Recently, the problem of Compressive Sensing (CS) has attracted lots of attention in the area of signal processing. So, much of the research in this field is being carried out in this issue. One of the applications where CS could be used is wireless sensor networks (WSNs). The structure of WSNs consists of many low power wireless sensors. This requires that any improved algorithm for this application must be optimized in terms of energy consumption. In other words, the computational complexity of algorithms must be as low as possible and should require minimal interaction between the sensors. For such networks, CS has been used in data gathering and data persistence scenario, in order to minimize the total number of transmissions and consequently minimize the network energy consumption and to save the storage by distributing the traffic load and storage throughout the network. In these applications, the compression stage of CS is performed in sensor nodes, whereas the recovering duty is done in the fusion center (FC) unit in a centralized manner. In some applications, there is no FC unit and the recovering duty must be performed in sensor nodes in a cooperative and Distributed manner which we have focused on in this paper. Indeed, the notable algorithm for this purpose is Distributed least absolute shrinkage and selection operation (D-LASSO) algorithm which is based on diffusion cooperation structure. This algorithm that compete to the state-of-the-art CS algorithms has a major disadvantage; it involves matrix inversion that may be computationally demanding for sufficiently large matrices. On this basis, in this paper, we have proposed a Distributed CS recovery algorithm for the WSNs with a bi-directional incremental mode of cooperation. Actually, we have proposed a comprehensive Distributed framework for the recovery of sparse signals in WSNs. Here, we applied this comprehensive structure to three problems with different constraints which results in three completely Distributed solutions named as Distributed bi-directional incremental basis pursuit (DBIBP), Distributed bi-directional incremental noise-aware basis pursuit (DBINBP) and Distributed bi-directional incremental regularized least squares (DBIRLS). The proposed algorithms solely involve linear combinations of vectors and soft thresholding operations. Hence, the computational load is significantly reduced in each sensor. In the proposed method each iteration consists of two phases; clockwise and anti-clockwise phases. At each iteration, in anti-clockwise phase, each node receives the local estimate from its previous neighbor and updates an auxiliary variable. Then in the clockwise phase, each node receives the updated auxiliary variable from its next neighbors to update the local estimate. On the other hand, information exchange in two directions in an incremental manner which we called it bi-directional incremental structure. In an incremental strategy, information flows in a sequential manner from one node to the adjacent node. Unlike the diffusion structure (like as D-LASSO) where each node communicates with all of their neighbors, the incremental mode of cooperation requires the least amount of communication and power. The low computational complexity and better steady state performance are the important features of the proposed methods.

The emerging field of Compressive Sensing enables the reconstruction of the signal from a small set of linear projections. Traditional Compressive Sensing approaches deal with a single signal; while one can jointly reconstruct multiple signals via Distributed Compressive Sensing algorithm, which exploits both the inter-and intra-signal correlations via joint sparsity models. Since the wavelet coefficients of many signals is sparse, in this paper, the wavelet transform is used as sparsifying transform, and a new wavelet-based Bayesian Distributed Compressive Sensing algorithm is proposed, which takes into account the inter-scale dependencies among the wavelet coefficients via hidden Markov tree model, as well as the inter-signal correlations. This paper uses Bayesian procedure to statistically model this correlation via the prior distributions. Also, in this work, a type-1 joint sparsity model is used for jointly sparse signals, in which every sparse coefficient vector is considered as the sum of a common component and an innovation component. In order to jointly reconstruct multiple sparse signals, the centralized approach is used in Distributed Compressive Sensing, in which all the data is processed in the fusion center. Also, variational Bayes procedure is used to infer the posterior distributions of unknown variables. Simulation results demonstrate that the structure exploited within the wavelet coefficients provides superior performance in terms of average reconstruction error and structural similarity index.

Stepped frequency radars attract many attentions due to their high range resolution. Conventional processing technique in these radars is based on the IDFT. In detecting moving targets, the IDFT has the problems of range shifting and range spreading, which result in degrading target amplitude, loss of range accuracy and range resolution. To overcome these problems, the velocity compensation method is used. Since the target velocity is unknown, one should compensate the received signal with all possible velocities and choose the one with the highest and sharpest IDFT output. In this paper, by using the Compressive Sensing based algorithms, a new method for determining the range and the velocity of moving targets in the stepped frequency radar is proposed. The results show that the proposed method does not have any problem with range shifting and range spreading, and has a better performance compared with other methods in literature. Coherent processing concept is also investigated. Simulations show that using the coherent processing, the performance of Compressive Sensing based radar detectors is considerably improved.

Wireless sensor network (WSN) is one of the most important components of the Internet of Things (IoT). IoT on the WSN layer, measures different parameters by different sensors embedded in the multi-sensor nodes. The limitation of energy sources in the sensor nodes is one of the most important challenges in exploiting WSNs. Routing and data aggregation are two basic methods to reduce the energy consumption in the WSNs. Compressive Sensing (CS) is one of the most effective techniques for data aggregation in WSNs. The most studies related to the use of CS techniques to reduce communication cost in the network are based on the single-sensor node WSNs. So, in this paper, we show that how CS techniques can be applied to the multi-sensor IoT-based WSNs. Given that the sparsity of the environmental data read by multi-sensor nodes is an important parameter for using the CS techniques in WSNs, various different scenarios have been analyzed from the point of view of data sparsity in this study, as well as transmission methods, and data aggregation techniques in a multi-sensor WSN. To evaluate the performance of the CS techniques in a multi-sensor WSN, all investigated scenarios are evaluated for two important techniques of CS named Compressive data gathering (CDG) and hybrid Compressive Sensing (HCS), and in order to show the efficiency of the system in using of the CS, these techniques have been compared to the conventional Non-CS method. We show that the use of HCS technique has a considerable effect on reducing communication costs in a multi-sensor IoT-based WSN.

In this paper, a new method is proposed to estimate the direction of arrival (DOA) using non-uniform linear array structure and modeling the measurement matrix as a DFT matrix. In order to estimate the DOA using Compressive Sensing (CS), continuous angle space should be divided into a discrete set using small steps. This division, leads to the increment of mutual coherence between columns of the measurement matrix and performance of the sparse recovery algorithms is degraded. To solve this problem, we propose a new method in which DFT matrix with mutual coherence of zero is used as the measurement matrix. In order to increase the accuracy of estimation, the size of DFT matrix or the number of antennas should be increased. Implementation of an array with large number of antennas is complex and expensive. A solution to decrease the number of antennas is using a non-uniform linear array and constructing a virtual uniform linear array. A virtual uniform linear array can be constructed by vectorizing the correlation matrix of the received signal of a non-uniform linear array. Increasing the number of antennas in the virtual array will increase the size of DFT matrix. Therefore, the accuracy of DOA estimation will be increased. Simulation results show that DOA estimation using Compressive Sensing, based on DFT measurement matrix, has a good performance in terms of mean square error of estimation.

Ever increasing development of wireless devices and wireless networks have increased the value of spectral space. Many efforts have been conducted to increase spectral utilization. The radio environment mapping opens new gates for developing low cost wireless devices. In this paper, a new method is proposed for increasing spectral utilization in Distributed networks. In this method Distributed Kalman filter, which is modified to increase estimation accuracy, is used to estimate position, velocity and power of primary transmitters. These data are used to select spectrum holes optimally and increase spectral utilization compared to centralized methods. Obtained r esults are evaluated through practical implementations and simulations. Innovations of this research include introducing and employing a linear model for estimating position of a transmitter using received power in line of sight (LoS) and non-line of sight (NLS) conditions, modifying extended kalman filter and implementation of Distributed spectrum Sensing; advantages of this method are illustrated compared to centralized methods.

Compressive sampling (CS) is a new technique for simultaneous sampling and compression of signals in which the sampling rate can be very small under certain conditions. Due to the limited number of samples, image reconstruction based on CS samples is a challenging task. Most of the existing CS image reconstruction methods have a high computational complexity as they are applied on the entire image. To reduce this complexity, block-based CS (BCS) image reconstruction algorithms have been developed in which the image sampling and reconstruction processes are applied on a block by block basis. In almost all the existing BCS methods, a fixed transform is used to achieve a sparse representation of the image. however such fixed transforms usually do not achieve very sparse representations, thereby degrading the reconstruction quality. To remedy this problem, we propose an adaptive block-based transform, which exploits the correlation and similarity of neighboring blocks to achieve sparser transform coefficients. We also propose an adaptive soft-thresholding operator to process the transform coefficients to reduce any potential noise and perturbations that may be produced during the reconstruction process, and also impose sparsity. Experimental results indicate that the proposed method outperforms several prominent existing methods using four different popular image quality assessment metrics.

In this paper, concentrated and Distributed Compressive loading quasi-static tests were conducted on sandwich structures with empty and foam filled honeycomb core. The sandwich structure used in this research was formed by aluminum plate and aluminum 5052 honeycomb structure. Foam used to fill the honeycomb structure was polyurethane foam with a density of 137.13 kg / m3.Concentrated loading quasi-static tests were performed by flat ended penetrator with a diameter of 10 mm and universal machine. Also, Distributed loading quasi-static tests were carried out by universal machine. In Distributed loading, force is applied uniformly to the entire structure surface. Displacement rate was 2 mm/min for both types of loading. The purpose of this paper was to study the filler material effect on energy absorption and destruction shape of sandwich structure, as well as comparison of the two types of loading in unfilled and foam filled honeycomb core sandwich panels. The results of quasi-static tests showed that filler material has positive effects on increasing energy absorption in both concentrated and Distributed loading. Polyurethane foam as filler material of honeycomb structure used in sandwich panel core increases specific absorbed energy of sandwich panel with foam filled core proportional to empty honeycomb core sandwich panel structure in concentrated and Distributed loading by 6% and 29% respectively.