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.

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.

Lossless embedding: A visually meaningful image encryption algorithm based on hyperchaos and compressive sensing

A novel visually meaningful image encryption algorithm is proposed based on a hyperchaotic system and compressive sensing(CS), which aims to improve the visual security of steganographic image and decrypted quality. First, a dynamic spiral block scrambling is designed to encrypt the sparse matrix generated by performing discrete wavelet transform(DWT)on the plain image. Then, the encrypted image is compressed and quantified to obtain the noise-like cipher image. Then the cipher image is embedded into the alpha channel of the carrier image in portable network graphics(PNG) format to generate the visually meaningful steganographic image. In our scheme, the hyperchaotic Lorenz system controlled by the hash value of plain image is utilized to construct the scrambling matrix, the measurement matrix and the embedding matrix to achieve higher security. In addition, compared with other existing encryption algorithms, the proposed PNG-based embedding method can blindly extract the cipher image, thus effectively reducing the transmission cost and storage space. Finally, the experimental results indicate that the proposed encryption algorithm has very high visual security.

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.

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.

Regularization by Multiple Dual Frames for Compressed Sensing Magnetic Resonance Imaging With Convergence Analysis

Plug-and-play priors are popular for solving illposed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-andplay priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual,which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering(BM3D)denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging(CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.

Airborne sparse flight array SAR 3D imaging based on compressed sensing in frequency domain

In airborne array synthetic aperture radar(SAR), the three-dimensional(3D) imaging performance and cross-track resolution depends on the length of the equivalent array. In this paper, Barker sequence criterion is used for sparse flight sampling of airborne array SAR, in order to obtain high cross-track resolution in as few times of flights as possible. Under each flight, the imaging algorithm of back projection(BP) and the data extraction method based on modified uniformly redundant arrays(MURAs) are utilized to obtain complex 3D image pairs. To solve the side-lobe noise in images, the interferometry between each image pair is implemented, and compressed sensing(CS) reconstruction is adopted in the frequency domain. Furthermore, to restore the geometrical relationship between each flight, the phase information corresponding to negative MURA is compensated on each single-pass image reconstructed by CS. Finally,by coherent accumulation of each complex image, the high resolution in cross-track direction is obtained. Simulations and experiments in X-band verify the availability.

Optical image encryption algorithm based on a new four-dimensional memristive hyperchaotic system and compressed sensing

Some existing image encryption schemes use simple low-dimensional chaotic systems, which makes the algorithms insecure and vulnerable to brute force attacks and cracking. Some algorithms have issues such as weak correlation with plaintext images, poor image reconstruction quality, and low efficiency in transmission and storage. To solve these issues,this paper proposes an optical image encryption algorithm based on a new four-dimensional memristive hyperchaotic system(4D MHS) and compressed sensing(CS). Firstly, this paper proposes a new 4D MHS, which has larger key space, richer dynamic behavior, and more complex hyperchaotic characteristics. The introduction of CS can reduce the image size and the transmission burden of hardware devices. The introduction of double random phase encoding(DRPE) enables this algorithm has the ability of parallel data processing and multi-dimensional coding space, and the hyperchaotic characteristics of 4D MHS make up for the nonlinear deficiency of DRPE. Secondly, a construction method of the deterministic chaotic measurement matrix(DCMM) is proposed. Using DCMM can not only save a lot of transmission bandwidth and storage space, but also ensure good quality of reconstructed images. Thirdly, the confusion method and diffusion method proposed are related to plaintext images, which require both four hyperchaotic sequences of 4D MHS and row and column keys based on plaintext images. The generation process of hyperchaotic sequences is closely related to the hash value of plaintext images. Therefore, this algorithm has high sensitivity to plaintext images. The experimental testing and comparative analysis results show that proposed algorithm has good security and effectiveness.

Three-Stages Hyperspectral Image Compression Sensing with Band Selection

Compressed sensing(CS),as an efficient data transmission method,has achieved great success in the field of data transmission such as image,video and text.It can robustly recover signals from fewer Measurements,effectively alleviating the bandwidth pressure during data transmission.However,CS has many shortcomings in the transmission of hyperspectral image(HSI)data.This work aims to consider the application of CS in the transmission of hyperspectral image(HSI)data,and provides a feasible research scheme for CS of HSI data.HSI has rich spectral information and spatial information in bands,which can reflect the physical properties of the target.Most of the hyperspectral image compressed sensing(HSICS)algorithms cannot effectively use the inter-band information of HSI,resulting in poor reconstruction effects.In this paper,A three-stage hyperspectral image compression sensing algorithm(Three-stages HSICS)is proposed to obtain intra-band and inter-band characteristics of HSI,which can improve the reconstruction accuracy of HSI.Here,we establish a multi-objective band selection(Mop-BS)model,amulti-hypothesis prediction(MHP)model and a residual sparse(ReWSR)model for HSI,and use a staged reconstruction method to restore the compressed HSI.The simulation results show that the three-stage HSICS successfully improves the reconstruction accuracy of HSICS,and it performs best among all comparison algorithms.

A High-Quality Adaptive Video Reconstruction Optimization Method Based on Compressed Sensing

The video compression sensing method based onmulti hypothesis has attracted extensive attention in the research of video codec with limited resources.However,the formation of high-quality prediction blocks in the multi hypothesis prediction stage is a challenging task.To resolve this problem,this paper constructs a novel compressed sensing-based high-quality adaptive video reconstruction optimizationmethod.Itmainly includes the optimization of prediction blocks(OPBS),the selection of searchwindows and the use of neighborhood information.Specifically,the OPBS consists of two parts:the selection of blocks and the optimization of prediction blocks.We combine the high-quality optimization reconstruction of foreground block with the residual reconstruction of the background block to improve the overall reconstruction effect of the video sequence.In addition,most of the existing methods based on predictive residual reconstruction ignore the impact of search windows and reference frames on performance.Therefore,Block-level search window(BSW)is constructed to cover the position of the optimal hypothesis block as much as possible.To maximize the availability of reference frames,Nearby reference frame information(NRFI)is designed to reconstruct the current block.The proposed method effectively suppresses the influence of the fluctuation of the prediction block on reconstruction and improves the reconstruction performance.Experimental results showthat the proposed compressed sensing-based high-quality adaptive video reconstruction optimization method significantly improves the reconstruction performance in both objective and supervisor quality.

Research on Asymmetric Fault Location of Wind Farm Collection System Based on Compressed Sensing

Aiming at the problem that most of the cables in the power collection systemof offshore wind farms are buried deep in the seabed,whichmakes it difficult to detect faults,this paper proposes a two-step fault location method based on compressed sensing and ranging equation.The first step is to determine the fault zone through compressed sensing,and improve the datameasurement,dictionary design and algorithmreconstruction:Firstly,the phase-locked loop trigonometric functionmethod is used to suppress the spike phenomenon when extracting the fault voltage,so that the extracted voltage valuewillnot have a large error due to the voltage fluctuation.Secondly,theλ-NIM dictionary is designed by using the node impedancematrix and the fault location coefficient to further reduce the influence of pseudo-fault points.Finally,the CoSaMP algorithmis improved with the generalized Jaccard coefficient to improve the reconstruction accuracy.The second step is to use the ranging equation to accurately locate the asymmetric fault of the wind farm collection system on the basis of determining the fault interval.The simulation results show that the proposedmethod ismore accurate than the compressedsensingmethod andimpedancemethod in fault section location and fault location accuracy,the relative error is reduced from 0.75%to 0.4%,and has a certain anti-noise ability.

Optimized Three-Dimensional Cardiovascular Magnetic Resonance Whole Heart Imaging Utilizing Non-Selective Excitation and Compressed Sensing in Children and Adults with Congenital Heart Disease

Background:In congenital heart disease(CHD)patients,detailed three-dimensional anatomy depiction plays a pivotal role for diagnosis and therapeutical decision making.Hence,the present study investigated the applicability of an advanced cardiovascular magnetic resonance(CMR)whole heart imaging approach utilizing nonselective excitation and compressed sensing for anatomical assessment and interventional guidance of CHD patients in comparison to conventional dynamic CMR angiography.Methods:86 consecutive pediatric patients and adults with congenital heart disease(age,1 to 74 years;mean,35 years)underwent CMR imaging including a freebreathing,ECG-triggered 3D nonselective SSFP whole heart acquisition using compressed SENSE(nsWHcs).Anatomical assessability and signal intensity ratio(SIR)measurements were compared with conventional dynamic 3D-/4D-MR angiography.Results:The most frequent diagnoses were partial anomalous pulmonary venous drainage(17/86,20%),transposition of the great arteries(15/86,17%),tetralogy of Fallot(12/86,14%),and a single ventricle(7/86,8%).Image quality of nsWHcs was rated as excellent/good in 98%of patients.nsWHcs resulted in a reliable depiction of all large thoracic vessels(anatomic assessability,99%–100%)and the proximal segments of coronary arteries and coronary sinus(>90%).nsWHcs achieved a homogenously distributed SIR in all cardiac cavities and thoracic vessels without a significant difference between pulmonary and systemic circulation(10.9±3.5 and 10.6±3.4;p=0.15),while 3D angiography showed significantly increased SIR for targeted vs.non-targeted circulation(PA-angiography,15.2±8.1 vs.5.8±3.6,p<0.001;PV-angiography,7.0±3.9 vs.17.3±6.8,p<0.001).Conclusions:The proposed nsWHcs imaging approach provided a consistently high image quality and a homogeneous signal intensity distribution within the pulmonary and systemic circulation in pediatric patients and adults with a wide spectrum of congenital heart diseases.nsWHcs enabled detailed anatomical assessment and three-dimensional reconstruction of all cardiac cavities and large thoracic vessels and can be regarded particularly useful for preprocedural planning and interventional guidance in CHD patients.

A Noise Reduction Method for Multiple Signals Combining Computed Order Tracking Based on Chirplet Path Pursuit and Distributed Compressed Sensing

With the development of multi-signal monitoring technology,the research on multiple signal analysis and processing has become a hot subject.Mechanical equipment often works under variable working conditions,and the acquired vibration signals are often non-stationary and nonlinear,which are difficult to be processed by traditional analysis methods.In order to solve the noise reduction problem of multiple signals under variable speed,a COT-DCS method combining the Computed Order Tracking(COT)based on Chirplet Path Pursuit(CPP)and Distributed Compressed Sensing(DCS)is proposed.Firstly,the instantaneous frequency(IF)is extracted by CPP,and the speed is obtained by fitting.Then,the speed is used for equal angle sampling of time-domain signals,and angle-domain signals are obtained by COT without a tachometer to eliminate the nonstationarity,and the angledomain signals are compressed and reconstructed by DCS to achieve noise reduction of multiple signals.The accuracy of the CPP method is verified by simulated,experimental signals and compared with some existing IF extraction methods.The COT method also shows good signal stabilization ability through simulation and experiment.Finally,combined with the comparative test of the other two algorithms and four noise reduction effect indicators,the COT-DCS based on the CPP method combines the advantages of the two algorithms and has better noise reduction effect and stability.It is shown that this method is an effective multi-signal noise reduction method.

Reduced Imaging Time and Improved Image Quality of 3D Isotropic T2-Weighted Magnetic Resonance Imaging with Compressed Sensing for the Female Pelvis

This study is to compare three-dimensional(3D)isotropic T2-weighted magnetic resonance imaging(MRI)with compressed sensing-sampling perfection with application optimized contrast(CS-SPACE)and the conventional image(3D-SPACE)sequence in terms of image quality,estimated signal-to-noise ratio(SNR),relative contrast-to-noise ratio(CNR),and the lesions’conspicuous of the female pelvis.Thirty-six females(age:51,28-73)with cervical carcinoma(n=20),rectal carcinoma(n=7),or uterine fibroid(n=9)were included.Patients underwent magnetic resonance(MR)imaging at a 3T scanner with the sequences of 3D-SPACE,CS-SPACE,and twodimensional(2D)T2-weighted turbo-spin echo(TSE).Quantitative analyses of estimated SNR and relative CNR between tumors and other tissues,image quality,and tissue conspicuity were performed.Two radiologists assessed the difference in diagnostic findings for carcinoma.Quantitative values and qualitative scores were analyzed,respectively.The estimated SNR and the relative CNR of tumor-to-muscle obturator internus,tumor-to-myometrium,and myometrium-to-muscle obturator internus was comparable between 3D-SPACE and CS-SPACE.The overall image quality and the conspicuity of the lesion scores of the CS-SPACE were higher than that of the 3D-SPACE(P<0.01).The CS-SPACE sequence offers shorter scan time,fewer artifacts,and comparable SNR and CNR to conventional 3D-SPACE,and has the potential to improve the performance of T2-weighted images.

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.

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.

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.

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.