Research On The Measurement Matrix And Adaptive Sampling Of Compressed Sensing Based On Fractional Chaos

In the era of rapid information growth,with the increasing demand for speed and efficiency of information acquisition,the theory of compressed sensing has flourished.Compressed sensing theory combines compression and sampling into one,projects high-dimensional signals into low-dimensional signals at the sampling frequency which is far below the Nyquist,and uses low-dimensional observations containing most of the information of the original signals to reconstruct precisely.At present,the influence of compressed sensing has penetrated into many fields such as imaging,wireless communication and biosensing,and it has shown broad application research prospects.In order to apply the theory of compressed sensing to practice better,this paper proposes a new method of measurment matrix construction and a new design scheme of adaptively assigning sampling rate.Firstly,the theory of compressed sensing and chaos theory are introduced.Nine kinds of fractional-order chaotic systems are studied,and the generated sequence is used to construct the measurement matrix of compressed sensing.When the chaotic system is in chaotic state,the chaotic characteristics are characterized by pseudo-randomness and initial value sensitivity.The sequence generated by the chaotic system is used to construct the measurement matrix of compressed sensing,which can improve the current situation that the reconstruction effect of some deterministic measurement matrix is not ideal,and also overcome the shortcomings of the uncertain elements of the stochastic class measurement matrix,large storage space and difficult hardware implementation.Compared with the integer order chaotic system,the fractional-order chaotic system has stronger memory function and can reflect the real situation in the real nature.Therefore,this paper applies the sequence generated by the fractional-order chaotic system to the measurement matrix of the compressed sensing.In this paper,the parameters and initial values of the classical nine fractional-order chaotic systems are set,and the chaotic sequence in chaotic state is obtained.The generated sequence is selected and normalized,and then applied to the measurement matrix construction of compressed sensing.The simulation results are verified by using image signals.The results show that the reconstruction of the measurement matrix using fractional-order chaotic sequences can achieve accurate reconstruction.Then,a new measurement matrix is constructed based on the fractional-order lorentz chaos(FOLorenz)system.In this paper,the measurement matrix of fractional-order chaotic cyclic convolution(CCCMM)is constructed by combining cyclic matrix,fractional-order lorentz chaotic sequence and convolution.The appropriate sampling interval of FOLorenz sequence generated is selected by Pearson correlation coefficient method,and it convolves with the cyclic matrix generated to construct the CCCMM.The CCCMM not only inherits the advantages of easy calculation of cyclic matrix and easy implementation on hardware,but also takes advantage of the pseudo-random fractional chaos to obtain accurate reconstructed signals,and at the same time gives consideration to the advantages of smoothing effect of convolution operation.The measurement matrix constructed in this paper is also proved to satisfy the restricted isometry property(RIP)with high probability.The simulation results show that the overall performance of CCCMM is better than that of using traditional measurement matrix.Finally,a new adaptive sampling rate allocation algorithm is proposed based on image segmentation.It not only not increases the total number of samples,but also obtains more accurate reconstructed signals,which means that means that the sampling rate needs to be reasonably automatic allocated.This paper calculates the eigenvalues of histogram of oriented gradient(HOG)for 500 images,and finds the number of values greater than a given limit.Then the image is reconstructed,the sampling rate is recorded when the peak signal-to-noise ratio reaches the lowest value set,furthermore,polynomial fitting is performed on the two sets of data to obtain the appropriate expression curve.After the signal is divided into blocks,adaptive sampling can be carried out by using this fitting formula.The simulation experiment shows that the performance of the adaptive sampling algorithm designed in this paper is very ideal in terms of objective evaluation index and subjective visual effect.