RELATIVE ASYMPTOTICS FOR ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO A PERTURBED MATRIX MEASURE ON THE UNIT CIRCLE

Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I.

Generation and Display System of Measurement Matrix Based on DMD

A measurement matrix is the key to sampling and signal reconstruction during the process of compressed sensing.On the basis of digital light processing(DLP)technology,ageneration and display system of measurement matrix based on digital micro-mirror device(DMD)is proposed and well designed.In this system,the generation and controlling of measurement matrix are implemented on a PC,which reduces the hardware requirement to generate a random matrix and overcomes the difficulty of the hardware implementation for the random matrix.It can set up the display number of the measurement matrix,the mode of display and display time according to the requirements from users.The display information can be designed to complete the display of measurement matrix with a better adaptability.The system can be easily embedded into a variety of compressed sensing applications,which can be used to generate and display the corresponding measurement matrice with strong portability.In addition,the DMD of this system will be used as a spatial optical modulator to manipulate near-infrared light in a fast,accurate and efficient way in several applications such as in 3D scanning devices and spectrometers.

The comprehensive measure model for urban traffic congestion based on value function

According to the distribution characteristics of traffic congestion in time and space, a measure index system of urban traffic congestion is set up based on the spatial and temporal distribution. Based on the analysis of the main characteristics of traffic congestion and the generation process of traffic congestion, the measure model for urban traffic congestion is constructed by the value function. Moreover, based on the measure values of traffic congestion in urban road networks with defined different levels, a method to prevent and control traffic congestion is designed. The application results confirm that the proposed method is feasible in comprehensive measures for urban traffic congestion and they are consistent with the results of other methods. The measuring results can therefore reflect the actual situation. The comprehensive measure model is scientific and the process is simple, and it has wide application prospects and practical value.

Near optimal condition of OMP algorithm in recovering sparse signal from noisy measurement

This paper analyzes the performance of the orthogonal matching pursuit （OMP） algorithm in recovering sparse signals from noisy measurement. Considering the fact that some matrices satisfy some restricted isometry properties （RIPs） but not the coherence condition, a superior RIP-based condition is proposed, which means that if the measurement matrix satisfies δk＋1 〈 1/（2 ＋ √k） and the minimum component signal-to-noise ratio （MCSNR） is bounded, the OMP algorithm can exactly identify the support of the original sparse signal within k iterations. Finally, the theoretical results are verified by numerical simulations con- cerning different values of MCSNR and noise levels.

Exponential stability of switched systems with impulsive effect

The exponential stability of a class of switched systems containing stableand unstable subsystems with impulsive effect is analyzed by using the matrix measure concept andthe average dwell-time approach. It is shown that if appropriately a large amount of the averagedwell-time and the ratio of the total activation time of the subsystems with negative matrix measureto the total activation time of the subsystems with nonnegative matrix measure is chosen, theexponential stability of a desired degree is guaranteed.Using the proposed switching scheme, westudied the robust exponential stability for a class of switched systems with impulsive effect andstructure perturbations.Simulations validate the main results.

EXPONENTIAL STABILITY OF INTERVAL DYNAMICAL SYSTEM WITH MULTIDELAY

Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.

New multi-camera calibration algorithm based on 1D objects

A new calibration algorithm for multi-camera systems using 1D calibration objects is proposed. The algorithm inte- grates the rank-4 factorization with Zhang (2004)'s method. The intrinsic parameters as well as the extrinsic parameters are re- covered by capturing with cameras the 1D object's rotations around a fixed point. The algorithm is based on factorization of the scaled measurement matrix, the projective depth of which is estimated in an analytical equation instead of a recursive form. For more than three points on a 1D object, the approach of our algorithm is to extend the scaled measurement matrix. The obtained parameters are finally refined through the maximum likelihood inference. Simulations and experiments with real images verify that the proposed technique achieves a good trade-off between the intrinsic and extrinsic camera parameters.

The signal selection and processing method for polarization measurement radar

Based on the ambiguity function, a novel signal processing method for the polarization measurement radar is developed. One advantage of this method is that the two orthogonal polarized signals do not have to be perpendicular to each other, which is required by traditional methods. The error due to the correlation of the two transmitting signals in the traditional method, can be reduced by this new approach. A concept called ambiguity function matrix （AFM） is introduced based on this method. AFM is a promising tool for the signal selection and design in the polarization scattering matrix measurement. The waveforms of the polarimetric radar are categorized and analyzed based on AFM in this paper. The signal processing flow of this method is explained. And the polarization scattering matrix measurement performance is testified by simulation. Furthermore, this signal processing method can be used in the inter-pulse interval measurement technique as well as in the instantaneous measurement technique.

A survey on distributed compressed sensing： theory and applications

The compressed sensing （CS） theory makes sample rate relate to signal structure and content. CS samples and compresses the signal with far below Nyquist sampling frequency simultaneously. However, CS only considers the intra-signal correlations, without taking the correlations of the multi-signals into account. Distributed compressed sensing （DCS） is an extension of CS that takes advantage of both the inter- and intra-signal correlations, which is wildly used as a powerful method for the multi-signals sensing and compression in many fields. In this paper, the characteristics and related works of DCS are reviewed. The framework of DCS is introduced. As DCS＇s main portions, sparse representation, measurement matrix selection, and joint reconstruction are classified and summarized. The applications of DCS are also categorized and discussed. Finally, the conclusion remarks and the further research works are provided.

Approximating the Spectral Abscissa for Switched Linear Systems via Coordinate Transformations

In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of minimums of least μ1 matrix set measures are obtained,which are utilized to approximate the spectral abscissa of the switched system.The approach is developed into tractable numerical algorithms that provide upper bound estimates of the spectral abscissa.Numerical simulations show the effectiveness of the proposed method.

Single Photon Compressive Imaging Based on Digital Grayscale Modulation Method

In single-pixel imaging or computational ghost imaging,the measurement matrix has a great impact on the performance of the imaging system,because it involves modulation of the optical signal and image reconstruction.The measurement matrix reported in the existing literatures is first binarized and then loaded onto the digital micro-mirror device(DMD)for optical modulation,that is,each pixel can only be modulated into on-off states.In this paper,we propose a digital grayscale modulation method for more efficient compressive sampling.On the basis of this,we demonstrate a single photon compressive imaging system.A control and counting circuit,based on field-programmable gate array(FPGA),is developed to control DMD to conduct digital grayscale modulation and count single-photon pulse output from the photomultiplier tube(PMT)simultaneously.The experimental results show that the imaging reconstruction quality can be improved by increasing the sparsity ratio properly and compressive sampling ratio(SR)of these gray-scale matrices.However,when the compressive SR and sparsity ratio are increased appropriately to a certain value,the reconstruction quality is usually saturated,and the imaging reconstruction quality of the digital grayscale modulation is better than that of binary modulation.

STABILITY ANALYSIS OF FUZZY DIFFERENTIAL EQUATIONS WITH DELAY

In this paper, the exponential stability of fuzzy differential equations with delay is investigated. By employing the formula for the variation of parameters, inequality technique and the norm and measure of matrix, an algebraic criterion for the exponential stability is obtained.

A Verifiable Secret Image Sharing Scheme Based on Compressive Sensing

This paper proposes a verifiable secret image sharing scheme based on compressive sensing, secret sharing, and image hashing. In this scheme, Toeplitz matrix generated by two chaotic maps is employed as measurement matrix. With the help of Shamir threshold scheme and image hashing, the receivers can obtain the stored values and the hash value of image. In the verifying stage and restoring stage, there must be at least t legal receivers to get the effective information. By comparing the hash value of the restored image with the hash value of original image, the scheme can effectively prevent the attacker from tampering or forging the shared images. Experimental results show that the proposed scheme has good recovery performance, can effectively reduce space, and is suitable for real-time transmission, storage, and verification.