Principles Of Compressed Sensing Research Articles

CS-SPT: Secure and Packet Loss-Resilient Audio Transmission Based on Compressive Sensing

Packet loss-resilient and security are two major challenges faced by real-time audio transmission over IP networks. Due to the capability of recovering the signal from a small set of samplings and the randomness in the acquisition process, compressive sensing (CS) has a vast prospect in dealing with these problems. In this paper, we propose a secure and packet loss-resistant real-time audio transmission framework (CS-SPT) based on the principle of CS. Inspired by the interleaving technique, an ultralow complexity scrambling matrix was adopted in the proposed CS-SPT to improve its packet loss-resilient capability by increasing the information redundancy. Moreover, the energy of ciphertext is homogenized using a diffusion operation. Experimental results show that compared with existing methods, the proposed CS-SPT not only improves the packet loss-resilient ability significantly but also can resist several major attacks, such as COAs and KPAs.

Deblending of Simultaneous-Source Seismic Data Using Bregman Iterative Shaping

Deblending plays an important role in preparing high-quality seismic data from modern blended simultaneous-source seismic data. The conventional methods become problematic when the random ambient noise becomes extremely strong and the inversion iteratively fits the random noise instead of the signal and blending interference. In this article, an improved method is proposed to separate blended seismic data. We treat the deblending problem as a regularization problem under the frame of compressed sensing (CS), and propose a new nonlinear Bregman iterative shaping (BIS) algorithm to solve the minimization problem. Based on the principle of CS, we transform the simultaneous-source data to the seislet-domain for inversion and separation, and verify the effectiveness and superiority of the proposed method by two theoretical model data and an actual marine streamer blended data. Compared with the traditional iterative shaping (TIS) algorithm, BIS adds data residuals to the observed data (the blended data) in each iteration, so that the error between the calculated data after each iteration and the main source signal in the known blended data is the smallest, and helps to recover the weaker information in the seismic data and obtain higher precision separation results. BIS uses a fixed soft threshold, which speeds up the convergence speed. In addition, BIS can effectively improve the separation accuracy when the given sparse domain threshold is not suitable.

Compressed sensing in fluorescence microscopy

Compressed sensing (CS) is a signal processing approach that solves ill-posed inverse problems, from under-sampled data with respect to the Nyquist criterium. CS exploits sparsity constraints based on the knowledge of prior information, relative to the structure of the object in the spatial or other domains. It is commonly used in image and video compression as well as in scientific and medical applications, including computed tomography and magnetic resonance imaging. In the field of fluorescence microscopy, it has been demonstrated to be valuable for fast and high-resolution imaging, from single-molecule localization, super-resolution to light-sheet microscopy. Furthermore, CS has found remarkable applications in the field of mesoscopic imaging, facilitating the study of small animals’ organs and entire organisms. This review article illustrates the working principles of CS, its implementations in optical imaging and discusses several relevant uses of CS in the field of fluorescence imaging from super-resolution microscopy to mesoscopy.

A Direction-of-Arrival Estimation Algorithm Based on Compressed Sensing and Density-Based Spatial Clustering and Its Application in Signal Processing of MEMS Vector Hydrophone.

Direction of arrival (DOA) estimation has always been a hot topic for researchers. The complex and changeable environment makes it very challenging to estimate the DOA in a small snapshot and strong noise environment. The direction-of-arrival estimation method based on compressed sensing (CS) is a new method proposed in recent years. It has received widespread attention because it can realize the direction-of-arrival estimation under small snapshots. However, this method will cause serious distortion in a strong noise environment. To solve this problem, this paper proposes a DOA estimation algorithm based on the principle of CS and density-based spatial clustering (DBSCAN). First of all, in order to make the estimation accuracy higher, this paper selects a signal reconstruction strategy based on the basis pursuit de-noising (BPDN). In response to the challenge of the selection of regularization parameters in this strategy, the power spectrum entropy is proposed to characterize the noise intensity of the signal, so as to provide reasonable suggestions for the selection of regularization parameters; Then, this paper finds out that the DOA estimation based on the principle of CS will get a denser estimation near the real angle under the condition of small snapshots through analysis, so it is proposed to use a DBSCAN method to process the above data to obtain the final DOA estimate; Finally, calculate the cluster center value of each cluster, the number of clusters is the number of signal sources, and the cluster center value is the final DOA estimate. The proposed method is applied to the simulation experiment and the micro electro mechanical system (MEMS) vector hydrophone lake test experiment, and they are proved that the proposed method can obtain good results of DOA estimation under the conditions of small snapshots and low signal-to-noise ratio (SNR).

Research on Image Optimization Technology Based on Compressed Sensing

Compressed Sensing (CS) theory is one of the most active research fields in electronic information engineering. CS theory overcomes the limits dictated by Nyquist sampling theorem. Compared to the required minimum sampling quantity, CS proves that the original signal can be restored with high probability by fewer measurements, which saves the time cost of data acquisition and processing without losing information features. CS theory can essentially be regarded as a tool for dealing with linear signal recovery problems, so it has obvious advantages in solving inverse problems of signals and images. Image degradation is one of them, and the process of restoring high-quality images is image optimization. In order to promote the academic research and practical application of CS theory, the basic principle of CS is introduced. Based on the previous research, this paper studies on CS-based image optimization technology in three main aspects: denoising, deblurring and super resolution. Finally, the problems and challenges are discussed, and the current trends are analyzed to provide reference and help for future work.

The Critical Study of Mutual Coherence Properties on Compressive Sensing Framework for Sparse Reconstruction Performance: Compression vs Measurement System

Compressive Sensing (CS) framework becomes well known since its ability to recover signal only by using less sampling required by Shanon-Nyquist theorem. The lack of required sampling is no longer constraint for having good reconstruction performance. The load is shifted to the reconstruction procedure instead of the sampling acquisition process. As long as the signal can be guaranteed sparse, the CS based method is able to provide high reconstruction accuracy. One of the CS principle is incoherence property, which can be represented by mutual coherence value. It represents the coherence between the sensing matrix and the sparse base dictionary. The theory said the less coherence between those two parameters, the more precise the reconstruction is. In fact, it is not consistently applied. The research presented on this paper find that, the theory is consistent for reconstruction on compression system, while it is not applied on the reconstruction of measurement system. Other properties are found to be more representative on assigning necessary condition for reconstruction performance on measurement system.

Compressed Impairment Sensing-Assisted and Interleaved-Double-FFT-Aided Modulation Improves Broadband Power Line Communications Subjected to Asynchronous Impulsive Noise

In power line communications (PLCs), the multipath-induced dispersion and the impulsive noise are the two fundamental impediments in the way of high-integrity communications. The conventional orthogonal frequency-division multiplexing (OFDM) system is capable of mitigating the multipath effects in PLCs, but it fails to suppress the impulsive noise effects. Therefore, in order to mitigate both the multipath effects and the impulsive effects in PLCs, in this paper, a compressed impairment sensing (CIS)-assisted and interleaved-double-FFT (IDFFT)-aided system is proposed for indoor broadband PLC. Similar to classic OFDM, data symbols are transmitted in the time-domain, while the equalization process is employed in the frequency domain in order to achieve the maximum attainable multipath diversity gain. In addition, a specifically designed interleaver is employed in the frequency domain in order to mitigate the impulsive noise effects, which relies on the principles of compressed sensing (CS). Specifically, by taking advantage of the interleaving process, the impairment impulsive samples can be estimated by exploiting the principle of CS and then cancelled. In order to improve the estimation performance of CS, we propose a beneficial pilot design complemented by a pilot insertion scheme. Finally, a CIS-assisted detector is proposed for the IDFFT system advocated. Our simulation results show that the proposed CIS-assisted IDFFT system is capable of achieving a significantly improved performance compared with the conventional OFDM. Furthermore, the tradeoffs to be struck in the design of the CIS-assisted IDFFT system are also studied.

Informational analysis for compressive sampling in radar imaging.

Compressive sampling or compressed sensing (CS) works on the assumption of the sparsity or compressibility of the underlying signal, relies on the trans-informational capability of the measurement matrix employed and the resultant measurements, operates with optimization-based algorithms for signal reconstruction and is thus able to complete data compression, while acquiring data, leading to sub-Nyquist sampling strategies that promote efficiency in data acquisition, while ensuring certain accuracy criteria. Information theory provides a framework complementary to classic CS theory for analyzing information mechanisms and for determining the necessary number of measurements in a CS environment, such as CS-radar, a radar sensor conceptualized or designed with CS principles and techniques. Despite increasing awareness of information-theoretic perspectives on CS-radar, reported research has been rare. This paper seeks to bridge the gap in the interdisciplinary area of CS, radar and information theory by analyzing information flows in CS-radar from sparse scenes to measurements and determining sub-Nyquist sampling rates necessary for scene reconstruction within certain distortion thresholds, given differing scene sparsity and average per-sample signal-to-noise ratios (SNRs). Simulated studies were performed to complement and validate the information-theoretic analysis. The combined strategy proposed in this paper is valuable for information-theoretic orientated CS-radar system analysis and performance evaluation.

Compressive Imaging and Characterization of Sparse Light Deflection Maps

Light rays incident on a transparent object of uniform refractive index undergo deflections, which uniquely characterize the surface geometry of the object. Associated with each point on the surface is a deflection map (or spectrum) which describes the pattern of deflections in various directions. This article presents a novel method to efficiently acquire and reconstruct sparse deflection spectra induced by smooth object surfaces. To this end, we leverage the framework of compressed sensing (CS) in a particular implementation of a schlieren deflectometer, i.e., an optical system providing linear measurements of deflection spectra with programmable spatial light modulation patterns. In particular, we design those modulation patterns on the principle of spread spectrum CS for reducing the number of observations. Interestingly, the ability of our device to simultaneously observe the deflection spectra on a dense discretization of the object surface is related to a particular multiple measurement vector mode...

Compressed sensing electron tomography

The recent mathematical concept of compressed sensing (CS) asserts that a small number of well-chosen measurements can suffice to reconstruct signals that are amenable to sparse or compressible representation. In addition to powerful theoretical results, the principles of CS are being exploited increasingly across a range of experiments to yield substantial performance gains relative to conventional approaches. In this work we describe the application of CS to electron tomography (ET) reconstruction and demonstrate the efficacy of CS-ET with several example studies. Artefacts present in conventional ET reconstructions such as streaking, blurring of object boundaries and elongation are markedly reduced, and robust reconstruction is shown to be possible from far fewer projections than are normally used. The CS-ET approach enables more reliable quantitative analysis of the reconstructions as well as novel 3D studies from extremely limited data.

An application of compressive sensing for image fusion

Compressive sensing (CS) has inspired significant interests because of its compressive capability and lack of complexity on the sensor side. This paper introduces a novel framework of image fusion based on the CS principle. First, we present a study of three sampling patterns and investigate their performance on CS reconstruction. We then propose a novel image fusion algorithm by using an improved sampling pattern. Finally, the CS-based image fusion approach is applied to various image modalities and evaluated both visually and in terms of fusion quality metrics. The simulations demonstrate that CS-based image fusion has a number of perceived advantages in comparison with image fusion in the multiresolution (MR) domain, providing a truly different and more advanced way for fusing multimodality images.

A Compressive Sensing and Unmixing Scheme for Hyperspectral Data Processing

Hyperspectral data processing typically demands enormous computational resources in terms of storage, computation, and input/output throughputs, particularly when real-time processing is desired. In this paper, a proof-of-concept study is conducted on compressive sensing (CS) and unmixing for hyperspectral imaging. Specifically, we investigate a low-complexity scheme for hyperspectral data compression and reconstruction. In this scheme, compressed hyperspectral data are acquired directly by a device similar to the single-pixel camera based on the principle of CS. To decode the compressed data, we propose a numerical procedure to compute directly the unmixed abundance fractions of given endmembers, completely bypassing high-complexity tasks involving the hyperspectral data cube itself. The reconstruction model is to minimize the total variation of the abundance fractions subject to a preprocessed fidelity equation with a significantly reduced size and other side constraints. An augmented Lagrangian-type algorithm is developed to solve this model. We conduct extensive numerical experiments to demonstrate the feasibility and efficiency of the proposed approach, using both synthetic data and hardware-measured data. Experimental and computational evidences obtained from this paper indicate that the proposed scheme has a high potential in real-world applications.