On the security of compressed sensing-based signal cryptosystem

With the development of the cyber-physical systems (CPS), the security analysis of the data therein becomes more and more important. Recently, due to the advantage of joint encryption and compression for data transmission in CPS, the emerging compressed sensing (CS)-based cryptosystem has attracted much attention, where security is of extreme importance. The existing methods only analyze the security of the plaintext under the assumption that the key is absolutely safe. However, for sparse plaintext, the prior sparsity knowledge of the plaintext could be exploited to partly retrieve the key, and then the plaintext, from the ciphertext. So, the existing methods do not provide a satisfactory security analysis. In this paper, it is conducted in the information theory frame, where the plaintext sparsity feature and the mutual information of the ciphertext, key, and plaintext are involved. In addition, the perfect secrecy criteria (Shannon-sense and Wyner-sense) are extended to measure the security. While the security level is given, the illegal access risk is also discussed. It is shown that the CS-based cryptosystem achieves the extended Wyner-sense perfect secrecy, but when the key is used repeatedly, both the plaintext and the key could be conditionally accessed.

Image encryption based on compressed sensing and blind source separation

A novel image encryption scheme based on compressed sensing and blind source separation is proposed in this work, where there is no statistical requirement to plaintexts. In the proposed method, for encryption, the plaintexts and keys are mixed with each other using a underdetermined matrix first, and then compressed under a project matrix. As a result, it forms a difficult underdetermined blind source separation (UBSS) problem without statistical features of sources. Regarding the decryption, given the keys, a new model will be constructed, which is solvable under compressed sensing (CS) frame. Due to the usage of CS technology, the plaintexts are compressed into the data with smaller size when they are encrypted. Meanwhile, they can be decrypted from parts of the received data packets and thus allows to lose some packets. This is beneficial for the proposed encryption method to suit practical communication systems. Simulations are given to illustrate the availability and the superiority of our method.

Improved image recovery from compressed data contaminated with impulsive noise

Compressed sensing (CS) is a new information sampling theory for acquiring sparse or compressible data with much fewer measurements than those otherwise required by the Nyquist/Shannon counterpart. This is particularly important for some imaging applications such as magnetic resonance imaging or in astronomy. However, in the existing CS formulation, the use of the â„“ 2 norm on the residuals is not particularly efficient when the noise is impulsive. This could lead to an increase in the upper bound of the recovery error. To address this problem, we consider a robust formulation for CS to suppress outliers in the residuals. We propose an iterative algorithm for solving the robust CS problem that exploits the power of existing CS solvers. We also show that the upper bound on the recovery error in the case of non-Gaussian noise is reduced and then demonstrate the efficacy of the method through numerical studies.

Effective anomaly detection in sensor networks data streams

This paper addresses a major challenge in data mining applications where the full information about the underlying processes, such as sensor networks or large online database, cannot be practically obtained due to physical limitations such as low bandwidth or memory, storage, or computing power. Motivated by the recent theory on direct information sampling called compressed sensing (CS), we propose a framework for detecting anomalies from these largescale data mining applications where the full information is not practically possible to obtain. Exploiting the fact that the intrinsic dimension of the data in these applications are typically small relative to the raw dimension and the fact that compressed sensing is capable of capturing most information with few measurements, our work show that spectral methods that used for volume anomaly detection can be directly applied to the CS data with guarantee on performance. Our theoretical contributions are supported by extensive experimental results on large datasets which show satisfactory performance.

Defining sub-regions in locally sparsified compressive sensing MRI

Magnetic Resonance Imaging (MRI) is an important imaging technique. However, it is a time consuming process. The aim of this study is to make the imaging process ef?cient. MR images are sparse in the sensing domain and Compressive Sensing exploits this sparsity. Locally sparsi?ed Compressed Sensing is a specialized case of CS which sub-divides the image and sparsi?es each region separately; later samples are taken based on sparsity level in that region. In this paper, a new structured approach is presented for de?ning the size and locality of sub-regions in image. Experiments were done on the regions de?ned by proposed framework and local sparsity constraints were used to achieve high sparsity level and to reduce the sample set. Experimental results and their comparison with global CS is presented in the paper.

Locally sparsified compressive sensing for improved MR image qualtity

The fact that medical images have redundant information is exploited by researchers for faster image acquisition. Sample set or number of measurements were reduced in order to achieve rapid imaging. However, due to inadequate sampling, noise artefacts are inevitable in Compressive Sensing (CS) MRI. CS utilizes the transform sparsity of MR images to regenerate images from under sampled data. Locally sparsified Compressed Sensing is an extension of simple CS. It localises sparsity constraints for sub-regions rather than using a global constraint. This paper, presents a framework to use local CS for improving image quality without increasing sampling rate or without making the acquisition process any slower. This was achieved by exploiting local constraints. Localising image into independent sub-regions allows different sampling rates within image. Energy distribution of MR images is not even and most of noise occurs due to under-sampling in high energy regions. By sampling sub-regions based on energy distribution, noise artefacts can be minimized. Experiments were done using the proposed technique. Results were compared with global CS and summarized in this paper.

A novel monotonic fixed-point algorithm for l1-regularized least square vector and matrix problem

Least square problem with l₁ regularization has been proposed as a promising method for sparse signal reconstruction (e.g., basis pursuit de-noising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as l₁-regularized least-square program (LSP). In this paper, we propose a novel monotonic fixed point method to solve large-scale l₁-regularized LSP. And we also prove the stability and convergence of the proposed method. Furthermore we generalize this method to least square matrix problem and apply it in nonnegative matrix factorization (NMF). The method is illustrated on sparse signal reconstruction, partner recognition and blind source separation problems, and the method tends to convergent faster and sparser than other l₁-regularized algorithms.

An introduction to compressive sensing and its potential applications in structural engineering

The Shannon/Nyquist sampling theorem specifies that to avoid losing information when capturing a signal, one must sample at least two times faster than the signal bandwidth. In order to capture and represent compressible signals at a rate significantly below the Nyquist rate, a new method, called compressive sensing (CS), is therefore proposed. CS theory asserts that one can recover certain signals from far fewer samples or measurements than traditional methods use. It employs non-adaptive linear projections that preserve the structure of the sparse signal; the signal is then reconstructed from these projections using an optimization process. It is believed that CS has far reaching implications, while most publications concentrate on signal processing fields (especially for images). In this paper, we provide a concise introduction of CS and then discuss some of its potential applications in structural engineering. The recorded vibration time history of a steel beam and the wave propagation result on a steel rebar are studied in detail. CS is adopted to reconstruct the time histories by using only parts of the signals. The results under different conditions are compared, which confirm that CS will be a promising tool for structural engineering.

Non-uniform sparsity in rapid compressive sensing MRI

Magnetic Resonance Imaging (MRI) is one of the prominent medical imaging techniques. This process is time-consuming and can take several minutes to acquire one image. The aim of this research is to reduce the imaging process time of MRI. This issue is addressed by reducing the number of acquired measurements using theory of Compressive Sensing (CS). Compressive Sensing exploits sparsity in MR images. Randomly under sampled k-space generates incoherent noise which can be handled using a nonlinear image reconstruction method. In this paper, a new framework is presented based on the idea to exploit non-uniform nature of sparsity in MR images, where local sparsity constrains were used instead of traditional global constraint, to further reduce the sample set. Experimental results and comparison with CS using global constraint are demonstrated.

Damage identification scheme based on compressive sensing

Civil infrastructures are critical to every nation, due to their substantial investment, long service period, and enormous negative impacts after failure. However, they inevitably deteriorate during their service lives. Therefore, methods capable of assessing conditions and identifying damage in a structure timely and accurately have drawn increasing attention. Recently, compressive sensing (CS), a significant breakthrough in signal processing, has been proposed to capture and represent compressible signals at a rate significantly below the traditional Nyquist rate. Due to its sound theoretical background and notable influence, this methodology has been successfully applied in many research areas. In order to explore its application in structural damage identification, a new CS-based damage identification scheme is proposed in this paper, by regarding damage identification problems as pattern classification problems. The time domain structural responses are transferred to the frequency domain as sparse representation, and then the numerical simulated data under various damage scenarios will be used to train a feature matrix as input information. This matrix can be used for damage identification through an optimization process. This will be one of the first few applications of this advanced technique to structural engineering areas. In order to demonstrate its effectiveness, numerical simulation results on a complex pipe soil interaction model are used to train the parameters and then to identify the simulated pipe degradation damage and free-spanning damage. To further demonstrate the method, vibration tests of a steel pipe laid on the ground are carried out. The measured acceleration time histories are used for damage identification. Both numerical and experimental verification results confirm that the proposed damage identification scheme will be a promising tool for structural health monitoring.

Locally sparsified compressive sensing in magnetic resonance imaging

Magnetic Resonance Imaging (MRI) is a widely used technique for acquiring images of human organs/tissues. Due to its complex imaging process, it consumes a lot of time to produce a high quality image. Compressive Sensing (CS) has been used by researchers for rapid MRI. It uses a global sparsity constraint with variable density random sampling and L1 minimisation. This work intends to speed up the imaging process by exploiting the non-uniform sparsity in the MR images. Locally Sparsified CS suggests that the image can be even better sparsified by applying local sparsity constraints. The image produced by local CS can further reduce the sample set. This paper establishes the basis for a methodology to exploit non-uniform nature of sparsity and to make the MRI process time efficient by using local sparsity constraints.