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.

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.

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.

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.

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.

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.

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.

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.

Primary Research of EIT Inverse Problem Based on CS （Compressed Sensing） Technique

EIT （electrical impedance tomography） problem should be represented by a group of partial differential equation, in numerical calculation： the nonlinear problem should be linearization approximately, and then linear equations set is obtained, so EIT image reconstruct problem should be considered as a classical ill-posed, ill-conditioned, linear inverse problem. Its biggest problem is the number of unknown is much more than the number of the equations, this result in the low imaging quality. Especially, it can not imaging in center area. For this problem, we induce the CS technique into EIT image reconstruction algorithm. The main contributions in this paper are： firstly, built up the relationship between CS and EIT definitely; secondly, sparse reconstruction is a critical step in CS, built up a general sparse regularization model based on EIT; finally, gives out some EIT imaging models based on sparse regularization method. For different scenarios, compared with traditional Tikhonov regularization （smooth regularization） method, sparse reconstruction method is not only better at anti-noise, and imaging in center area, but also faster and better resolution.

Compressed sensing estimation of sparse underwater acoustic channels with a large time delay spread

The estimation of sparse underwater acoustic channels with a large time delay spread is investigated under the framework of compressed sensing. For these types of channels, the excessively long impulse response will significantly degrade the convergence rate and tracking capability of the traditional estimation algorithms such as least squares （LS）, while excluding the use of the delay-Doppler spread function due to huge computational complexity. By constructing a Toeplitz matrix with a training sequence as the measurement matrix, the estimation problem of long sparse acoustic channels is formulated into a compressed sensing problem to facilitate the efficient exploitation of sparsity. Furthermore, unlike the traditional l1 norm or exponent-based approximation l0 norm sparse recovery strategy, a novel variant of approximate l0 norm called AL0 is proposed, minimization of which leads to the derivation of a hybrid approach by iteratively projecting the steepest descent solution to the feasible set. Numerical simulations as well as sea trial experiments are compared and analyzed to demonstrate the superior performance of the proposed algorithm.

基于Compressed Sensing框架的图像多描述编码方法

基于新兴的压缩感知(Compressed Sensing,CS)理论,提出了一种抗丢包能力强且结构简单易实现的多描述编码方法.首先对变换后的图像进行交织抽取分块,再对各子块进行随机观测、量化、打包形成多个描述子码流.解码端根据接收码流情况通过求解优化问题重建原图像.由于随机观测过程简单易实现,故该方法可以以较低的计算复杂度构造出较多的描述子.实验结果表明,在同样的丢包率下,本文方法的重构质量(PSNR)明显优于SPIHT多描述编码方法,且计算复杂度较低.

Imaging algorithm of multi-ship motion target based on compressed sensing

An imaging algorithm based on compressed sensing（CS） for the multi-ship motion target is presented. In order to reduce the quantity of data transmission in searching the ships on a large sea area, both range and azimuth of the moving ship targets are converted into sparse representation under certain signal basis. The signal reconstruction algorithm based on CS at a distant calculation station, and the Keystone and fractional Fourier transform（FRFT） algorithm are used to compensate range migration and obtain Doppler frequency. When the sea ships satisfy the sparsity, the algorithm can obtain higher resolution in both range and azimuth than the conventional imaging algorithm. Some simulations are performed to verify the reliability and stability.

Reconstruction and transmission of astronomical image based on compressed sensing

In the process of image transmission, the famous JPEG and JPEG-2000 compression methods need more transmission time as it is difficult for them to compress the image with a low compression rate. Recently the compressed sensing（CS） theory was proposed, which has earned great concern as it can compress an image with a low compression rate, meanwhile the original image can be perfectly reconstructed from only a few compressed data. The CS theory is used to transmit the high resolution astronomical image and build the simulation environment where there is communication between the satellite and the Earth. Number experimental results show that the CS theory can effectively reduce the image transmission and reconstruction time. Even with a very low compression rate, it still can recover a higher quality astronomical image than JPEG and JPEG-2000 compression methods.

Comparison of MRI Under-Sampling Techniques for Compressed Sensing with Translation Invariant Wavelets Using FastTestCS: A Flexible Simulation Tool

A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.

Off-Grid Compressed Channel Estimation with Parallel Interference Cancellation for Millimeter Wave Massive MIMO

Millimeter wave(mmWave)massive multiple-input multiple-output(MIMO)plays an important role in the fifth-generation(5G)mobile communications and beyond wireless communication systems owing to its potential of high capacity.However,channel estimation has become very challenging due to the use of massive MIMO antenna array.Fortunately,the mmWave channel has strong sparsity in the spatial angle domain,and the compressed sensing technology can be used to convert the original channel matrix into the sparse matrix of discrete angle grid.Thus the high-dimensional channel matrix estimation is transformed into a sparse recovery problem with greatly reduced computational complexity.However,the path angle in the actual scene appears randomly and is unlikely to be completely located on the quantization angle grid,thus leading to the problem of power leakage.Moreover,multiple paths with the random distribution of angles will bring about serious interpath interference and further deteriorate the performance of channel estimation.To address these off-grid issues,we propose a parallel interference cancellation assisted multi-grid matching pursuit(PIC-MGMP)algorithm in this paper.The proposed algorithm consists of three stages,including coarse estimation,refined estimation,and inter-path cyclic iterative inter-ference cancellation.More specifically,the angular resolution can be improved by locally refining the grid to reduce power leakage,while the inter-path interference is eliminated by parallel interference cancellation(PIC),and the two together improve the estimation accuracy.Simulation results show that compared with the traditional orthogonal matching pursuit(OMP)algorithm,the normalized mean square error(NMSE)of the proposed algorithm decreases by over 14dB in the case of 2 paths.

Investigation of prior image constrained compressed sensing-based spectral X-ray CT image reconstruction

To improve spectral X-ray CT reconstructed image quality, the energy-weighted reconstructed image xbins^W and the separable paraboloidal surrogates（SPS） algorithm are proposed for the prior image constrained compressed sensing（PICCS）-based spectral X-ray CT image reconstruction. The PICCS-based image reconstruction takes advantage of the compressed sensing theory, a prior image and an optimization algorithm to improve the image quality of CT reconstructions.To evaluate the performance of the proposed method, three optimization algorithms and three prior images are employed and compared in terms of reconstruction accuracy and noise characteristics of the reconstructed images in each energy bin.The experimental simulation results show that the image xbins^W is the best as the prior image in general with respect to the three optimization algorithms; and the SPS algorithm offers the best performance for the simulated phantom with respect to the three prior images. Compared with filtered back-projection（FBP）, the PICCS via the SPS algorithm and xbins^W as the prior image can offer the noise reduction in the reconstructed images up to 80. 46%, 82. 51%, 88. 08% in each energy bin,respectively. M eanwhile, the root-mean-squared error in each energy bin is decreased by 15. 02%, 18. 15%, 34. 11% and the correlation coefficient is increased by 9. 98%, 11. 38%,15. 94%, respectively.