Minimum Transmission Data Gathering Trees for Compressive Sensing in Wireless Sensor Networks

Compressed sensing (CS) is a sparse signal sampling methodology for efficiently acquiring and reconstructing a signal from relatively few measurements. Recent work shows that CS is well-suited to be applied to problems in genomics, including probe design in microarrays, RNA interference (RNAi), and taxonomic assignment in metagenomics. The principle of using different CS recovery methods in these applications has thus been established, but a comprehensive study of using a wide range of CS methods has not been done. For each of these applications, we apply three hitherto unused CS methods, namely, l1-magic, CoSaMP, and l1-homotopy, in conjunction with CS measurement matrices such as randomly generated CS m matrix, Hamming matrix, and projective geometry-based matrix. We find that, in RNAi, the l1-magic (the standard package for l1 minimization) and l1-homotopy methods show significant reduction in reconstruction error compared to the baseline. In metagenomics, we find that l1-homotopy as well as CoSaMP estimate concentration with significantly reduced time when compared to the GPSR and WGSQuikr methods.

Compressive sensing (CS) is an innovative approach to simultaneously measure and compress signals such as biomedical signals that are sparse or compressible. A major effort in CS is to design a measurement matrix that can be used to encode and compress such signals. The measurement matrix structure has a direct impact on the computational and storage costs as well as the recovered signal quality. Sparse measurement matrices (i.e. with few non-zero elements) may drastically reduce these costs. We propose a permuted Kronecker-based sparse measurement matrix for sensing and data recovery in CS applications. In our study, we use three classes of sub-matrices (normalized Gaussian, Bernoulli, and BCH-based matrices) to create the proposed measurement matrix. Using ECG signals from the MIT-BIH Arrhythmia database, we show that the reconstructed signal quality is comparable to the ones achieved using well known CS methods. Our methodology results in an overall reduction in storage and computations, both during the sensing and recovery process. This approach can be generalized to other classes of eligible measurement matrices in CS.

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%.

Motivated by the increasing need for fast distributed processing of large-scale graphs such as the Web graph and various social networks, we study a number of fundamental graph problems in the message-passing model, where we have k machines that jointly perform computation on an arbitrary n-node (typically, n > k) input graph. The graph is assumed to be randomly partitioned among the k ≥ 2 machines (a common implementation in many real world systems). The communication is point-to-point, and the goal is to minimize the time complexity i.e., the number of communication rounds, of solving various fundamental graph problems.We present lower bounds that quantify the fundamental time limitations of distributively solving graph problems. We first show a lower bound of Ω(n/k) rounds for computing a spanning tree (ST) of the input graph. This result also implies the same bound for other fundamental problems such as computing a minimum spanning tree (MST), breadth-first tree (BFS), and shortest paths tree (SPT). We also show an Ω(n/k2) lower bound for connectivity ST verification and other related problems. Our lower bounds develop and use new bounds in random-partition communication complexity.To complement our lower bounds, we also give algorithms for various fundamental graph problems, e.g., PageRank, MST, connectivity, ST verification, shortest paths, cuts, spanners, covering problems, densest subgraph, subgraph isomorphism, finding triangles, etc. We show that problems such as PageRank, MST, connectivity, and graph covering can be solved in O(n/k) time (the notation O hides polylog(n) factors and an additive polylog(n) term); this shows that one can achieve almost linear (in k) speedup, whereas for shortest paths, we present algorithms that run in O(n/Ok) time (for (1 + e)-factor approximation) and in O(n/k) time (for O(log n)-factor approximation) respectively.Our results are a step towards understanding the complexity of distributively solving large-scale graph problems.

Time delay estimation (TDE) is a hot research topic in wireless location technology. Compressed sensing (CS) theory has been widely applied to image reconstruction and direction of arrival estimation since it was proposed in 2004. The sparse model can be constructed in time domain for estimating the time delay by using the CS theory. The measurement matrix plays a crucial role in the processing of signal reconstruction which is the core problem of CS theory. Therefore the research in the measurement matrix has becomes a hotspot in recent years. The existing measurement matrix is mainly divided into two categories, i.e., random measurement matrix and deterministic measurement matrix. The performance of random measurement matrix has bottlenecks. Firstly, because of the redundant measurement matrix data, the generation and storage of the random number put forward a high requirement for hardware. Secondly the random matrix can only satisfy the restricted isometry property in a statistical sense. The research of the deterministic measurement matrix is of great value under this background. The parity check matrix of low density parity check (LDPC) code has good performance in CS theory. However, the method of randomly selecting non-zero element position has a certain probability to generate a measurement matrix with a short loop structure during generating LDPC code measurement matrix. The robustness of the reconstruction performance decreases with the increase of iteration times. A novel quasi-cyclic CS algorithm based on progressive edge-growth is constructed to estimate the time delay. The purpose of this article is to deal with the need to store a large number of data in existing measurement matrix during time delay, by using the CS theory. The algorithm presented here can achieve TDE in a high precision. First, the theoretical bridge between CS and the maximum likelihood decoding is established. And the design criterion of measurement matrix based on the LDPC code is derived. The sparse measurement matrix with quasi-cyclic structure is constructed by introducing the idea of progressive edge-growth. Finally, the orthogonal matching pursuit algorithm is used to estimate the time delay. Furthermore, the computational complexity of the algorithm and the data storage of the measurement matrix are analyzed theoretically. Simulations show that the correct reconstruction probability of the proposed approach is higher than those of the Gauss random matrix and random LDPC matrix under the same dimension. Compared with the random LDPC matrix, the proposed method can improve performance at the expense of less complexity under the condition of the same data storage.

One ultimate goal of wireless sensor networks is to collect the sensed data from a set of sensors and transmit them to some sink node via a data gathering tree. In this work, we are interested in data aggregation, where the sink node wants to know the value for a certain function of all sensed data, such as minimum, maximum, average, and summation. Given a data aggregation tree, sensors receive messages from children periodically, merge them with its own packet, and send the new packet to its parent. The problem of finding an aggregation tree with the maximum lifetime has been proved to be NP-hard and can be generalized to finding a spanning tree with the minimum maximum vertex load, where the load of a vertex is a nondecreasing function of its degree in the tree. Although there is a rich body of research in those problems, they either fail to meet a theoretical bound or need high running time. In this paper, we develop a novel algorithm with provable performance bounds for the generalized problem. We show that the running time of our algorithm is in the order of O(mnα(m, n)), where m is the number of edges, n is the number of sensors, and α is the inverse Ackerman function. Though our work is motivated by applications in sensor networks, the proposed algorithm is general enough to handle a wide range of degree-oriented spanning tree problems, including bounded degree spanning tree problem and minimum degree spanning tree problem. When applied to these problems, it incurs a lower computational cost in comparison to existing methods. Simulation results validate our theoretical analysis.

Recently, multimedia has developed and become very important for transferring images securely through public networks. This paper uses the COOT optimization algorithm with compressive sensing (CS) for image encryption. A good method was proposed for encryption using compressive sensing with COOT optimization and chaos to encrypt images and obtain optimal encryption with the least correlation between pixels. This method will strengthen the encryption against various types of attacks. The natural image was sparsed using discreet wavelet transform (DWT) and the FAN transform. The image is divided into several blocks, and CS is applied to each block. The best measurement matrix was obtained using a COOT-optimized algorithm. All blocks are masked to get the compressed image, and the pixels are quantified. Next, the COOT optimization is used to Shuffle the image pixels to achieve the minimum correlation between the pixels. Then, a logistic map will be used to uniform the image pixel values by diffusion to get the final encrypted image. Chen’s chaotic and logistic map initial values are obtained from the input image after its division into four parts by taking a value from each part. The evaluation results obtained for this algorithm showed that it performs highly compared to other conventional methods. The average PSNR for the reconstructed images was 35.244, the average NPCR and UACI were 90.53 and 29.54, respectively, and the average correlation was (D = 0.0018, V = 0.0031, H = 0.0039). The results proved that the method is strong enough and very efficient to withstand attacks.

The validity of the compressed sensing (CS) is premised on the sparsity of the signals. In general, a signal is sparse if it can be linearly represented by few column combinations of a certain basis matrix. However, when signals exhibit some complex structure, or in other words, are difficult or inconvenient to be linearly represented, existing many CS methods may suffer from poor performance. In this paper, by introducing a sample set and the widely used kernel trick to CS, we investigate a sample based nonlinear compressed sensing (SNCS) model. In particular, with the help of kernel trick, our SNCS model can capture the nonlinear sparse structure of signals, and hence leads to a better performance than that of the traditional CS. On the other hand, due to the introduction of sample set, our SNCS model performs again better than a recent emerged kernel trick compressed sensing (KTCS) model. What's more, the optimization problem induced by our SNCS model still keeps concise and is easily solved by traditional CS methods.

Synthesis of sparse planar arrays can effectively reduce hardware costs and computational complexity in phased array 3-D imaging sonar systems. Traditional stochastic methods, such as simulated annealing, require multiple experiments and parameter adjustments to obtain optimal results. Methods based on compressed sensing (CS) can overcome this defect. However, when applied to large arrays, CS methods require vast computational complexity and may not obtain optimal sparse results because of violating the restricted isometry property. To make CS methods more practical, a distributed convex optimization CS method is proposed here for the sparse planar array synthesis in 3-D imaging sonar systems. This method is based on the CS theory, solving the minimum number of active elements under certain beam pattern constraints using the iterative reweighted l 1-norm minimization algorithm. Then, a multistage distributed framework is proposed to decompose the array into multistage subarrays, and the array synthesis is performed sequentially for each stage subarray to reduce computational complexity and obtain higher sparsity rates. Some applications of sparse planar array synthesis are employed to evaluate the efficiency of the proposed method.

Functional near- infrared spectroscopy (fNIRS) as an emerging optical neuroimaging technique has attracted the interest and attention of many investigators. With the growth of fNIRS data volume, effective data compression methods are urgent. Compressive sensing (CS) has been demonstrated a promising tool to deal with biomedical data. However, whether the compressibility of fNIRS data can discriminate different brain states is unclear. In this study, the fNIRS signals from fifteen attention-deficit/hyperactivity disorder (ADHD) children and fifteen typically developing (TD) children were recorded during an N-back task and a Go/NoGo task respectively. A block sparse Bayesian learning-based CS method was used to reconstruct the compressed fNIRS data. To assess the performance of the CS method, we adopted two metrics, structural similarity index (SSIM) and mean squared error (MSE), both of them effective in evaluating the compressibility of fNIRS data. Then, the two metrics were analyzed to discriminate the brain states of ADHD children and TD children during the two tasks using the multivariate pattern analysis (MVPA) method. As indicated by the results, the CS method could reconstruct the compressed fNIRS data with a high reconstruction quality at different compression ratio ([Formula: see text] and [Formula: see text]). Furthermore, the MVPA method could distinguish different brain states with high accuracy, and identify that the prefrontal cortex is a key brain region for distinguishing ADHD vs. TD or N-back vs. Go/NoGo. These findings indicated that CS is very promising for the storage and transmission of massive fNIRS data, and the compressibility of fNIRS data is a potential biomarker for the diagnosis of ADHD.

With the aim of developing a fast yet accurate algorithm for compressive sensing (CS) reconstruction of natural images, we combine in this paper the merits of two existing categories of CS methods: the structure insights of traditional optimization-based methods and the speed of recent network-based ones. Specifically, we propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general $$ norm CS reconstruction model. To cast ISTA into deep network form, we develop an effective strategy to solve the proximal mapping associated with the sparsity-inducing regularizer using nonlinear transforms. All the parameters in ISTA-Net (e.g. nonlinear transforms, shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than being hand-crafted. Moreover, considering that the residuals of natural images are more compressible, an enhanced version of ISTA-Net in the residual domain, dubbed ISTA-Net+, is derived to further improve CS reconstruction. Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform existing state-of-the-art optimization-based and network-based CS methods by large margins, while maintaining fast computational speed. Our source codes are available: http://jianzhang.tech/projects/ISTA-Net.

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.

We develop a novel algorithm for range and velocity joint estimating in randomized stepped frequency radar. By exploiting sparseness of the targets and invoking compressed sensing (CS) theory, higher resolution can be achieved. However, in actual radar system, some previous CS methods probably suffer from off-grid point effect, which causes performance degradation of the methods. We produce an adaptive CS method to mitigate the off-grid point effect. The performance of the proposed algorithm on accuracy and resolution of range-velocity joint estimate are illustrated by simulations and field experiments.

Impulsive noise is always present in real-world image Compressive Sensing (CS) acquisition systems, where existing CS reconstruction performance may seriously deteriorate. In this article, we propose a robust CS formulation for image reconstruction to suppress outliers in the presence of impulsive noise. To address this issue, we consider a novel truncated-Cauchy loss function as the metric of residual error to elevate the reconstruction robustness. Specifically, we design a complementary priors model to incorporate nonconvex nonlocal low-rank prior and deep denoiser prior for high-accuracy image reconstruction. By means of the half-quadratic optimization theory and generalized soft-thresholding technique, we also develop an alternative optimization algorithm for solving the induced nonconvex optimization problem. Numerical simulations demonstrate the robustness and accuracy of the proposed robust CS method compared to some recent CS methods for image reconstruction in impulsive noise.

Compressive sensing is a simultaneous data acquisition and compression technique, which can significantly reduce data bandwidth, data storage volume, and power. We apply this technique for transient photometric events. In this work, we analyze the effect of noise on the detection of these events using compressive sensing (CS). We show numerical results on the impact of source and measurement noise on the reconstruction of transient photometric curves, generated due to gravitational microlensing events. In our work, we define source noise as background noise, or any inherent noise present in the sampling region of interest. For our models, measurement noise is defined as the noise present during data acquisition. These results can be generalized for any transient photometric CS measurements with source noise and CS data acquisition measurement noise. Our results show that the CS measurement matrix properties have an effect on CS reconstruction in the presence of source noise and measurement noise. We provide potential solutions for improving the performance by tuning some of the properties of the measurement matrices. For source noise applications, we show that choosing a measurement matrix with low mutual coherence can lower the amount of error caused due to CS reconstruction. Similarly, for measurement noise addition, we show that by choosing a lower expected value of the binomial measurement matrix, we can lower the amount of error due to CS reconstruction.