Robust signal recovery algorithm for structured perturbation compressive sensing

It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.

Compression techniques of mechanical vibration signals based on optimal sparse representations

This paper presents the result of an experimental study on the compression of mechanical vibration signals. The signals are collected from both rotating and reciprocating machineries by the accelerometers and a data acquisition （DAQ） system. Four optimal sparse representation methods for compression have been considered including the method of frames （ MOF）, best orthogonal basis （ BOB）, matching pursuit （MP） and basis pursuit （BP）. Furthermore, several indicators including compression ratio （CR）, mean square error （MSE）, energy retained （ER） and Kurtosis are taken to evaluate the performance of the above methods. Experimental results show that MP outperforms other three methods.

A method to compress vibration signals using wavelet packet transformation combined with sub-band vector quantization

A novel compression method for mechanical vibrating signals,binding with sub-band vector quantization(SVQ) by wavelet packet transformation(WPT) and discrete cosine transformation(DCT) is proposed.Firstly,the vibrating signal is decomposed into sub-bands by WPT.Then DCT and adaptive bit allocation are done per sub-band and SVQ is performed in each sub-band.It is noted that,after DCT,we only need to code the first components whose numbers are determined by the bits allocated to that sub-band.Through an actual signal,our algorithm is proven to improve the signal-to-noise ratio(SNR) of the reconstructed signal effectively,especially in the situation of lowrate transmission.

Multimodal compression applied to biomedical data

In this paper, we introduce a novel approach to compress jointly a medical image and a multichannel bio-signals (e.g. ECG, EEG). This technique is based on the idea of Multimodal Compression (MC) which requires only one codec instead of multiple codecs. Objectively, biosignal samples are merged in the spatial domain of the image using a specific mixing function. Afterwards, the whole mixture is compressed using JPEG 2000. The spatial mixing function inserts samples in low-frequency regions, defined using a set of operations, including down-sampling, interpolation, and quad-tree decomposition. The decoding is achieved by inverting the process using a separation function. Results show that this technique allows better performances in terms of Compression Ratio (CR) compared to approaches which encode separately modalities. The reconstruction quality is evaluated on a set of test data using the PSNR (Peak Signal Noise Ratio) and the PRD (Percent Root Mean Square Difference), respectively for the image and biosignals.

A Hybrid Compression Method for Compound Power Quality Disturbance Signals in Active Distribution Networks

In the compression of massive compound power quality disturbance(PQD) signals in active distribution networks, the compression ratio(CR) and reconstruction error(RE) act as a pair of contradictory indicators, and traditional compression algorithms have difficulties in simultaneously satisfying a high CR and low RE. To improve the CR and reduce the RE, a hybrid compression method that combines a strong tracking Kalman filter(STKF), sparse decomposition, Huffman coding, and run-length coding is proposed in this study. This study first uses a sparse decomposition algorithm based on a joint dictionary to separate the transient component(TC) and the steady-state component(SSC) in the PQD. The TC is then compressed by wavelet analysis and by Huffman and runlength coding algorithms. For the SSC, values that are greater than the threshold are reserved, and the compression is finally completed. In addition, the threshold of the wavelet depends on the fading factor of the STKF to obtain a high CR. Experimental results of real-life signals measured by fault recorders in a dynamic simulation laboratory show that the CR of the proposed method reaches as high as 50 and the RE is approximately 1.6%, which are better than those of competing methods. These results demonstrate the immunity of the proposed method to the interference of Gaussian noise and sampling frequency.

Coherence-based performance analysis of the generalized orthogonal matching pursuit algorithm

The performance guarantees of generalized orthogonal matching pursuit（ gOMP） are considered in the framework of mutual coherence. The gOMP algorithmis an extension of the well-known OMP greed algorithmfor compressed sensing. It identifies multiple N indices per iteration to reconstruct sparse signals.The gOMP with N≥2 can perfectly reconstruct any K-sparse signals frommeasurement y = Φx if K 〈1/N（1/μ-1） ＋1,where μ is coherence parameter of measurement matrix Φ. Furthermore,the performance of the gOMP in the case of y = Φx ＋ e with bounded noise ‖e‖2≤ε is analyzed and the sufficient condition ensuring identification of correct indices of sparse signals via the gOMP is derived,i. e.,K 〈1/N（1/μ-1）＋1-（2ε/Nμxmin） ,where x min denotes the minimummagnitude of the nonzero elements of x. Similarly,the sufficient condition in the case of G aussian noise is also given.

A Reducing Iteration Orthogonal Matching Pursuit Algorithm for Compressive Sensing

In recent years, Compressed Sensing（CS） has been a hot research topic. It has a wide range of applications, such as image processing and speech signal processing owing to its characteristic of removing redundant information by reducing the sampling rate. The disadvantage of CS is that the number of iterations in a greedy algorithm such as Orthogonal Matching Pursuit（OMP） is fixed, thus limiting reconstruction precision.Therefore, in this study, we present a novel Reducing Iteration Orthogonal Matching Pursuit（RIOMP） algorithm that calculates the correlation of the residual value and measurement matrix to reduce the number of iterations.The conditions for successful signal reconstruction are derived on the basis of detailed mathematical analyses.When compared with the OMP algorithm, the RIOMP algorithm has a smaller reconstruction error. Moreover, the proposed algorithm can accurately reconstruct signals in a shorter running time.

Reconfigurable single-shot incoherent optical signal processing system for chirped microwave signal compression

We propose and demonstrate a reconfigurable and single-shot incoherent optical signal processing system for chirped microwave signal compression, using a programmable optical filter and a multiwavelength laser(MWL). The system is implemented by temporally modulating a specially shaped MWL followed by a suitable linear dispersive medium. A microwave dispersion value up to 1.33 ns/GHz over several GHz bandwidth is achieved based on this approach. Here we demonstrate a singleshot compression for different linearly chirped microwave signals over several GHz bandwidth. In addition, the robustness of the proposed system when input RF signals are largely distorted is also discussed.

Construction of compressed sensing matrixes based on the singular pseudo-symplectic space over finite fields

Compressed sensing（CS） provides a new approach to acquire data as a sampling technique and makes it sure that a sparse signal can be reconstructed from few measurements. The construction of compressed matrixes is a central problem in compressed sensing. This paper provides a construction of deterministic CS matrixes, which are also disjunct and inclusive matrixes, from singular pseudo-symplectic space over finite fields of characteristic 2. Our construction is superior to De Vore＇s construction under some conditions and can be used to reconstruct sparse signals through an efficient algorithm.