The security of Unmanned Aerial Vehicle (UAV) swarms is threatened by the deployment of anti-UAV systems under complicated environments such as battlefield. Specifically, the faults caused by anti-UAV systems exhibit sparse and compressible characteristics. In this paper, in order to improve the survivability of UAV swarms under complicated environments, we propose a novel multi-abnormality self-detecting and faults location method, which is based on compressed sensing (CS) and takes account of the communication characteristics of UAV swarms. The method can locate the faults when UAV swarms are suffering physical damages or signal attacks. Simulations confirm that the proposed method performs well in terms of abnormalities detecting and faults location when the faults quantity is less than 17% of the quantity of UAVs.

Image quality depends on the randomness of the k-space signal under-sampling in compressed sensing MRI (CS-MRI), especially for two-dimensional image acquisition. We investigate the feasibility of non-random signal under-sampling CS-MRI to stabilize the quality of reconstructed images and avoid arbitrariness in sampling point selection. Regular signal under-sampling for the phase-encoding direction is adopted, in which sampling points are chosen at equal intervals for the phase-encoding direction while varying the sampling density. Curvelet transform was adopted to remove the aliasing artifacts due to regular signal under-sampling. To increase the incoherence between the measurement matrix and the sparsifying transform function, the scale of the curvelet transform was varied in each iterative image reconstruction step. We evaluated the obtained images by the peak-signal-to-noise ratio and root mean squared error in localized 3×3 pixel regions. Simulation studies and experiments showed that the signal-to-noise ratio and the structural similarity index of reconstructed images were comparable to standard random under-sampling CS. This study demonstrated the feasibility of non-random under-sampling based CS by using the multi-scale curvelet transform as a sparsifying transform function. The technique may help to stabilize the obtained image quality in CS-MRI.

In this paper, we consider network monitoring techniques to estimate communication qualities in wide-area mobile networks, where an enormous number of heterogeneous components such as base stations, routers, and servers are deployed. We assume that average delays of neighboring base stations are comparable, most of servers have small delays, and delays at core routers are negligible. Under these assumptions, we propose Heterogeneous Delay Tomography (HDT) to estimate the average delay at each network component from end-to-end round trip times (RTTs) between mobile terminals and servers. HDT employs a crowdsourcing approach to collecting RTTs, where voluntary mobile users report their empirical RTTs to a data collection center. From the collected RTTs, HDT estimates average delays at base stations in the Graph Fourier Transform (GFT) domain and average delays at servers, by means of Compressed Sensing (CS). In the crowdsourcing approach, the performance of HDT may be degraded when the voluntary mobile users are unevenly distributed. To resolve this problem, we further extend HDT by considering the number of voluntary mobile users. With simulation experiments, we evaluate the performance of HDT.

Compressed sensing is an effective compression algorithm. It is widely used to measure signals in distributed sensor networks (DSNs). Considering the limited resources of DSNs, the measurement matrices used in DSNs must be simple. In this paper, we construct a deterministic measurement matrix based on Gordon-Mills-Welch (GMW) sequence. The column vectors of the proposed measurement matrix are generated by cyclically shifting a GMW sequence. Compared with some state-of-the-art measurement matrices, the proposed measurement matrix has relative lower computational complexity and needs less storage space. It is suitable for resource-constrained DSNs. Moreover, because the proposed measurement matrix can be realized by using simple shift register, it is more practical. The simulation result shows that, in terms of recovery quality, the proposed measurement matrix performs better than some state-of-the-art measurement matrices.

Generalized approximate message passing (GAMP) is introduced into distributed compressed sensing (DCS) to reconstruct jointly sparse signals under the mixed support-set model. A GAMP algorithm with known support-set is presented and the matching pursuit generalized approximate message passing (MPGAMP) algorithm is modified. Then, a new joint recovery algorithm, referred to as the joint MPGAMP algorithm, is proposed. It sets up the jointly shared support-set of the signal ensemble with the support exploration ability of matching pursuit and recovers the signals' amplitudes on the support-set with the good reconstruction performance of GAMP. Numerical investigation shows that the joint MPGAMP algorithm provides performance improvements in DCS reconstruction compared to joint orthogonal matching pursuit, joint look ahead orthogonal matching pursuit and regular MPGAMP.

Compressed Sensing (CS) is known to provide better channel estimation performance than the Least Square (LS) method for channel estimation. However, multipath delays may not be resolved if they span between the grids. This grid problem of CS is an obstacle to super resolution channel estimation. An Atomic Norm (AN) minimization is one of the methods for estimating continuous parameters. The AN minimization can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. There are studies showing that the AN minimization method has better resolution than conventional CS methods. In this paper, we propose a channel estimation method based on the AN minimization for Spread Spectrum (SS) systems. The accuracy of the proposed channel estimation is compared with the conventional LS method and Dantzig Selector (DS) of the CS. In addition to the application of channel estimation in wireless communication, we also show that the AN minimization can be applied to Global Positioning System (GPS) using Gold sequence.

By exploiting the inherent sparsity of wireless channels, the channel estimation in an orthogonal frequency division multiplexing (OFDM) system can be cast as a compressed sensing (CS) problem to estimate the channel more accurately. Practically, matching pursuit algorithms such as orthogonal matching pursuit (OMP) are used, where path delays of the channel is guessed based on correlation values for every quantized delay with residual. This full search approach requires a predefined grid of delays with high resolution, which induces the high computational complexity because correlation values with residual at a huge number of grid points should be calculated. Meanwhile, the correlation values with high resolution can be obtained by interpolation between the correlation values at a low resolution grid. Also, the interpolation can be implemented with a low pass filter (LPF). By using this fact, in this paper we substantially reduce the computational complexity to calculate the correlation values in channel estimation using CS.

Compressed sensing theory provides a new approach to acquire data as a sampling technique and makes sure that a sparse signal can be reconstructed from few measurements. The construction of compressed sensing matrices is a main problem in compressed sensing theory (CS). In this paper, the deterministic constructions of compressed sensing matrices based on affine singular linear space over finite fields are presented and a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. By choosing appropriate parameters, our sparse compressed sensing matrices are superior to the DeVore's matrices. Then we use a new formulation of support recovery to recover the support sets of signals with sparsity no more than k on account of binary compressed sensing matrices satisfying disjunct and inclusive properties.

In compressed sensing, most previous researches have studied the recovery performance of a sparse signal x based on the acquired model y=Φx+n, where n denotes the noise vector. There are also related studies for general perturbation environment, i.e., y=(Φ+E)x+n, where E is the measurement perturbation. IHT and HTP algorithms are the classical algorithms for sparse signal reconstruction in compressed sensing. Under the general perturbations, this paper derive the required sufficient conditions and the error bounds of IHT and HTP algorithms.

A new method for adaptive digital beamforming technique with compressed sensing (CS) for sparse receiving arrays with gain/phase uncertainties is presented. Because of the sparsity of the arriving signals, CS theory can be adopted to sample and recover receiving signals with less data. But due to the existence of the gain/phase uncertainties, the sparse representation of the signal is not optimal. In order to eliminating the influence of the gain/phase uncertainties to the sparse representation, most present study focus on calibrating the gain/phase uncertainties first. To overcome the effect of the gain/phase uncertainties, a new dictionary optimization method based on the total least squares (TLS) algorithm is proposed in this paper. We transfer the array signal receiving model with the gain/phase uncertainties into an EIV model, treating the gain/phase uncertainties effect as an additive error matrix. The method we proposed in this paper reconstructs the data by estimating the sparse coefficients using CS signal reconstruction algorithm and using TLS method toupdate error matrix with gain/phase uncertainties. Simulation results show that the sparse regularized total least squares algorithm can recover the receiving signals better with the effect of gain/phase uncertainties. Then adaptive digital beamforming algorithms are adopted to form antenna beam using the recovered data.

There is a strong demand for super-resolution time of arrival (TOA) estimation techniques for radar applications that can that can exceed the theoretical limits on range resolution set by frequency bandwidth. One of the most promising solutions is the use of compressed sensing (CS) algorithms, which assume only the sparseness of the target distribution but can achieve super-resolution. To preserve the reconstruction accuracy of CS under highly correlated and noisy conditions, we introduce a random resampling approach to process the received signal and thus reduce the coherent index, where the frequency-domain-based CS algorithm is used as noise reduction preprocessing. Numerical simulations demonstrate that our proposed method can achieve super-resolution TOA estimation performance not possible with conventional CS methods.

With the extensive use of location based devices, trajectories of various kinds of moving objects can be collected and stored. As time going on, the volume of trajectory data increases exponentially, which presents a series of problems in storage, transmission and analysis. Moreover, GPS trajectories are never perfectly accurate and sometimes with high noise. Therefore, how to overcome these problems becomes an urgent task in trajectory data mining and related applications. In this paper, an adaptive noise filtering trajectory compression and recovery algorithm based on Compressed Sensing (CS) is proposed. Firstly, a noise reduction model is introduced to filter the high noise in GPS trajectories. Secondly, the compressed data can be obtained by the improved GPS Trajectory Data Compression Algorithm. Thirdly, an adaptive GPS trajectory data recovery algorithm is adopted to restore the compressed trajectories to their original status approximately. Finally, comprehensive experiments on real and synthetic datasets demonstrate that the proposed algorithm is not only good at noise filtering, but also with high compression ratio and recovery performance compared to current algorithms.

Compressed Sensing based CMOS image sensor (CS-CIS) is a new generation of CMOS image sensor that significantly reduces the power consumption. For CS-CIS, the image quality and data volume of output are two important issues to concern. In this paper, we first proposed an algorithm to generate a series of deterministic and ternary matrices, which improves the image quality, reduces the data volume and are compatible with CS-CIS. Proposed matrices are derived from the approximate DCT and trimmed in 2D-zigzag order, thus preserving the energy compaction property as DCT does. Moreover, we proposed matrix row operations adaptive to the proposed matrix to further compress data (measurements) without any image quality loss. At last, a low-cost VLSI architecture of measurements compression with proposed matrix row operations is implemented. Experiment results show our proposed matrix significantly improve the coding efficiency by BD-PSNR increase of 4.2 dB, comparing with the random binary matrix used in the-state-of-art CS-CIS. The proposed matrix row operations for measurement compression further increases the coding efficiency by 0.24 dB BD-PSNR (4.8% BD-rate reduction). The VLSI architecture is only 4.3 K gates in area and 0.3 mW in power consumption.

This letter deals with an audio declipping problem and proposes a multiple matrix rank minimization approach. We assume that short-time audio signals satisfy the autoregressive (AR) model and formulate the declipping problem as a multiple matrix rank minimization problem. To solve this problem, an iterative algorithm is provided based on the iterative partial matrix shrinkage (IPMS) algorithm. Numerical examples show its efficiency.

Block compressed sensing with random permutation (BCS-RP) has been shown to be very effective for image Encryption-then-Compression (ETC) applications. However, in the BCS-RP scheme, the statistical information of the blocks is disclosed, because the encryption is conducted within each small block of the image. To solve this problem, a two-dimension compressed sensing (2DCS) with 2D random permutation (2DRP) strategy for image ETC applications is proposed in this letter, where the 2DRP strategy is used for encrypting the image and the 2DCS scheme is used for compressing the encrypted image. Compared with the BCS-RP scheme, the proposed approach has two benefits. Firstly, it offers better security. Secondly, it obtains a significant gain of peak signal-to-noise ratio (PSNR) of the reconstructed-images.

In this paper, we consider to develop a recovery algorithm of a sparse signal for a compressed sensing (CS) framework over finite fields. A basic framework of CS for discrete signals rather than continuous signals is established from the linear measurement step to the reconstruction. With predetermined priori distribution of a sparse signal, we reconstruct it by using a message passing algorithm, and evaluate the performance obtained from simulation. We compare our simulation results with the theoretic bounds obtained from probability analysis.

Block compressed sensing (CS) with optimal permutation is a promising method to improve sampling efficiency in CS-based image compression. However, the existing optimal permutation scheme brings a large amount of extra data to encode the permutation information because it needs to know the permutation information to accomplish signal reconstruction. When the extra data is taken into consideration, the improvement in sampling efficiency of this method is limited. In order to solve this problem, a new optimal permutation strategy for block CS (BCS) is proposed. Based on the proposed permutation strategy, an improved optimal permutation based BCS method called BCS-NOP (BCS with new optimal permutation) is proposed in this paper. Simulation results show that the proposed approach reduces the amount of extra data to encode the permutation information significantly and thereby improves the sampling efficiency compared with the existing optimal permutation based BCS approach.

An improved beamformer, which uses joint estimation of the reconstructed interference-plus-noise (IPN) covariance matrix and array steering vector (ASV), is proposed. It can mitigate the problem of performance degradation in situations where the desired signal exists in the sample covariance matrix and the steering vector pointing has large errors. In the proposed method, the covariance matrix is reconstructed by weighted sum of the exterior products of the interferences' ASV and their individual power to reject the desired signal component, the coefficients of which can be accurately estimated by the compressed sensing (CS) and total least squares (TLS) techniques. Moreover, according to the theorem of sequential vector space projection, the actual ASV is estimated from an intersection of two subspaces by applying the alternating projection algorithm. Simulation results are provided to demonstrate the performance of the proposed beamformer, which is clearly better than the existing robust adaptive beamformers.

Multi-hypothesis prediction technique, which exploits inter-frame correlation efficiently, is widely used in block-based distributed compressive video sensing. To solve the problem of inaccurate prediction in multi-hypothesis prediction technique at a low sampling rate and enhance the reconstruction quality of non-key frames, we present a resample-based hybrid multi-hypothesis scheme for block-based distributed compressive video sensing. The innovations in this paper include: (1) multi-hypothesis reconstruction based on measurements reorganization (MR-MH) which integrates side information into the original measurements; (2) hybrid multi-hypothesis (H-MH) reconstruction which mixes multiple multi-hypothesis reconstructions adaptively by resampling each reconstruction. Experimental results show that the proposed scheme outperforms the state-of-the-art technique at the same low sampling rate.

This paper presents a measurement-domain intra prediction coding framework that is compatible with compressive sensing (CS)-based image sensors. In this framework, we propose a low-complexity intra prediction algorithm that can be directly applied to measurements captured by the image sensor. We proposed a structural random 0/1 measurement matrix, embedding the block boundary information that can be extracted from the measurements for intra prediction. Furthermore, a low-cost Very Large Scale Integration (VLSI) architecture is implemented for the proposed framework, by substituting the matrix multiplication with shared adders and shifters. The experimental results show that our proposed framework can compress the measurements and increase coding efficiency, with 34.9% BD-rate reduction compared to the direct output of CS-based sensors. The VLSI architecture of the proposed framework is 9.1 Kin area, and achieves the 83% reduction in size of memory bandwidth and storage for the line buffer. This could significantly reduce both the energy consumption and bandwidth in communication of wireless camera systems, which are expected to be massively deployed in the Internet of Things (IoT) era.