonly used for the measurement matrix to guarantee the reliable recovery of sparse signals from linear measurements. Although many works have indicated that random matrices with excellent recovery performance satisfy the RIP with high probability, Toeplitz-structured matrices arise naturally in real scenarios, such as applications of linear time-invariant systems. Thus, the corresponding measurement matrix can be modeled as a Toeplitz (partial) structured matrix instead of a completely random matrix. The structure characteristics introduce coherence and cause the performance degradation of the measurement matrix. To enhance the recovery performance of the Toeplitz structured measurement matrix in multichannel convolution source separation, an efficient construction of measurement matrix is presented, referred to as sparse random block-banded Toeplitz matrix (SRBT). The sparse signal is pre-randomized by locally scrambling its sample locations. Then, the signal is subsampled using the sparse random banded matrix. Finally, the mixing measurements are obtained. Based on the analysis of eigenvalues, the theoretical results indicate that the SRBT matrix satisfies the RIP with high probability. Simulation results show that the SRBT matrix almost matches the recovery performance of random matrices. Compared with the existing banded block Toeplitz matrix, SRBT significantly improves the probability of successful recovery. Additionally, SRBT has the advantages of low storage requirements and fast computation in reconstruction.

The compressive sensing has been applied to develop an effective framework for simultaneously localizing multiple targets in wireless sensor networks. Nevertheless, existing methods implicitly use analog measurements, which have infinite bit precision. In this letter, we focus on off-grid target localization using quantized measurements with only several bits. To address this, we propose a novel localization framework for jointly estimating target locations and dealing with quantization errors, based on the novel application of the variational Bayesian Expectation-Maximization methodology. Simulation results highlight its superior performance.

In this letter, we propose a generalized quadrature spatial modulation technique (GQSM) which offers additional bits per channel use (bpcu) gains and a low complexity greedy detector algorithm, structured orthogonal matching pursuit (S-OMP)- GQSM, based on compressive sensing (CS) framework. Simulation results show that the bit error rate (BER) performance of the proposed greedy detector is very close to maximum likelihood (ML) and near optimal detectors based on convex programming.

Compressive spectral imaging (CSI) systems capture the 3D spatiospectral data by measuring the 2D compressed focal plane array (FPA) coded projection with the help of reconstruction algorithms exploiting the sparsity of signals. However, the contradiction between the multi-dimension of the scenes and the limited dimension of the sensors has limited improvement of recovery performance. In order to solve the problem, a novel CSI system based on a coded aperture snapshot spectral imager, RGB-CASSI, is proposed, which has two branches, one for CASSI, another for RGB images. In addition, considering that conventional reconstruction algorithms lead to oversmoothing, a RGB-guided low-rank (RGBLR) method for compressive hyperspectral image reconstruction based on compressed sensing and coded aperture spectral imaging system is presented, in which the available additional RGB information is used to guide the reconstruction and a low-rank regularization for compressive sensing and a non-convex surrogate of the rank is also used instead of nuclear norm for seeking a preferable solution. Experiments show that the proposed algorithm performs better in both PSNR and subjective effects compared with other state-of-art methods.

In this letter, robust sparse signal recovery is considered in the presence of heavy-tailed impulsive noise. Two Bayesian approaches are developed where a Bayesian framework is constructed by utilizing the Laplace distribution to model the noise. By rewriting the noise-fitting term as a reweighted quadratic function which is optimized in the sparse signal space, the Type I Maximum A Posteriori (MAP) approach is proposed. Next, by exploiting the hierarchical structure of the sparse prior and the likelihood function, we develop the Type II Evidence Maximization approach optimized in the hyperparameter space. The numerical results verify the effectiveness of the proposed methods in the presence of impulsive noise.

In order to significantly reduce the time and space needed, compressive sensing builds upon the fundamental assumption of sparsity under a suitable discrete dictionary. However, in many signal processing applications there exists mismatch between the assumed and the true sparsity bases, so that the actual representative coefficients do not lie on the finite grid discretized by the assumed dictionary. Unlike previous work this paper introduces the unified compressive measurement operator into atomic norm denoising and investigates the problems of recovering the frequency support of a combination of multiple sinusoids from sub-Nyquist samples. We provide some useful properties to ensure the optimality of the unified framework via semidefinite programming (SDP). We also provide a sufficient condition to guarantee the uniqueness of the optimizer with high probability. Theoretical results demonstrate the proposed method can locate the nonzero coefficients on an infinitely dense grid over a wide range of SNR case.

Spectral compressive sensing is a novel approach that enables extraction of spectral information from a spectral-sparse signal, exclusively from its compressed measurements. Thus, the approach has received considerable attention from various fields. However, standard compressive sensing algorithms always require a sparse signal to be on the grid, whose spacing is the standard resolution limit. Thus, these algorithms severely degenerate while handling spectral compressive sensing, owing to the off-the-grid issue. Some off-the-grid algorithms were recently proposed to solve this problem, but they are either inaccurate or computationally expensive. In this paper, we propose a novel algorithm named parameterized ℓ1-minimization (PL1), which can efficiently solves the off-the-grid spectral estimation problem with relatively low computational complexity.

Autonomous Underwater Vehicle (AUV) can be utilized to directly measure the geomagnetic map in deep sea. The traditional map interpolation algorithms based on sampling continuation above the sea level yield low resolution and accuracy, which restricts the applications such as the deep sea geomagnetic positioning, navigation, searching and surveillance, etc. In this letter, we propose a Three-Dimensional (3D) Compressive Sensing (CS) algorithm in terms of the real trajectory of AUV which can be optimized with the required accuracy. The geomagnetic map recovered with the CS algorithm shows high precision compared with traditional interpolation schemes, by which the magnetic positioning accuracy can be greatly improved.

Compressive sensing is attractive to distributed video coding with respect to two issues: low complexity in encoding and low data rate in transmission. In this paper, a novel compressive sensing-based distributed video coding system is presented based on a combination of predictive coding and Wyner-Ziv difference coding of compressively sampled frames. Experimental results show that the data volume in transmission in the proposed method is less than one tenth of the distributed compressive video sensing. The quality of decoded video was evaluated in terms of PSNR and structural similarity index as well as visual inspections.

Many basic tasks in Wireless Sensor Networks (WSNs) rely heavily on the availability and accuracy of target locations. Since the number of targets is usually limited, localization benefits from Compressed Sensing (CS) in the sense that measurements can be greatly reduced. Though some CS-based localization schemes have been proposed, all of these solutions make an assumption that all targets are located on a pre-sampled and fixed grid, and perform poorly when some targets are located off the grid. To address this problem, we develop an adaptive dictionary algorithm where the grid is adaptively adjusted. To achieve this, we formulate localization as a joint parameter estimation and sparse signal recovery problem. Additionally, we transform the problem into a tractable convex optimization problem by using Taylor approximation. Finally, the block coordinate descent method is leveraged to iteratively optimize over the parameters and sparse signal. After iterations, the measurements can be linearly represented by a sparse signal which indicates the number and locations of targets. Extensive simulation results show that the proposed adaptive dictionary algorithm provides better performance than state-of-the-art fixed dictionary algorithms.

The compressive sensing (CS) theory has been recognized as a promising technique to achieve the target localization in wireless sensor networks. However, most of the existing works require the prior knowledge of transmitting powers of targets, which is not conformed to the case that the information of targets is completely unknown. To address such a problem, in this paper, we propose a novel CS-based approach for multiple target localization and power estimation. It is achieved by formulating the locations and transmitting powers of targets as a sparse vector in the discrete spatial domain and the received signal strengths (RSSs) of targets are taken to recover the sparse vector. The key point of CS-based localization is the sensing matrix, which is constructed by collecting RSSs from RF emitters in our approach, avoiding the disadvantage of using the radio propagation model. Moreover, since the collection of RSSs to construct the sensing matrix is tedious and time-consuming, we propose a CS-based method for reconstructing the sensing matrix from only a small number of RSS measurements. It is achieved by exploiting the CS theory and designing an difference matrix to reveal the sparsity of the sensing matrix. Finally, simulation results demonstrate the effectiveness and robustness of our localization and power estimation approach.

Traditional speech enhancement (SE) algorithms usually have fluctuant performance when they deal with different types of noisy speech signals. In this paper, we propose multi-task Bayesian compressive sensing based speech enhancement (MT-BCS-SE) algorithm to achieve not only comparable performance to but also more stable performance than traditional SE algorithms. MT-BCS-SE algorithm utilizes the dependence information among compressive sensing (CS) measurements and the sparsity of speech signals to perform SE. To obtain sufficient sparsity of speech signals, we adopt overcomplete dictionary to transform speech signals into sparse representations. K-SVD algorithm is employed to learn various overcomplete dictionaries. The influence of the overcomplete dictionary on MT-BCS-SE algorithm is evaluated through large numbers of experiments, so that the most suitable dictionary could be adopted by MT-BCS-SE algorithm for obtaining the best performance. Experiments were conducted on well-known NOIZEUS corpus to evaluate the performance of the proposed algorithm. In these cases of NOIZEUS corpus, MT-BCS-SE is shown that to be competitive or even superior to traditional SE algorithms, such as optimally-modified log-spectral amplitude (OMLSA), multi-band spectral subtraction (SSMul), and minimum mean square error (MMSE), in terms of signal-noise ratio (SNR), speech enhancement gain (SEG) and perceptual evaluation of speech quality (PESQ) and to have better stability than traditional SE algorithms.

The compressive sensing (CS) theory has been widely used in synthetic aperture radar (SAR) imaging for its ability to reconstruct image from an extremely small set of measurements than what is generally considered necessary. Because block-based CS approaches in SAR imaging always cause block boundaries between two adjacent blocks, resulting in namely the block artefacts. In this paper, we propose a weighted overlapped block-based compressive sensing (WOBCS) method to reduce the block artefacts and accomplish SAR imaging. It has two main characteristics: 1) the strategy of sensing small and recovering big and 2) adaptive weighting technique among overlapped blocks. This proposed method is implemented by the well-known CS recovery schemes like orthogonal matching pursuit (OMP) and BCS-SPL. Promising results are demonstrated through several experiments.

Network coding (NC) is considered a new paradigm for distributed networks. However, NC has an all-or-nothing property. In this paper, we propose a sparse recovery approach using sparse sensing matrix to solve the NC all-or-nothing problem over a finite field. The effectiveness of the proposed approach is evaluated based on a sensor network.

This paper investigates the data persistence problem with compressive sensing (CS) in wireless sensor networks (WSNs) where the sensed readings should be temporarily stored among the entire network in a distributed manner until gathered by a mobile sink. Since there is an energy-performance tradeoff, conventional CS-based schemes only focus on reducing the energy consumption or improving the CS construction performance. In this paper, we propose an efficient Compressive Sensing based Data Persistence (CSDP) scheme to achieve the optimum balance between energy consumption and reconstruction performance. Unlike most existing CS-based schemes which require packets visiting the entire network to reach the equilibrium distribution, in our proposed scheme information exchange is only performed among neighboring nodes. Therefore, such an approach will result in a non-uniform distribution of measurements, and the CS measurement matrix depends heavily on the node degree. The CS reconstruction performance and energy consumption are analyzed. Simulation results confirm that the proposed CSDP scheme consumes the least energy and computational overheads compared with other representative schemes, while almost without sacrificing the CS reconstruction performance.

In this paper, a novel scheme of the adaptive sampling of block compressive sensing is proposed for natural images. In view of the contents of images, the edge proportion in a block can be used to represent its sparsity. Furthermore, according to the edge proportion, the adaptive sampling rate can be adaptively allocated for better compressive sensing recovery. Given that there are too many blocks in an image, it may lead to a overhead cost for recording the ratio of measurement of each block. Therefore, K-means method is applied to classify the blocks into clusters and for each cluster a kind of ratio of measurement can be allocated. In addition, we design an iterative termination condition to reduce time-consuming in the iteration of compressive sensing recovery. The experimental results show that compared with the corresponding methods, the proposed scheme can acquire a better reconstructed image at the same sampling rate.