Kronecker Compressive Sensing Research Articles

Channel Estimation for Hybrid mmWave Systems Using Generalized Kronecker Compressive Sensing (G-KCS) With Successive Decision-Aided Recovery

Channel Estimation for Hybrid mmWave Systems Using Generalized Kronecker Compressive Sensing (G-KCS) With Successive Decision-Aided Recovery

Joint communication and radar sensing in 5G mobile network by compressive sensing

Radio sensing can be integrated with communication in what the authors call future perceptive mobile networks. Due to the complicated signal structure, it is challenging to estimate sensing parameters such as delay, angle of arrival, and Doppler when joint communication and radar/radio sensing is applied in perceptive mobile networks. Radio sensing with signals compatible with a fifth-generation (5G) new radio standard using one-dimension (1D) to 3D compressive sensing (CS) techniques under 5G channel conditions is studied. In the case of 1D–3D CS techniques, they formulate the parameter estimation as a sparse signal recovery problem. These algorithms demonstrate respective advantages, but also show shortcomings in dealing with clustered channels. To effectively exploit the cluster structure in multipath channels, they also propose a 2D cluster Kronecker CS algorithm for significantly improved sensing parameter estimation via introducing a prior probability distribution. Simulation results are provided and they focus the respective advantages and disadvantages of these techniques that validate the effectiveness of the proposed algorithms.

Exploiting Block-sparsity for Hyperspectral Kronecker Compressive Sensing: a Tensor-based Bayesian Method.

Bayesian methods are attracting increasing attention in the field of compressive sensing (CS), as they are applicable to recover signals from random measurements. However, these methods have limited use in many tensor-based cases such as hyperspectral Kronecker compressive sensing (HKCS), because they exploit the sparsity in only one dimension. In this paper, we propose a novel Bayesian model for HKCS in an attempt to overcome the above limitation. The model exploits multi-dimensional block-sparsity such that the information redundancies in all dimensions are eliminated. Laplace prior distributions are employed for sparse coefficients in each dimension, and their coupling is consistent with the multi-dimensional block-sparsity model. Based on the proposed model, we develop a tensor-based Bayesian reconstruction algorithm, which decouples the hyperparameters for each dimension via a low-complexity technique. Experimental results demonstrate that the proposed method is able to provide more accurate reconstruction than existing Bayesian methods at a satisfactory speed. Additionally, the proposed method can not only be used for HKCS, it also has the potential to be extended to other multi-dimensional CS applications and to multi-dimensional block-sparse-based data recovery.

Efficient Measurement Method for Spatiotemporal Compressive Data Gathering in Wireless Sensor Networks

By means of compressive sensing (CS) technique, this paper considers the collection of sensor data with spatiotemporal correlations in wireless sensor networks (WSNs). In energy-constrained WSNs, one-dimensional CS methods need a lot of data transmissions since they are less applicable in fully exploiting the spatiotemporal correlations, while the Kronecker CS (KCS) methods suffer performance degradations when the signal dimension increases. In this paper, an appropriate sensing matrix as well as an efficient sensing method is proposed to further reduce the data transmissions without the loss of the recovery performance. Different matrices for the temporal signal of each sensor node are separately designed. The corresponding energy-efficient data gathering method is presented, which only transmitting a subset of sensor readings to recover data of the entire WSN. Theoretical analysis indicates that the sensing structure could have the relatively small mutual coherence according to the selection of matrix. Compared with the existing spatiotemporal CS (CS-ST) method, the simulation results show that the proposed efficient measurement method could reduce data transmissions by about 25% with the similar recovery performance. In addition, compared with the conventional KCS method, for 95% successful recovery, the proposed sensing structure could improve the recovery performance by about 20%.

Spatial-Temporal Data Collection with Compressive Sensing in Mobile Sensor Networks.

Compressive sensing (CS) provides an energy-efficient paradigm for data gathering in wireless sensor networks (WSNs). However, the existing work on spatial-temporal data gathering using compressive sensing only considers either multi-hop relaying based or multiple random walks based approaches. In this paper, we exploit the mobility pattern for spatial-temporal data collection and propose a novel mobile data gathering scheme by employing the Metropolis-Hastings algorithm with delayed acceptance, an improved random walk algorithm for a mobile collector to collect data from a sensing field. The proposed scheme exploits Kronecker compressive sensing (KCS) for spatial-temporal correlation of sensory data by allowing the mobile collector to gather temporal compressive measurements from a small subset of randomly selected nodes along a random routing path. More importantly, from the theoretical perspective we prove that the equivalent sensing matrix constructed from the proposed scheme for spatial-temporal compressible signal can satisfy the property of KCS models. The simulation results demonstrate that the proposed scheme can not only significantly reduce communication cost but also improve recovery accuracy for mobile data gathering compared to the other existing schemes. In particular, we also show that the proposed scheme is robust in unreliable wireless environment under various packet losses. All this indicates that the proposed scheme can be an efficient alternative for data gathering application in WSNs.

Cube-based perceptual weighted Kronecker Compressive Sensing: Can we avoid non-visible redundancies acquisition?

Compressive sensing approach directly avoids the acquisition of statistical redundancies of a signal. However, perceptual redundancies of images and videos due to the human eye sensitivity are not considered so far. Besides, an effective sampling scheme is needed to multidimensional signal reconstruction using a low number of measurements to avoid all redundancies. In this paper, along with the Kronecker structure of the sampling matrix we design various weighting matrices based on the spatio-temporal contrast sensitivity function to avoid acquisition of non-visible redundancies. Moreover, inspired by the block-based compressive sensing, we divide a group of pictures in a video sequence into cubes. Hence, the size of measurement and sparsifying basis matrices are reduced and the reconstruction algorithm can be implemented in parallel. We further show that our simple linear sampling approach can be competitive with motion compensation method. Simulation results verify that our proposed method notably outperforms the other state-of-the-art methods.

Tensor compressed video sensing reconstruction by combination of fractional-order total variation and sparsifying transform

High reconstructed performance compressed video sensing (CVS) with low computational complexity and memory requirement is very challenging. In order to reconstruct the high quality video frames with low computational complexity, this paper proposes a tensor-based joint sparseness regularization CVS reconstruction model FrTVCST (fractional-order total variation combined with sparsifying transform), in which a high-order tensor fractional-order total variation (FrTV) regularization and a tensor discrete wavelet transform (DWT) L0 norm regularization are combined. Furthermore, an approach for choosing the regularization parameter that controls the influence of the two terms in this joint model is proposed. Afterwards, a tensor gradient projection algorithm extended from smoothed L0 (SL0) is deduced to solve this combined tensor FrTV and DWT joint regularization constrained minimization problem, using a smooth approximation of the L0 norm. Compared with several state-of-the-art CVS reconstruction algorithms, such as the Kronecker compressive sensing (KCS), generalized tensor compressive sensing (GTCS), N-way block orthogonal matching pursuit (N-BOMP), low-rank tensor compressive sensing (LRTCS), extensive experiments with commonly used video data sets show the competitive performance of the proposed algorithm with respect to the peak signal-to-noise ratio (PSNR) and subjective visual quality.

Fast OMP algorithm for 3D parameters super‐resolution estimation in bistatic MIMO radar

A fast super-resolution method for joint Doppler frequency, direction of departure and direction of arrival estimation in bistatic MIMO radar is presented. First, the 3D echo signal model of bistatic MIMO radar with uniform linear transmit and uniform linear receive array is established. Then, the Kronecker compressive sensing (KCS) is introduced to improve the 3D parameters estimation performance. Moreover, a novel fast orthogonal matching pursuit (OMP) algorithm utilising 3D fast Fourier transformation is also presented to reduce the computation burden of KCS. Finally, the effectiveness of the method is validated by the simulation.

Multiple‐input–multiple‐output radar super‐resolution three‐dimensional imaging based on a dimension‐reduction compressive sensing

A super-resolution method for three-dimensional (3D) imaging by combining a narrowband multiple-input–multiple-output (MIMO) radar and compressive sensing (CS) theory is presented. First, a narrowband bistatic MIMO radar with uniform linear transmit array and uniform rectangular receive array is proposed. After analysing the 3D echo signal, Kronecker CS (KCS) is introduced to solve the problem of low resolution in 3D image, which is caused by the limited transmit and receive array. Considering the great complexity of KCS in improving the 3D resolution jointly, a dimension-reduction CS approach is presented to reduce its storage and computation burden. Furthermore, the restricted property of the dimension-reduction dictionary is analysed to insure the accurate recovery. Finally, the effectiveness of the method is validated by the results of comparative simulations.

Neighbor-Aided Spatial-Temporal Compressive Data Gathering in Wireless Sensor Networks

The integration between data collection methods in wireless sensor networks (WSNs) and compressive sensing (CS) provides energy efficient paradigms. Single-dimensional CS approaches are inapplicable in spatial and temporal correlated WSNs while the Kronecker compressive sensing (KCS) model suffers performance degradation along with the increasing data dimensions. In this letter, a neighbor-aided compressive sensing (NACS) scheme is proposed for efficient data gathering in spatial and temporal correlated WSNs. During every sensing period, the sensor node just sends the raw readings within the sensing period to a randomly and uniquely selected neighbor. Then, the CS measurements created by the neighbor are sent to the sink node directly. The equivalent sensing matrix is proved to satisfy both structured random matrix (SRM) and generalized KCS models. And, by introducing the idea of SRM to KCS, the recovery performance of KCS is significantly improved. Simulation results demonstrate that compared with the conventional KCS models, the proposed NACS model can achieve vastly superior recovery performance and receptions with much fewer transmissions.

3D sparse signal recovery via 3D orthogonal matching pursuit

We define the concept of 3D atom, 3D dictionary, and 3D projection.We decomposes a 3D signal into certain 3D atoms.A 3D signal is measured with 3D separable sensing operator on three dimensions.We propose the 3D-OMP recovery algorithm.The 3D-OMP is able to degrade the recovery complexity significantly. Though many three-dimensional (3D) compressive sensing schemes have been proposed, recovery algorithms in most of these schemes are designed for 1D or 2D signals, which cause some serious drawbacks, e.g., huge memory usage, and high decoder complexity. This paper proposes a 3D separable operator (3DSO) which is able to completely exploit the spatial and spectral correlation to sparsify and samples the 3D signal in three dimensions. A 3D orthogonal matching pursuit (3D-OMP) algorithm is then employed to recover the 3D sparse signal, which is able to reduce the computational complexity of the decoder significantly with guaranteed accuracy. In the proposed algorithm, we represent each 3D signal as a weighted sum of 3D atoms, which allow us to sample the 3D signal with 3D separable sensing operator. Then the best matched atoms are selected to construct the 3D support set, and the 3D signal is optimally recovered from the 3D support set in the sense of the least squares. We have performed some experiments to evaluate the performance of the 3D-OMP, KCS, global measurements and independent recovery. Experimental results show that the 3D-OMP approach achieves better recovery quality and gains higher probability of successful recovery than the KCS.Display Omitted Though many three-dimensional (3D) compressive sensing schemes have been proposed, recovery algorithms in most of these schemes are designed for 1D or 2D signals, which cause some serious drawbacks, e.g., huge memory usage, and high decoder complexity. This paper proposes a 3D separable operator (3DSO) which is able to completely exploit the spatial and spectral correlation to sparsify and samples the 3D signal in three dimensions. A 3D orthogonal matching pursuit (3D-OMP) algorithm is then employed to recover the 3D sparse signal, which is able to reduce the computational complexity of the decoder significantly with guaranteed accuracy. In the proposed algorithm, we represent each 3D signal as a weighted sum of 3D atoms, which allow us to sample the 3D signal with 3D separable sensing operator. Then the best matched atoms are selected to construct the 3D support set, and the 3D signal is optimally recovered from the 3D support set in the sense of the least squares. Experimental results show that the 3D-OMP approach achieves higher recovery quality but requires less computational time than the Kronecker Compressive Sensing (KCS) scheme.

Compressive sensing of sparse tensors.

Compressive sensing (CS) has triggered an enormous research activity since its first appearance. CS exploits the signal's sparsity or compressibility in a particular domain and integrates data compression and acquisition, thus allowing exact reconstruction through relatively few nonadaptive linear measurements. While conventional CS theory relies on data representation in the form of vectors, many data types in various applications, such as color imaging, video sequences, and multisensor networks, are intrinsically represented by higher order tensors. Application of CS to higher order data representation is typically performed by conversion of the data to very long vectors that must be measured using very large sampling matrices, thus imposing a huge computational and memory burden. In this paper, we propose generalized tensor compressive sensing (GTCS)-a unified framework for CS of higher order tensors, which preserves the intrinsic structure of tensor data with reduced computational complexity at reconstruction. GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes. In addition, we propound two reconstruction procedures, a serial method and a parallelizable method. We then compare the performance of the proposed method with Kronecker compressive sensing (KCS) and multiway compressive sensing (MWCS). We demonstrate experimentally that GTCS outperforms KCS and MWCS in terms of both reconstruction accuracy (within a range of compression ratios) and processing speed. The major disadvantage of our methods (and of MWCS as well) is that the compression ratios may be worse than that offered by KCS.

Compressive Sensing Optimization for Signal Ensembles in WSNs

Compressive sensing (CS) is a new approach to simultaneous sensing and compressing that is highly promising for fully distributed compression in wireless sensor networks (WSNs). While a wide investigation has been performed about theory and practice of CS for individual signals, real and practical cases, in general, involve multiple signals, extending the problem of compression from 1-D single-sensor to 2-D multiple-sensors data. In this paper the two most prominent frameworks on sparsity and compressibility of multidimensional signals and signal ensembles, Distributed compressed sensing (DCS) and Kronecker compressive sensing (KCS), are investigated. In this paper we compare these two frameworks against a common set of artificial signals properly built to embody the main characteristics of natural signals. We further investigate how, in a real deployment, DCS can be used to reduce the power consumption and to prolong lifetime. In particular an extensive analysis is performed using real commercial off-the-shelf (COTS) hardware evaluating how different kind of compression matrices can affect the jointly reconstruction, trying to achieve the better tradeoff between quality and energy expenditure.