2D Compressed Sensing Research Articles

Multilevel Privacy Protection for Social Media Based on 2-D Compressive Sensing

Multilevel Privacy Protection for Social Media Based on 2-D Compressive Sensing

Comprehensive Neonatal Cardiac, Feed and Wrap, Non-contrast, Non-sedated, Free-breathing Compressed Sensing 4D Flow MRI Assessment.

Cardiac MRI is an important imaging tool in congenital cardiac disease, but its use has been limited in the neonatal population as general anesthesia has been needed for breath-holding. Technological advances in four-dimensional (4D) flow MRI have now made nonsedated free-breathing acquisition protocols a viable clinical option, but the method requires prospective validation in neonates. To test the feasibility of compressed sensing (CS) 4D flow MRI in the neonatal population and to compare with standard previously validated two-dimensional (2D) phase-contrast (PC) flow MRI. Prospective, cohort, image quality. A total of 14 healthy neonates (median [range] age: 2.5 [0-80] days; 8 male). Noncontrast 2D cine gradient echo sequence with through-plane velocity encoding (PC) sequence and compressed sensing (CS) three-dimensional (3D), time-resolved, cine phase-contrast MRI with 3D velocity-encoding (4D flow MRI) at 3 T. Aortic 2D PC, and aortic, pulmonary trunk and superior vena cava CS 4D flow MRI were acquired using the feed and wrap technique (nonsedated) and quantified using commercially available software. Aortic flow and peak velocity were compared between methods. Internal consistency of 4D flow MRI was determined by comparing mean forward flow of the main pulmonary artery (MPA) vs. the sum of left and right pulmonary artery flows (LPA and RPA) and by comparing mean ascending aorta forward flow (AAo) vs. the sum of superior vena cava (SVC) and descending aorta flows (DAo). Flow and peak-velocity comparisons were assessed using paired t-tests, with P < 0.05 considered significant, and Bland-Altman analysis. Interobserver and intraobserver agreement and internal consistency were analyzed by intraclass correlation co-efficient (ICC). There was no statistically significant difference between ascending aortic forward flow between 2D PC and CS 4D Flow MRI (P=0.26) with a bias of 0.11 mL (-0.59 to 0.82 mL) nor peak velocity (P =0.11), with a bias of -5cm/sec and (-26 to 16 cm/sec). There was excellent interobserver and intraobserver agreement for each vessel (interobserver ICC: AAo 1.00; DAo 0.94, SVC 0.90, MPA 0.99, RPA 0.98, LPA 0.96; intraobserver ICC: AAo 1.00; DAo 0.99, SVC 0.98, MPA 1.00, RPA 1.00, LPA 0.99). Internal consistency measures showed excellent agreement for both mean forward flow of main pulmonary artery vs. the sum of left and right pulmonary arteries (ICC: 0.95) and mean ascending aorta forward flow vs. the sum of superior vena cava and descending aorta flows (ICC: 1.00). Sedation-free neonatal feed and wrap MRI is well tolerated and feasible. CS 4D flow MRI quantification is similar to validated 2D PC free-breathing imaging with excellent interobserver and intraobserver agreement. 1 TECHNICAL EFFICACY: Stage 2.

2D Compressed Sensing Using Nonlocal Low-Rank Prior Reconstruction for Cipher-Image Coding

In recent years, cipher-image coding by using compressed sensing (CS) has became a hot topic. However, the ratio-distortion (R-D) performance of the previous methods are barely satisfactory. In order to address this concern, a 2D CS (2DCS) scheme by using nonlocal low-rank prior (NLP) reconstruction is proposed in this letter. Firstly, the scrambling encryption is applied to mask the plaintext image. Secondly, the cipher image is compressed by 2DCS. Lastly, an iterative singular value thresholding (ISVT) algorithm is developed, which can reconstruct the image effectively by exploring the NLP information of the image. Simulation results show that the proposed method outperforms the previous CS-based methods in terms of R-D performance.

Exploiting 2D compressed sensing and information entropy for secure color image compression and encryption

Compared to 1D compressed sensing (CS), 2D CS is more efficient for compressing the plaintext image from two directions, but security level of current 2D CS-based ciphers is unsatisfactory. To solve this problem, this paper presents a novel color image compression and encryption algorithm by combining 2D CS, information entropy and chaos. Firstly, the color image is decomposed into red, green and blue components, then they are sparsely transformed by the discrete wavelet transform (DWT) to get three sparse matrices. Next, the obtained matrices are observed by two asymptotical deterministic random measurement matrices based on information entropy and counter (ADMMIC), which not only encrypts the plaintext image, but also compresses it in proportion to reduce the transmission bandwidth and storage space. Subsequently, the corresponding measurement value matrices are shuffled by a double random scrambling based on Arnold map and index vector (DRSAIV) to eliminate the correlation between adjacent pixels. Furthermore, the obtained permutated matrices are diffused by a simultaneous multiple random diffusion of inter–intra components (SMRDIC) to obtain the final cipher image, the plaintext pixel to be diffused, the key matrix involved in diffusion and the position of the obtained ciphertext pixel are all unpredictable, which makes statistical attack invalid. In addition, information entropy values of plaintext image are obtained to generate the initial values of the used chaotic systems, which greatly improve the ability to resist the known-plaintext and chosen-plaintext attacks. Simulation results and security analyses verify that this algorithm has good compression and high security.

Robust Coding of Encrypted Images via 2D Compressed Sensing

In many practical scenarios, image encryption should be implemented before image compression. This leads to the requirement of compressing encrypted images. Compressed sensing (CS), a breakthrough in signal processing, has been demonstrated to be an effective method for compressing encrypted images with robustness. However, for the exiting CS-based image encryption-then-compression (ETC) systems, image encryption is usually performed by using linear operations. When linear operations are used, we cannot achieve low computational complexity and high security in the meantime. To solve this problem, a novel 2D CS (2DCS) based ETC (2DCS-ETC) scheme is proposed in this paper. First, two nonlinear operations, including global random permutation (GRP) and negative-positive transformation (NPT), are utilized to encrypt the original image for high security purpose. Second, the encrypted image is compressed by using 2DCS for low computational complexity purpose. Furthermore, a gray mapping operation is embedded prior to CS encoding. Since gray mapping strategy can reduce the dynamic range of the CS samples, this strategy is also helpful for the rate distortion (R-D) performance improvement. Third, a 2D projected gradient with embedding decryption (2DPG-ED) algorithm is proposed, which can be utilized for the original image reconstruction even if the encrypted image is not sparse anymore. Compared with the previous CS-based ETC methods, the proposed approach can simultaneously achieve high security and low computational complexity with better robustness.

Fast two‐dimensional sparse signal gridless recovery algorithm for MIMO array SAR 3D imaging

Multiple-input multiple-output (MIMO) array synthetic aperture radar (SAR) can be used to directly obtain the three-dimensional (3D) imagery of the illuminated scene with a single track. Due to the length limitations of synthetic aperture and antenna array, the super-resolution algorithms within the framework of 2D compressive sensing (CS) have been conceived to reconstruct the azimuth-cross-track plane image because of its spatial sparsity. Since the desired scatterers are presupposed to be distributed over a series of fixed grid points, the location accuracy of the existing 2D CS algorithms is relatively low. To overcome this problem, a fast 2D gridless recovery (GLR) algorithm for the 2D imaging signal model established in the real domain is proposed in this study. First, two different forms of 2D real-valued signal models with uniform or random sampling on the azimuth-cross-track plane are reconstructed by means of unitary transformation. Further, the real-domain based 2D sparse signal gridless reconstruction approach is derived. Finally, extensive simulation results validate that the proposed 2D real-valued GLR approach can approximately improve the computational efficiency by a factor of ten in terms of CPU time when compared with that of the 2D GLR algorithm in the complex domain.

Resolution-dependent influences of compressed sensing in quantitative T2 mapping of articular cartilage.

This study evaluates the resolution-dependent influences of compressed sensing (CS) in MRI quantification of T2 mapping in articular cartilage with osteoarthritis (OA). T2-weighed 2D experiments of healthy and OA cartilage were fully sampled in k-space with five echo times at both 17.6 μm and 195.3 μm in-plane resolutions; termed as microscopic MRI (μMRI) and macroscopic MRI (mMRI) respectively. These fully sampled k-space data were under-sampled at various 2D CS accelerating factors (AF = 4-32). The under-sampled data were reconstructed individually into 2D images using nonlinear reconstruction, which were used to calculate the T2 maps. The bulk and zonal variations of T2 values in cartilage were evaluated at different AFs. The study finds that the T2 images at AFs up to 8 preserved major visual information and produced negligible artifacts for μMRI. The T2 values remained accurate for different sub-tissue zones at various AFs. The absolute difference between the CS (AF up to 32) and the Ground Truth (i.e., using 100% of the k-space data) of the mean T2 values through the whole tissue depth was higher in mMRI versus μMRI. For mMRI (where the resolution mimics the clinical MRI of human cartilage), the quantitative T2 mapping at AFs up to 4 showed negligible variations. This study demonstrates that both clinical MRI and μMRI can benefit from the use of CS in image acquisition, and μMRI benefits more from the use of CS by acquiring much less data, without losing significant accuracy in the quantification of T2 maps in osteoarthritic cartilage.

Echo Preprocessing to Enhance SNR for 2D CS-Based ISAR Imaging Method.

A new CS-based inverse synthetic aperture radar (ISAR) imaging framework is proposed to enhance both the image performance and the robustness at a low SNR. An ISAR echo preprocessing method for enhancing the ISAR imaging quality of compressed sensing (CS) based algorithms is developed by implementing matched filtering, echo denoising and matrix optimization sequentially. After the preprocessing, the two-dimensional (2D) SL0 algorithm is applied to reconstruct an ISAR image in the range and cross-range plane through a series of 2D matrices using the 2D CS theory, rather than converting the 2D convex optimization problem to the one-dimensional (1D) problem in the image reconstruction process. The proposed preprocessing framework is verified by simulations and experiment. Simulations and experimental results show that the ISAR image obtained by the 2D sparse recovery algorithm with our proposed method has a better performance.

Compressed sensing in quantitative determination of GAG concentration in cartilage by microscopic MRI

To evaluate the potentials of compressed sensing (CS) in MRI quantification of glycosaminoglycan (GAG) concentration in articular cartilage at microscopic resolution. T1 -weighted 2D experiments of cartilage were fully sampled in k-space with five inversion times at 17.6 μm resolution. These fully sampled k-space data were re-processed, by undersampling at various 1D and 2D CS undersampling factors (UFs). The undersampled data were reconstructed individually into 2D images using nonlinear reconstruction, which were used to calculate 2D maps of T1 and GAG concentration. The values of T1 and GAG in cartilage were evaluated at different UFs (up to 16, which used 6.25% of the data). K-space sampling pattern and zonal variations were also investigated. Using 2D variable density sampling pattern, the T1 images at UFs up to eight preserved major visual information and produced negligible artifacts. The GAG concentration remained accurate for different sub-tissue zones at various UFs. The variation of the mean GAG concentration through the whole tissue depth was 1.20%, compared to the fully sampled results. The maximum variation was 2.24% in the deep zone of cartilage. Using 1D variable density sampling pattern, the quantitative T1 mapping and GAG concentration at UFs up to 4 showed negligible variations. This study demonstrates that CS could be beneficial in microscopic MRI (µMRI) studies of cartilage by acquiring less data, without losing significant accuracy in the quantification of GAG concentration. Magn Reson Med 79:3163-3171, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

A fast and efficient approach to color-image encryption based on compressive sensing and fractional Fourier transform

This paper introduces a novel method of fast and efficient measurement matrices and random phase masks for color image encryption, in which Kronecker product (KP) is combined with chaotic map. The encryption scheme is based on two-dimension (2D) compressive sensing (CS) and fraction Fourier transform (FrFT). In this algorithm, the KP is employed to extend low dimension seed matrices to obtain high dimension measurement matrices and random phase masks. The low dimension seed matrices are generated by controlling chaotic map. The original image is simultaneously encrypted and compressed by the 2D CS, then re-encrypted with FrFT. The proposed encryption scheme fulfills high speed, low complexity and high security. Numerical simulation results demonstrate the excellent performance and security of the proposed scheme.

Prior data assisted compressed sensing: A novel MR imaging strategy for real time tracking of lung tumors

Hybrid radiotherapy-MRI devices promise real time tracking of moving tumors to focus the radiation portals to the tumor during irradiation. This approach will benefit from the increased temporal resolution of MRI's data acquisition and reconstruction. In this work, the authors propose a novel spatial-temporal compressed sensing (CS) imaging strategy for the real time MRI--prior data assisted compressed sensing (PDACS), which aims to improve the image quality of the conventional CS without significantly increasing reconstruction times. Conventional 2D CS requires a random sampling of partial k-space data, as well as an iterative reconstruction that simultaneously enforces the image's sparsity in a transform domain as well as maintains the fidelity to the acquired k-space. PDACS method requires the additional acquisition of the prior data, and for reconstruction, it additionally enforces fidelity to the prior k-space domain similar to viewsharing. In this work, the authors evaluated the proposed PDACS method by comparing its results to those obtained from the 2D CS and viewsharing methods when performed individually. All three methods are used to reconstruct images from lung cancer patients whose tumors move and who are likely to benefit from lung tumor tracking. The patients are scanned, using a 3T MRI, under free breathing using the fully sampled k-space with 2D dynamic bSSFP sequence in a sagittal plane containing lung tumor. These images form a reference set for the evaluation of the partial k-space methods. To create partial k-space, the fully sampled k-space is retrospectively undersampled to obtain a range of acquisition acceleration factors, and reconstructed with 2D-CS, PDACS, and viewshare methods. For evaluation, metrics assessing global image artifacts as well as tumor contour shape fidelity are determined from the reconstructed images. These analyses are performed both for the original 3T images and those at a simulated 0.5T equivalent noise level. In the 3.0T images, the PDACS strategy is shown to give superior results compared to viewshare and conventional 2D CS using all metrics. The 2D-CS tends to perform better than viewshare at the low acceleration factors, while the opposite is true at the high acceleration factors. At simulated 0.5T images, PDACS method performs only marginally better than the viewsharing method, both of which are superior compared to 2D CS. The PDACS image reconstruction time (0.3 s/image) is similar to that of the conventional 2D CS. The PDACS method can potentially improve the real time tracking of moving tumors by significantly increasing MRI's data acquisition speeds. In 3T images, the PDACS method does provide a benefit over the other two methods in terms of both the overall image quality and the ability to accurately and automatically contour the tumor shape. MRI's data acquisition may be accelerated using the simpler viewsharing strategy at the lower, 0.5T magnetic field, as the marginal benefit of the PDACS method may not justify its additional reconstruction times.

Iterative gradient projection algorithm for two-dimensional compressive sensing sparse image reconstruction

The basic theories and techniques in compressive sensing (CS) are established on the sampling and reconstruction of one-dimensional (1D) signals. When it is applied to two-dimensional (2D) images, the images are first stacked in a large vector. However, this vectorization not only destroys the spatial structure of the 2D image, but also increases computational complexity and memory requirements. As a result, some researchers proposed the concept of 2D CS. The major challenge of 2D CS is to design a reconstruction algorithm that can directly reconstruct the 2D image data from the 2D random projection. In this paper, a 2D CS sparse image reconstruction algorithm based on iterative gradient projection is proposed. In the proposed algorithm, the sparse solution is searched iteratively in the 2D solution space and then updated by gradient descent of the total variation (TV) and bivariate shrinkage in the dual-tree discrete wavelet transform (DDWT) domain. Numerous experiments are performed on several natural images. Compared with several state-of-the-art reconstruction algorithms, the proposed algorithm is more efficient and robust, not only yielding higher peak-signal-to-noise ratio but also reconstructing images of better subjective visual quality.

Performance of 2D Compressive Sensing on Wide-Beam Through-the-Wall Imaging

Compressive sensing has become an accepted and powerful alternative to conventional data sampling schemes. Hardware simplicity, data, and measurement time reduction and simplified imagery are some of its most attractive strengths. This work aims at exploring the possibilities of using sparse vector recovery theory for actual engineering and defense- and security-oriented applications. Conventional through-the-wall imaging using a synthetic aperture configuration can also take advantage of compressive sensing by reducing data acquisition rates and omitting certain azimuth scanning positions. An ultra-wideband stepped frequency system carrying wide beam antennas performs through-the-wall imaging of a real scene, including a hollow concrete block wall and a corner reflector behind it. Random downsampling rates lower than those announced by Nyquist's theorem both in the fast-time and azimuth domains are studied, as well as downsampling limitations for accurate imaging. Separate dictionaries are considered and modeled depending on the objects to be reconstructed: walls or point targets. Results show that an easy interpretation of through-the-wall scenes using the l1-norm and orthogonal matching pursuit algorithms is possible thanks to the simplification of the reconstructed scene, for which only as low as 25% of the conventional SAR data are needed.