Light field data, which is composed of multi-view images, have various 3D applications. However, the cost of acquiring many images from slightly different viewpoints sometimes makes the use of light fields impractical. Here, compressive sensing is a new way to obtain the entire light field data from only a few camera shots instead of taking all the images individually. In paticular, the coded aperture/mask technique enables us to capture light field data in a compressive way through a single camera. A pixel value recorded by such a camera is a sum of the light rays that pass though different positions on the coded aperture/mask. The target light field can be reconstructed from the recorded pixel values by using prior information on the light field signal. As prior information, the current state of the art uses a dictionary (light field atoms) learned from training datasets. Meanwhile, it was reported that general bases such as those of the discrete cosine transform (DCT) are not suitable for efficiently representing prior information. In this study, however, we demonstrate that a 4D-DCT basis works surprisingly well when it is combined with a weighting scheme that considers the amplitude differences between DCT coefficients. Simulations using 18 light field datasets show the superiority of the weighted 4D-DCT basis to the learned dictionary. Furthermore, we analyzed a disparity-dependent property of the reconstructed data that is unique to light fields.

Object tracking is one of the fundamental problems in computer vision. However, there is still a need to improve the overall capability in various tracking circumstances. In this letter, a patches-collaborative compressive tracking (PCCT) algorithm is presented. Experiments on various challenging benchmark sequences demonstrate that the proposed algorithm performs favorably against several state-of-the-art algorithms.

Because the perceptual compressive sensing framework can achieve a much better performance than the legacy compressive sensing framework, it is very promising for the compressive sensing based image compression system. In this paper, we propose an innovative adaptive perceptual block compressive sensing scheme. Firstly, a new block-based statistical metric which can more appropriately measure each block's sparsity and perceptual sensibility is devised. Then, the approximated theoretical minimum measurement number for each block is derived from the new block-based metric and used as weight for adaptive measurements allocation. The obtained experimental results show that our scheme can significantly enhance both objective and subjective performance of a perceptual compressive sensing framework.

We propose an effective technique for estimation of targets by ground penetrating radar (GPR) using model-based compressive sensing (CS). We demonstrate the technique's performance by applying it to detection of buried landmines. The conventional CS algorithm enables the reconstruction of sparse subsurface images using much reduced measurement by exploiting its sparsity. However, for landmine detection purposes, CS faces some challenges because the landmine is not exactly a point target and also faces high level clutter from the propagation in the medium. By exploiting the physical characteristics of the landmine using model-based CS, the probability of landmine detection can be increased. Using a small pixel size, the landmine reflection in the image is represented by several pixels grouped in a three dimensional plane. This block structure can be used in the model based CS processing for imaging the buried landmine. The evaluation using laboratory data and datasets obtained from an actual mine field in Cambodia shows that the model-based CS gives better reconstruction of landmine images than conventional CS.

Spatial compressive sensing (SCS) has recently been applied to direction-of-arrival (DOA) estimation, owing to its advantages over conventional versions. However the performance of compressive sensing (CS)-based estimation methods degrades when the true DOAs are not exactly on the discretized sampling grid. We solve the off-grid DOA estimation problem using the deterministic maximum likelihood (DML) estimation method. In this letter, on the basis of the convexity of the DML function, we propose a computationally efficient algorithm framework for off-grid DOA estimation. Numerical experiments demonstrate the superior performance of the proposed methods in terms of accuracy, robustness and speed.

Crowd collectiveness, i.e., a quantitative metric for collective motion, has received increasing attention in recent years. Most of existing methods build a collective network by assuming each agent in the crowd interacts with neighbors within fixed radius r region or fixed k nearest neighbors. However, they usually use a universal r or k for different crowded scenes, which may yield inaccurate network topology and lead to lack of adaptivity to varying collective motion scenarios, thereby resulting in poor performance. To overcome these limitations, we propose a compressive sensing (CS) based method for measuring crowd collectiveness. The proposed method uncovers the connections among agents from the motion time series by solving a CS problem, which needs not specify an r or k as a priori. A descriptor based on the average velocity correlations of connected agents is then constructed to compute the collectiveness value. Experimental results demonstrate that the proposed method is effective in measuring crowd collectiveness, and performs on par with or better than the state-of-the-art methods.

Due to the fact that natural images are approximately sparse in Discrete Cosine Transform (DCT) or wavelet basis, the Compressive Sensing (CS) can be employed to decode both the host image and watermark with zero error, despite not knowing the host image. In this paper, Limited-Random Sequence (LRS) matrix is utilized to implement the blind CS detection, which benefits from zero error and lower complexity. The performance in Bit Error Rate (BER) and error-free detection probability confirms the validity and efficiency of the proposed scheme.

Compressive sensing (CS)-based channel estimation considerably reduces pilot symbols usage by exploiting the sparsity of the propagation channel in the delay-Doppler domain. In this paper, we consider the application of Bayesian approaches to the sparse channel estimation in orthogonal frequency division multiplexing (OFDM) systems. Taking advantage of the block-sparse structure and statistical properties of time-frequency selective channels, the proposed Bayesian method provides a more efficient and accurate estimation of the channel status information (CSI) than do conventional CS-based methods. Moreover, our estimation scheme is not limited to the Gaussian scenario but is also available for channels that have non-Gaussian priors or unknown probability density functions. This characteristic is notably useful when the prior statistics of channel coefficients cannot be precisely estimated. We also design a combo pilot pattern to improve the performance of the proposed estimation scheme. Simulation results demonstrate that our method performs well at high Doppler frequencies.

Tonal signals are shown as spectral peaks in the frequency domain. When the number of spectral peaks is small and the spectral signal is sparse, Compressive Sensing (CS) can be adopted to locate the peaks with a low-cost sensing system. In the CS scheme, a time domain signal is modelled as $oldsymbol{y}=Phi F^{-1}oldsymbol{s}$, where y and s are signal vectors in the time and frequency domains. In addition, F-1 and $Phi$ are an inverse DFT matrix and a random-sampling matrix, respectively. For a given y and $Phi$, the CS method attempts to estimate s with l0 or l1 optimization. To generate the peak candidates, we adopt the frequency-domain information of $ esmile{oldsymbol{s}}$ = $oldsymbol{F} esmile{oldsymbol{y}}$, where $ esmile{y}$ is the extended version of y and $ esmile{oldsymbol{y}}left(oldsymbol{n} ight)$ is zero when n is not elements of CS time instances. In this paper, we develop Gaussian statistics of $ esmile{oldsymbol{s}}$. That is, the variance and the mean values of $ esmile{oldsymbol{s}}left(oldsymbol{k} ight)$ are examined.

Compressive sensing (CS) exploits the sparsity or compressibility of signals to recover themselves from a small set of nonadaptive, linear measurements. The number of measurements is much smaller than Nyquist-rate, thus signal recovery is achieved at relatively expense. Thus, many signal processing problems which do not require exact signal recovery have attracted considerable attention recently. In this paper, we establish a framework for parameter estimation of a signal corrupted by additive colored Gaussian noise (ACGN) based on compressive measurements. We also derive the Cramer-Rao lower bound (CRB) for the frequency estimation problems in compressive domain and prove some useful properties of the CRB under different compressive measurements. Finally, we show that the theoretical conclusions are along with experimental results.

A narrowband interference (NBI) estimation and mitigation method based on compressive sensing (CS) for communication systems with repeated training sequences is investigated in this letter. The proposed CS-based differential measuring method is performed through the differential operation on the inter-block-interference-free regions of the received adjacent training sequences. The sparse NBI signal can be accurately recovered from a time-domain measurement vector of small size under the CS framework, without requiring channel information or dedicated resources. Theoretical analysis and simulation results show that the proposed method is robust to NBI under multi-path fading channels.

We propose a variant of OMP algorithm named BROMP for sparse solution. In our algorithm, the update rule of MP algorithm is employed to reduce the number of least square calculations and the refining strategy is introduced to further improve its performance. Simulations show that the proposed algorithm performs better than the OMP algorithm with significantly lower complexity.

By exploiting the inherent sparsity of wireless propagation channels, the theory of compressive sensing (CS) provides us with novel technologies to estimate the channel state information (CSI) that require considerably fewer samples than traditional pilot-aided estimation methods. In this paper, we describe the block-sparse structure of the fast time-varying channel and apply the model-based CS (MCS) for channel estimation in orthogonal frequency division multiplexing (OFDM) systems. By exploiting the structured sparsity, the proposed MCS-based method can further compress the channel information, thereby allowing a more efficient and precise estimation of the CSI compared with conventional CS-based approaches. Furthermore, a specific pilot arrangement is tailored for the proposed estimation scheme. This so-called random grouped pilot pattern can not only effectively protect the measurements from the inter-carrier interference (ICI) caused by Doppler spreading but can also enable the measurement matrix to meet the conditions required for MCS with relatively high probability. Simulation results demonstrate that our method has good performance at high Doppler frequencies.

This paper describes a new method for lossy audio signal compression via compressive sensing (CS). In this method, a structured shrinkage operator is employed to decompose the audio signal into three layers, with two sparse layers, tonal and transient, and additive noise, and then, both the tonal and transient layers are compressed using CS. Since the shrinkage operator is able to take into account the structure information of the coefficients in the transform domain, it is able to achieve a better sparse approximation of the audio signal than traditional methods do. In addition, we propose a sparsity allocation algorithm, which adjusts the sparsity between the two layers, thus improving the performance of CS. Experimental results demonstrated that the new method provided a better compression performance than conventional methods did.

Compressive sensing is a promising technique in data acquisition field. A central problem in compressive sensing is that for a given sparse signal, we wish to recover it accurately, efficiently and stably from very few measurements. Inspired by mathematical analysis, we introduce a combining scheme between stability and robustness in reconstruction problems using compressive sensing. By choosing appropriate parameters, we are able to construct a condition for reconstruction map to perform properly.

In this paper, we propose a new method for wideband spectrum sensing using compressed measurements of the received wideband signal; we can directly separate information of the sub-channels and perform detection in each. Wideband spectrum sensing empowers us to rapidly access the vacant sub-channels in high utilization regime. Regarding the fact that at each time instant some sub-channels are vacant, the received signal is sparse in some bases. Then we could apply the Compressive Sensing (CS) algorithms and take the compressed measurements. On the other hand, the primary user signals in different sub-channels could have different modulation types; therefore, the signal in each sub-channel is chosen among a signal space. Knowing these signal spaces, the secondary user could separate information of different sub-channels employing the compressed measurements. We perform filtering and detection based on these compressed measurements; this decreases the computational complexity of the wideband spectrum sensing. In addition, we model the received wideband signal as a vector which has a block-sparse representation on a basis consisting of all sub-channel bases whose elements occur in clusters. Based on this feature of the received signal, we propose another wideband spectrum sensing method with lower computational complexity. In order to evaluate the performance of the proposed method, we employ the Monte-Carlo simulation. According to simulations if the compression rate is selected appropriately according to the CS theorems and the problem model, the detection performance of our method leads to the performance of the ideal filter bank-based method, which uses the ideal and impractical narrow band filters.

Numerous examples in image processing have demonstrated that human visual perception can be exploited to improve processing performance. This paper presents another showcase in which some visual information is employed to guide adaptive block-wise compressive sensing (ABCS) for image data, i.e., a varying CS-sampling rate is applied on different blocks according to the visual contents in each block. To this end, we propose a visual analysis based on the discrete cosine transform (DCT) coefficients of each block reconstructed at the decoder side. The analysis result is sent back to the CS encoder, stage-by-stage via a feedback channel, so that we can decide which blocks should be further CS-sampled and what is the extra sampling rate. In this way, we can perform multiple passes of reconstruction to improve the quality progressively. Simulation results show that our scheme leads to a significant improvement over the existing ones with a fixed sampling rate.

Compressive sensing (CS) shows that a sparse or compressible signal can be exactly recovered from its linear measurements at a rate significantly lower than the Nyquist rate. As an extreme case, 1-bit compressive sensing (1-bit CS) states that an original sparse signal can be recovered from the 1-bit measurements. In this paper, we intrduce a Fast and Accurate Two-Stage (FATS) algorithm for 1-bit compressive sensing. Simulations show that FATS not only significantly increases the signal reconstruction speed but also improves the reconstruction accuracy.

Limited Random Sequence (LRS) is quite important for Analog-to-Information Converter (AIC) because it determines the random sampling scheme and the resultant performance. LRS is established with the elements of “0” and “1”. The “1” appears randomly in the segment of the sequence, so that the production of the original signal and LRS can be considered as the approximation of the random sampling of the original signal. The random sampling result can perfectly recover the signal with Compressive Sensing (CS) algorithm. In this paper, a high order LRS is proposed for the AIC design in Distributed Compressive Sensing (DCS), which has the following three typical features: 1) The high order LRS has the elements of integer which can indicate the index number of the sensor in DCS. 2) High order LRS can adapt to the sparsity variation of the original signal detected by each sensor. 3) Employing the AIC with high order LRS, the DCS algorithm can recover the signal with very low sampling rate, usually above 2 orders less than the traditional distributed sensors. In the paper, the scheme and the construction algorithm of high order LRS are proposed. The performance is evaluated with the application studies of the distributed sensor network and the camera picture correspondingly.

of late, many researchers have been interested in sparse representation of signals and its applications such as Compressive Sensing in Cognitive Radio (CR) networks as a way of overcoming the issue of limited bandwidth. Compressive sensing based wideband spectrum sensing is a novel approach in cognitive radio systems. Also in these systems, using spatial-frequency opportunistic reuse is emerged interestingly by constructing and deploying spatial-frequency Power Spectral Density (PSD) maps. Since the CR sensors are distributed in the region of support, the sensed PSD by each sensor should be transmitted to a master node (base-station) in order to construct the PSD maps in space and frequency domains. When the number of sensors is large, this data transmission which is required for construction of PSD map can be challenging. In this paper, in order to transmit the CR sensors' data to the master node, the compressive sensing based scheme is used. Therefore, the measurements are sampled in a lower sampling rate than of the Nyquist rate. By using the proposed method, an acceptable PSD map for cognitive radio purposes can be achieved by only 30% of full data transmission. Also, simulation results show the robustness of the proposed method against the channel variations in comparison with classical methods. Different solution schemes such as Basis Pursuit, Lasso, Lars and Orthogonal Matching Pursuit are used and the quality performance of them is evaluated by several simulation results over a Rician channel with respect to several different compression and Signal to Noise Ratios. It is also illustrated that the performance of Basis Pursuit and Lasso methods outperform the other compression methods particularly in higher compression rates.