Chaotic CS Encryption:An Efficient Image Encryption Algorithm Based on Chebyshev Chaotic System and Compressive Sensing

Images are the most important carrier of human information. Moreover, how to safely transmit digital imagesthrough public channels has become an urgent problem. In this paper, we propose a novel image encryptionalgorithm, called chaotic compressive sensing (CS) encryption (CCSE), which can not only improve the efficiencyof image transmission but also introduce the high security of the chaotic system. Specifically, the proposed CCSEcan fully leverage the advantages of the Chebyshev chaotic system and CS, enabling it to withstand various attacks,such as differential attacks, and exhibit robustness. First, we use a sparse trans-form to sparse the plaintext imageand then use theArnold transformto perturb the image pixels. After that,we elaborate aChebyshev Toeplitz chaoticsensing matrix for CCSE. By using this Toeplitz matrix, the perturbed image is compressed and sampled to reducethe transmission bandwidth and the amount of data. Finally, a bilateral diffusion operator and a chaotic encryptionoperator are used to perturb and expand the image pixels to change the pixel position and value of the compressedimage, and ultimately obtain an encrypted image. Experimental results show that our method can be resistant tovarious attacks, such as the statistical attack and noise attack, and can outperform its current competitors.

Enhancing visual security: An image encryption scheme based on parallel compressive sensing and edge detection embedding

A novel image encryption scheme based on parallel compressive sensing and edge detection embedding technology is proposed to improve visual security. Firstly, the plain image is sparsely represented using the discrete wavelet transform.Then, the coefficient matrix is scrambled and compressed to obtain a size-reduced image using the Fisher–Yates shuffle and parallel compressive sensing. Subsequently, to increase the security of the proposed algorithm, the compressed image is re-encrypted through permutation and diffusion to obtain a noise-like secret image. Finally, an adaptive embedding method based on edge detection for different carrier images is proposed to generate a visually meaningful cipher image. To improve the plaintext sensitivity of the algorithm, the counter mode is combined with the hash function to generate keys for chaotic systems. Additionally, an effective permutation method is designed to scramble the pixels of the compressed image in the re-encryption stage. The simulation results and analyses demonstrate that the proposed algorithm performs well in terms of visual security and decryption quality.

Digital broadcast channel estimation with compressive sensing

In order to reduce the pilot number and improve spectral efficiency, recently emerged compressive sensing （CS） is applied to the digital broadcast channel estimation. According to the six channel profiles of the European Telecommunication Standards Institute（ETSI） digital radio mondiale （DRM） standard, the subspace pursuit （SP） algorithm is employed for delay spread and attenuation estimation of each path in the case where the channel profile is identified and the multipath number is known. The stop condition for SP is that the sparsity of the estimation equals the multipath number. For the case where the multipath number is unknown, the orthogonal matching pursuit （OMP） algorithm is employed for channel estimation, while the stop condition is that the estimation achieves the noise variance. Simulation results show that with the same number of pilots, CS algorithms outperform the traditional cubic-spline-interpolation-based least squares （LS） channel estimation. SP is also demonstrated to be better than OMP when the multipath number is known as a priori.

Combination of multi-focus Raman spectroscopy and compressive sensing for parallel monitoring of single-cell dynamics

To overcome the low efficiency of conventional confocal Raman spectroscopy,many efforts have been devoted to parallelizing the Raman excitation and acquisition,in which the scattering from multiple foci is projected onto different locations on a spectrometer's CCD,along either its vertical,horizontal dimension,or even both.While the latter projection scheme relieves the limitation on the row numbers of the CCD,the spectra of multiple foci are recorded in one spectral channel,resulting in spectral overlapping.Here,we developed a method under a com-pressive sensing framework to demultiplex the superimposed spectra of multiple cells during their dynamic processes.Unlike the previous methods which ignore the information connection be-tween the spectra of the cells recorded at different time,the proposed method utilizes a prior that a cell's spectra acquired at different time have the same sparsity structure in their principal components.Rather than independently demultiplexing the mixed spectra at the individual time intervals,the method demultiplexes the whole spectral sequence acquired continuously during the dynamic process.By penalizing the sparsity combined from all time intervals,the collaborative optimization of the inversion problem gave more accurate recovery results.The performances of the method were substantiated by a 1D Raman tweezers array,which monitored the germination of multiple bacterial spores.The method can be extended to the monitoring of many living cells randomly scattering on a coverslip,and has a potential to improve the throughput by a few orders.

Face hallucination via compressive sensing

Face hallucination or super-resolution is an inverse problem which is underdetermined,and the compressive sensing(CS)theory provides an effective way of seeking inverse problem solutions.In this paper,a novel compressive sensing based face hallucination method is presented,which is comprised of three steps:dictionary learning、sparse coding and solving maximum a posteriori(MAP)formulation.In the first step,the K-SVD dictionary learning algorithm is adopted to obtain a dictionary which can sparsely represent high resolution(HR)face image patches.In the second step,we seek the sparsest representation for each low-resolution(LR)face image paches input using the learned dictionary,super resolution image blocks are obtained from the sparsest coefficients and dictionaries,which then are assembled into super-resolution(SR)image.Finally,MAP formulation is introduced to satisfy the consistency restrictive condition and obtain the higher quality HR images.The experimental results demonstrate that our approach can achieve better super-resolution faces compared with other state-of-the-art method.

Color Image Compression and Encryption Algorithm Based on 2D Compressed Sensing and Hyperchaotic System

With the advent of the information security era,it is necessary to guarantee the privacy,accuracy,and dependable transfer of pictures.This study presents a new approach to the encryption and compression of color images.It is predicated on 2D compressed sensing(CS)and the hyperchaotic system.First,an optimized Arnold scrambling algorithm is applied to the initial color images to ensure strong security.Then,the processed images are con-currently encrypted and compressed using 2D CS.Among them,chaotic sequences replace traditional random measurement matrices to increase the system’s security.Third,the processed images are re-encrypted using a combination of permutation and diffusion algorithms.In addition,the 2D projected gradient with an embedding decryption(2DPG-ED)algorithm is used to reconstruct images.Compared with the traditional reconstruction algorithm,the 2DPG-ED algorithm can improve security and reduce computational complexity.Furthermore,it has better robustness.The experimental outcome and the performance analysis indicate that this algorithm can withstand malicious attacks and prove the method is effective.

Fast compressed sensing spectral measurement with adaptive gradient multiscale resolution

We propose a fast,adaptive multiscale resolution spectral measurement method based on compressed sensing.The method can apply variable measurement resolution over the entire spectral range to reduce the measurement time by over 75%compared to a global high-resolution measurement.Mimicking the characteristics of the human retina system,the resolution distribution follows the principle of gradually decreasing.The system allows the spectral peaks of interest to be captured dynamically or to be specified a priori by a user.The system was tested by measuring single and dual spectral peaks,and the results of spectral peaks are consistent with those of global high-resolution measurements.

A Novel UWB Signal Sampling Method for Localization based on Compressive Sensing

Ultra-wide-band (UWB) signals are suitable for localization, since their high time resolution can provide precise time of arrival (TOA) estimation. However, one major challenge in UWB signal processing is the requirement of high sampling rate which leads to complicated signal processing and expensive hardware. In this paper, we present a novel UWB signal sampling method called UWB signal sampling via temporal sparsity (USSTS). Its sampling rate is much lower than Nyquist rate. Moreover, it is implemented in one step and no extra processing unit is needed. Simulation results show that USSTS can not recover the signal precisely, but for the use in localization, the accuracy of TOA estimation is the same as that in traditional methods. Therefore, USSTS gives a novel and effective solution for the use of UWB signals in localization.

Near-source noise suppression of AMT by compressive sensing and mathematical morphology filtering

In deep mineral exploration, the acquisition of audio magnetotelluric （AMT） data is severely affected by ambient noise near the observation sites; This near-field noise restricts investigation depths. Mathematical morphological filtering （MMF） proved effective in suppressing large-scale strong and variably shaped noise, typically low-frequency noise, but can not deal with pulse noise of AMT data. We combine compressive sensing and MMF. First we use MMF to suppress the large-scale strong ambient noise; second, we use the improved orthogonal match pursuit （IOMP） algorithm to remove the residual pulse noise. To remove the noise and protect the useful AMT signal, a redundant dictionary that matches with spikes and is insensitive to the useful signal is designed. Synthetic and field data from the Luzong field suggest that the proposed method suppresses the near-source noise and preserves the signal well; thus, better results are obtained that improve the output of either MMF or IOMP.

Joint 2D DOA and Doppler frequency estimation for L-shaped array using compressive sensing

A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix,three smaller scale matrices with independent azimuth,elevation and Doppler frequency are introduced adopting a separable observation model.Afterwards,the estimation is achieved by L1-norm minimization and the Bayesian CS algorithm.In addition,under the L-shaped array topology,the azimuth and elevation are separated yet coupled to the same radial Doppler frequency.Hence,the pair matching problem is solved with the aid of the radial Doppler frequency.Finally,numerical simulations corroborate the feasibility and validity of the proposed algorithm.

Compressive sensing based multiuser detector for massive MBM MIMO uplink

Media based modulation(MBM)is expected to be a prominent modulation scheme,which has access to the high data rate by using radio frequency(RF)mirrors and fewer transmit antennas.Associated with multiuser multiple input multiple output(MIMO),the MBM scheme achieves better performance than other conventional multiuser MIMO schemes.In this paper,the massive MIMO uplink is considered and a conjunctive MBM transmission scheme for each user is employed.This conjunctive MBM transmission scheme gathers aggregate MBM signals in multiple continuous time slots,which exploits the structured sparsity of these aggregate MBM signals.Under this kind of scenario,a multiuser detector with low complexity based on the compressive sensing(CS)theory to gain better detection performance is proposed.This detector is developed from the greedy sparse recovery technique compressive sampling matching pursuit(CoSaMP)and exploits not only the inherently distributed sparsity of MBM signals but also the structured sparsity of multiple aggregate MBM signals.By exploiting these sparsity,the proposed CoSaMP based multiuser detector achieves reliable detection with low complexity.Simulation results demonstrate that the proposed CoSaMP based multiuser detector achieves better detection performance compared with the conventional methods.

Compressive Sensing Algorithms for Signal Processing Applications: A Survey

In digital signal processing (DSP), Nyquistrate sampling completely describes a signal by exploiting its bandlimitedness. Compressed Sensing (CS), also known as compressive sampling, is a DSP technique efficiently acquiring and reconstructing a signal completely from reduced number of measurements, by exploiting its compressibility. The measurements are not point samples but more general linear functions of the signal. CS can capture and represent sparse signals at a rate significantly lower than ordinarily used in the Shannon’s sampling theorem. It is interesting to notice that most signals in reality are sparse;especially when they are represented in some domain (such as the wavelet domain) where many coefficients are close to or equal to zero. A signal is called K-sparse, if it can be exactly represented by a basis, , and a set of coefficients , where only K coefficients are nonzero. A signal is called approximately K-sparse, if it can be represented up to a certain accuracy using K non-zero coefficients. As an example, a K-sparse signal is the class of signals that are the sum of K sinusoids chosen from the N harmonics of the observed time interval. Taking the DFT of any such signal would render only K non-zero values . An example of approximately sparse signals is when the coefficients , sorted by magnitude, decrease following a power law. In this case the sparse approximation constructed by choosing the K largest coefficients is guaranteed to have an approximation error that decreases with the same power law as the coefficients. The main limitation of CS-based systems is that they are employing iterative algorithms to recover the signal. The sealgorithms are slow and the hardware solution has become crucial for higher performance and speed. This technique enables fewer data samples than traditionally required when capturing a signal with relatively high bandwidth, but a low information rate. As a main feature of CS, efficient algorithms such as -minimization can be used for recovery. This paper gives a survey of both theoretical and numerical aspects of compressive sensing technique and its applications. The theory of CS has many potential applications in signal processing, wireless communication, cognitive radio and medical imaging.

Correspondence normalized ghost imaging on compressive sensing

Ghost imaging （GI） offers great potential with respect to conventional imaging techniques. It is an open problem in GI systems that a long acquisition time is be required for reconstructing images with good visibility and signal-to-noise ratios （SNRs）. In this paper, we propose a new scheme to get good performance with a shorter construction time. We call it correspondence normalized ghost imaging based on compressive sensing （CCNGI）. In the scheme, we enhance the signal-to-noise performance by normalizing the reference beam intensity to eliminate the noise caused by laser power fluctuations, and reduce the reconstruction time by using both compressive sensing （CS） and time-correspondence imaging （CI） techniques. It is shown that the qualities of the images have been improved and the reconstruction time has been reduced using CCNGI scheme. For the two-grayscale ＂double-slit＂ image, the mean square error （MSE） by GI and the normalized GI （NGI） schemes with the measurement number of 5000 are 0.237 and 0.164, respectively, and that is 0.021 by CCNGI scheme with 2500 measurements. For the eight-grayscale ＂lena＂ object, the peak signal-to-noise rates （PSNRs） are 10.506 and 13.098, respectively using G1 and NGI schemes while the value turns to 16.198 using CCNGI scheme. The results also show that a high-fidelity GI reconstruction has been achieved using only 44% of the number of measurements corresponding to the Nyquist limit for the two-grayscale ＂double-slit＂ object. The qualities of the reconstructed images using CCNGI are almost the same as those from GI via sparsity constraints （GISC） with a shorter reconstruction time.

AN IMPROVED SPARSITY ADAPTIVE MATCHING PURSUIT ALGORITHM FOR COMPRESSIVE SENSING BASED ON REGULARIZED BACKTRACKING

Sparsity Adaptive Matching Pursuit (SAMP) algorithm is a widely used reconstruction algorithm for compressive sensing in the case that the sparsity is unknown. In order to match the sparsity more accurately, we presented an improved SAMP algorithm based on Regularized Backtracking (SAMP-RB). By adapting a regularized backtracking step to SAMP algorithm in each iteration stage, the proposed algorithm can flexibly remove the inappropriate atoms. The experimental results show that SAMP-RB reconstruction algorithm greatly improves SAMP algorithm both in reconstruction quality and computational time. It has better reconstruction efficiency than most of the available matching pursuit algorithms.

Robust signal recovery algorithm for structured perturbation compressive sensing

It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.

Angle estimation for bistatic MIMO radar with unknown mutual coupling based on three-way compressive sensing

The problem of angle estimation for bistatic multiple-input multiple-output radar in the present of unknown mutual coupling (MC) is investigated, and a three-way compressive sensing (TWCS) estimation algorithm is developed. To exploit the inherent multi-dimensional structure of received data, a trilinear tensor model is firstly formulated. Then the de-coupling operation is followed. Thereafter, the high-order singular value decomposition is applied to compress the high dimensional tensor to a much smaller one. The estimation of the compressed direction matrices are linked to the compressed trilinear model, and finally two over-complete dictionaries are constructed for angle estimation. Also, Cramer-Rao bounds for angle and MC estimation are derived. The proposed TWCS algorithm is effective from the perspective of estimation accuracy as well as the computational complexity, and it can achieve automatically paired angle estimation. Simulation results show that the proposed method has much better estimation accuracy than the existing algorithms in the low signal-to-noise ratio scenario, and its estimation performance is very close to the parallel factor analysis (PARAFAC) algorithm at the high SNR regions. © 2017 Beijing Institute of Aerospace Information.

The Identification of Frequency Hopping Signal Using Compressive Sensing

Compressive sensing (CS) creates a new framework of signal reconstruction or approximation from a smaller set of incoherent projection compared with the traditional Nyquist-rate sampling theory. Recently, it has been shown that CS can solve some signal processing problems given incoherent measurements without ever reconstructing the signals. Moreover, the number of measurements necessary for most compressive signal processing application such as detection, estimation and classification is lower than that necessary for signal reconstruction. Based on CS, this paper presents a novel identification algorithm of frequency hopping (FH) signals. Given the hop interval, the FH signals can be identified and the hopping frequencies can be estimated with a tiny number of measurements. Simulation results demonstrate that the method is effective and efficient.

Video Coding Based on Compressive Sensing via CoSaMP

Compressive sampling matching pursuit （CoSaMP） algorithm integrates the idea of combining algorithm to ensure running speed and provides rigorous error bounds which provide a good theoretical guarantee to convergence. And compressive sensing （CS） can help us ease the pressure of hardware facility from the requirements of the huge amount in information processing. Therefore, a new video coding framework was proposed, which was based on CS and curvelet transform in this paper. Firstly, this new framework uses curvelet transform and CS to the key frame of test sequence, and then gains recovery frame via CoSaMP to achieve data compress. In the classic CoSaMP method, the halting criterion is that the number of iterations is fixed. Therefore, a new stopping rule is discussed to halting the algorithm in this paper to obtain better performance. According to a large number of experimental results, we ran see that this new framework has better performance and lower RMSE. Through the analysis of the experimental data, it is found that the selection of number of measurements and sparsity level has great influence on the new framework. So how to select the optimal parameters to gain better performance deserves worthy of further study.

Deformation and failure characteristics of sandstone under uniaxial compression using distributed fiber optic strain sensing

This paper investigates the deformation and fracture propagation of sandstone specimen under uniaxial compression using the distributed fiber optic strain sensing(DFOSS)technology.It shows that the DFOSS-based circumferential strains are in agreement with the data monitored with the traditional strain gage.The DFOSS successfully scans the full-field view of axial and circumferential strains on the specimen surface.The spatiotemporal strain measurement based on DFOSS manifests crack closure and elastoplastic deformation,detects initialization of microcrack nucleation,and identifies strain localization within the specimen.The DFOSS well observes the effects of rock heterogeneity on rock deformation.The advantage of DFOSS-based strain acquisition includes the high spatiotemporal resolution of signals and the ability of full-surface strain scanning.The introduction to the DFOSS technology yields a better understanding of the rock damage process under uniaxial compression.

Compressive Sensing Based Wireless Localization in Indoor Scenarios

The sparse nature of location finding in the spatial domain makes it possible to exploit the Compressive Sensing (CS) theory for wireless location.CS-based location algorithm can largely reduce the number of online measurements while achieving a high level of localization accuracy,which makes the CS-based solution very attractive for indoor positioning.However,CS theory offers exact deterministic recovery of the sparse or compressible signals under two basic restriction conditions of sparsity and incoherence.In order to achieve a good recovery performance of sparse signals,CS-based solution needs to construct an efficient CS model.The model must satisfy the practical application requirements as well as following theoretical restrictions.In this paper,we propose two novel CS-based location solutions based on two different points of view:the CS-based algorithm with raising-dimension pre-processing and the CS-based algorithm with Minor Component Analysis (MCA).Analytical studies and simulations indicate that the proposed novel schemes achieve much higher localization accuracy.