Application of Stochastic Resonance Signal Recovery

Stochastic resonance（SR） enhances the nonlinear system behavior with the assistance of noise, including the sensitivity and selectivity of the response to the exterior stimulus. The energy-transfer mechanism makes the weak information revealed in the output spectrum, while the time-waveform is distorted. The distortion analysis was made both from the particle＇s dynan-fics and signal processing. The factors causing the deviation in the output are presented and the function of the recovery system is proposed. By the investigation of the particle＇s motion track in the bistable system and the suggested recovery system, the influences of noise and system parameters on the recovery course were discussed. Moreover, the pulse distortion appearing the recovery waveform caused by the particle＇s transitions at the bistable potential＇ inflexions was explained. Due to different characteristics, cascaded-bistable SR or mono-stable SR was introduced to process different types of signals. The final recovery signal is just the suggested recovery system＇s response to the SR output. Meanwhile, the recovery system is optional, as parameter-tuned or parameter-fixed. Since the method requires no average processing, it is applicable to a single sample with limited length. The numerical simulations reveal that the SR recovery method can recover the waveform containing weak information submerged ha noise effectively. The engineering application to the vibration analysis of metal cutting chose the combination of mono-stable SR and the parameter-fixed recovery system. Because the optimal SR state is not required strongly, the system parameters are tuned in a wider range than the traditional SR processing methods.

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.

Pulse Signal Recovery Method Based on Sparse Representation

Pulse signal recovery is to extract useful amplitude and time information from the pulse signal contaminated by noise. It is a great challenge to precisely recover the pulse signal in loud background noise. The conventional approaches,which are mostly based on the distribution of the pulse energy spectrum,do not well determine the locations and shapes of the pulses. In this paper,we propose a time domain method to reconstruct pulse signals. In the proposed approach,a sparse representation model is established to deal with the issue of the pulse signal recovery under noise conditions. The corresponding problem based on the sparse optimization model is solved by a matching pursuit algorithm. Simulations and experiments validate the effectiveness of the proposed approach on pulse signal recovery.

REQUIRED NUMBER OF ITERATIONS FOR SPARSE SIGNAL RECOVERY VIA ORTHOGONAL LEAST SQUARES

In countless applications,we need to reconstruct a K-sparse signal x∈R n from noisy measurements y=Φx+v,whereΦ∈R^(m×n)is a sensing matrix and v∈R m is a noise vector.Orthogonal least squares(OLS),which selects at each step the column that results in the most significant decrease in the residual power,is one of the most popular sparse recovery algorithms.In this paper,we investigate the number of iterations required for recovering x with the OLS algorithm.We show that OLS provides a stable reconstruction of all K-sparse signals x in[2.8K]iterations provided thatΦsatisfies the restricted isometry property(RIP).Our result provides a better recovery bound and fewer number of required iterations than those proposed by Foucart in 2013.

DOA estimation in unknown colored noise using covariance differencing and sparse signal recovery

A direction-of-arrival （DOA） estimation algorithm is presented based on covariance differencing and sparse signal recovery, in which the desired signal is embedded in noise with unknown covariance. The key point of the algorithm is to eliminate the noise component by forming the difference of original and transformed covariance matrix, as well as cast the DOA estimation considered as a sparse signal recovery problem. Concerning accuracy and complexity of estimation, the authors take a vectorization operation on difference matrix, and further enforce sparsity by reweighted l1-norm penalty. We utilize data-validation to select the regularization parameter properly. Meanwhile, a kind of symmetric grid division and refinement strategy is introduced to make the proposed algorithm effective and also to mitigate the effects of limiting estimates to a grid of spatial locations. Compared with the covariance-differencing-based multiple signal classification （MUSIC） method, the proposed is of salient features, including increased resolution, improved robustness to colored noise, distinguishing the false peaks easily, but with no requiring of prior knowledge of the number of sources.

A Relaxed-PPA Contraction Method for Sparse Signal Recovery

Sparse signal recovery is a topic of considerable interest,and the literature in this field is already quite immense.Many problems that arise in sparse signal recovery can be generalized as a convex programming with linear conic constraints.In this paper,we present a new proximal point algorithm(PPA) termed as relaxed-PPA(RPPA) contraction method,for solving this common convex programming.More precisely,we first reformulate the convex programming into an equivalent variational inequality(VI),and then efficiently explore its inner structure.In each step,our method relaxes the VI-subproblem to a tractable one,which can be solved much more efficiently than the original VI.Under mild conditions,the convergence of the proposed method is proved.Experiments with l1 analysis show that RPPA is a computationally efficient algorithm and compares favorably with the recently proposed state-of-the-art algorithms.

STABLE RECOVERY OF SPARSELY CORRUPTED SIGNALS THROUGH JUSTICE PURSUIT DE-NOISING

This paper considers a corrupted compressed sensing problem and is devoted to recover signals that are approximately sparse in some general dictionary but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise.We provide new restricted isometry property(RIP)analysis to achieve stable recovery of sparsely corrupted signals through Justice Pursuit De-Noising(JPDN)with an additional parameter.Our main tool is to adapt a crucial sparse decomposition technique to the analysis of the Justice Pursuit method.The proposed RIP condition improves the existing representative results.Numerical simulations are provided to verify the reliability of the JPDN model.

WiFi Indoor Positioning and Tracking Algorithm Based on Compressive Sensing and Sage-Husa Adaptive Kalman Filter

Aiming at the problem that the positioning accuracy of WiFi indoor positioning technology based on location fingerprint has not reached the requirements of practical application, a WiFi indoor positioning and tracking algorithm combining adaptive affine propagation (AAPC), compressed sensing (CS) and Kalman filter is proposed. In the off-line phase, AAPC algorithm is used to generate clustering fingerprints with optimal clustering effect performance;In the online phase, CS and nearest neighbor algorithm are used for position estimation;Finally, the Kalman filter and physical constraints are combined to perform positioning and tracking. By collecting a large number of real experimental data, it is proved that the developed algorithm has higher positioning accuracy and more accurate trajectory tracking effect.

A NEW SUFFICIENT CONDITION FOR SPARSE RECOVERY WITH MULTIPLE ORTHOGONAL LEAST SQUARES

A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x∈R^(n).We show that MOLS provides stable reconstruction of all K-sparse signals x from y=Ax+w in|6K/ M|iterations when the matrix A satisfies the restricted isometry property(RIP)with isometry constantδ_(7K)≤0.094.Compared with the existing results,our sufficient condition is not related to the sparsity level K.

STABLE AND ROBUST RECOVERY OF APPROXIMATELY k-SPARSE SIGNALS WITH PARTIAL SUPPORT INFORMATION IN NOISE SETTINGS VIA WEIGHTED ℓ_(p)(0

In the existing work,the recovery of strictly k-sparse signals with partial support information was derived in theℓ2 bounded noise setting.In this paper,the recovery of approximately k-sparse signals with partial support information in two noise settings is investigated via weightedℓp(0<p≤1)minimization method.The restricted isometry constant(RIC)conditionδt k<1 pη2 p−1+1 on the measurement matrix for some t∈[1+2−p 2+pσ,2]is proved to be sufficient to guarantee the stable and robust recovery of signals under sparsity defect in noisy cases.Herein,σ∈[0,1]is a parameter related to the prior support information of the original signal,andη≥0 is determined by p,t andσ.The new results not only improve the recent work in[17],but also include the optimal results by weightedℓ1 minimization or by standardℓp minimization as special cases.

Stable recovery of signals from frame coefficients with erasures at unknown locations

In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy partial frame coefficients with erasures occurring at unknown locations. In this continuing work, we settle this problem by obtaining a complete characterization of frames that provide stable reconstructions. We show that an encoding frame provides a stable signal recovery from noisy partial frame coefficients at unknown locations if and only if it is totally robust with respect to erasures. We present several characterizations for either totally robust frames or almost robust frames. Based on these characterizations several explicit construction algorithms for totally robust and almost robust frames are proposed. As a consequence of the construction methods, we obtain that the probability for a randomly generated frame to be totally robust with respect to a fixed number of erasures is one.

THE EXACT RECOVERY OF SPARSE SIGNALS VIA ORTHOGONAL MATCHING PURSUIT

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit （OMP） algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all k-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is also presented. Generally, the computation for the restricted isometry constant （RIC） in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all k-sparse signals.

Multi-static InISAR imaging for ships under sparse aperture

This paper concentrates on super-resolution imaging of the ship target under the sparse aperture situation.Firstly,a multi-static configuration is utilized to solve the coherent processing interval(CPI)problem caused by the slow-speed motion of ship targets.Then,we realize signal restoration and image reconstruction with the alternating direction method of multipliers(ADMM).Furthermore,we adopt the interferometric technique to produce the three-dimensional(3D)images of ship targets,namely interferometric inverse synthetic aperture radar(InISAR)imaging.Experiments based on the simulated data are utilized to verify the validity of the proposed method.

Houshiheisan and its components promote axon regeneration after ischemic brain injury

Houshiheisan,a classic prescription in traditional Chinese medicine,contains Flos Chrysanthemi,Radix Saposhnikoviae,Ramulus Cinnamomi,Rhizoma Chuanxiong,Radix et Rhizoma Asari,Radix Platycodonis,Rhizoma Atractylodis macrocephalae,Poria,Rhizoma Zingiberis,Radix Angelicae sinensis,Radix et Rhizoma Ginseng,Radix Scutellariae and Concha Ostreae.According to traditional Chinese medicine theory,Flos Chrysanthemi,Radix Saposhnikoviae,Ramulus Cinnamomi,Rhizoma Chuanxiong,Radix et Rhizoma Asari and Radix Platycodonis are wind-dispelling drugs;Rhizoma Atractylodis macrocephalae,Poria,Rhizoma Zingiberis,Radix Angelicae sinensis and Radix et Rhizoma Ginseng are deficiency-nourishing drugs.A large number of randomized controlled trials have shown that Houshiheisan is effective in treating stroke,but its mechanism of action is unknown.Axonal remodeling is an important mechanism in neural protection and regeneration.Therefore,this study explored the effect and mechanism of action of Houshiheisan on the repair of axons after cerebral ischemia.Rat models of focal cerebral ischemia were established by ligating the right middle cerebral artery.At 6 hours after model establishment,rats were intragastrically administered 10.5 g/kg Houshiheisan or 7.7 g/kg wind-dispelling drug or 2.59 g/kg deficiency-nourishing drug.These medicines were intragastrically administered as above every 24 hours for 7 consecutive days.Houshiheisan,and its wind-dispelling and deficiency-nourishing components reduced the neurological deficit score and ameliorated axon and neuron lesions after cerebral ischemia.Furthermore,Houshiheisan,and its wind-dispelling and deficiency-nourishing components decreased the expression of proteins that inhibit axonal remodeling：amyloid precursor protein,neurite outgrowth inhibitor protein A（Nogo-A）,Rho family small GTPase A（Rho A） and Rho-associated kinase 2（Rock2）,and increased the expression of growth associated protein-43,microtubule-associated protein-2,netrin-1,Ras-related C3 botulinum toxin substrate 1（Rac1） and cell division cycle 42（Cdc42）.The effect of Houshiheisan was stronger than wind-dispelling drugs or deficiency-nourishing drugs alone.In conclusion,Houshiheisan,and wind-dispelling and deficiency-nourishing drugs promote the repair of axons and nerve regeneration after cerebral ischemia through Nogo-A/Rho A/Rock2 and Netrin-1/Rac1/Cdc42 signaling pathways.These effects are strongest with Houshiheisan.

Tone Modulation in a Passive OTDM Multiplexer for Clock Recovery from a 160 Gbit/s OTDM Signal

Tone modulation in a passive OTDM multiplexer for clock recovery from a 160-Gbit/s OTDM signal by using a base-rate receiver is demonstrated. We performed synchronous demultiplexing in back-to-back arrangement and optical sampling after 320-km transmission.

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.

Sparse recovery method for far-field and near-field sources localization using oblique projection

In this paper, we propose a novel source localization method to estimate parameters of arbitrary field sources, which may lie in near-field region or far-field region of array aperture. The proposed method primarily constructs two special spatial-temporal covariance matrixes which can avoid the array aperture loss, and then estimates the frequencies of signals to obtain the oblique projection matrixes. By using the oblique projection technique, the covariance matrixes can be transformed into several data matrixes which only contain single source information, respectively. At last, based on the sparse signal recovery method, these data matrixes are utilized to solve the source localization problem. Compared with the existing typical source localization algorithms, the proposed method improves the estimation accuracy, and provides higher angle resolution for closely spaced sources scenario. Simulation results are given to demonstrate the performance of the proposed algorithm.

Quantitative Uncertainty Principles for the Canonical Fourier-Bessel Transform

The aim of this paper is to establish an extension of quantitative uncertainty principles and an algorithm for signal recovery about the essential supports related to a Bessel type of(LCT)so called canonical Fourier-Bessel transform.

Fractional Fourier transform on R^(2)and an application

We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the pointwise convergence for the inverse FRFT,we introduce the fractional convolution and establish the corresponding approximate identities.Then the well-defined inverse FRFT is given via approximation by suitable means,such as fractional Gauss means and Able means.Furthermore,if the signal F_(α,β)f is received,we give the process of recovering the original signal f with MATLAB.In L^(2)(R^(2)),the general Plancherel theorem,direct sum decomposition,and the general Heisenberg inequality for the FRFT are obtained.