Image Compressive Sampling And Its Application Based On Chaotic Sensing Matrix

Image sampling technology is the prerequisite for image compression,transmission and storage,as well as human advanced cognitive behavior including image understanding,classification and reasoning.However,the traditional Shannon-Nyquist sampling theorem is hard to cope with the increasing demand for image resolution in the era of “big data”,and it cannot effectively fit the resource allocation of hardware devices.Therefore,people always expect to seek a “hardware compression” image sampling theory in order to break through the limitation of traditional sampling theorem and make more reasonable use of limited resources.Relying on the trilogy of compressive sampling(CS) theory,this paper takes the construction of chaotic sensing operator as the core research point and the efficient realization of image compressive imaging as the research goal,and aims at designing efficient,low-complexity and hardware-feasible image compressive sampling(ICS) technology based on chaotic sensing matrices.To realize the goal,we implement some exploratory and novel researches on theory and applications,respectively.First of all,we systematically and detailedly analyze the basic theory of CS including the sparse representation model of signal,the construction of sensing matrix,and the selection of underdetermined recovery algorithm.We focus on the connections between chaos theory and CS technology,which will achieve the cross fusion of nonlinear system,image processing,information theory and other related fields.Secondly,three efficient image compressive sampling algorithms based on chaotic sensing matrices are proposed from different perspectives,which can overcome the core defects of using traditional sensing operators in similar ICS frameworks.Based on the proposed chaotic compressive sampling algorithms,we construct two typical chaotic compressive imaging applications,which will provide a solid support of realizing ICS for real imaging applications.The main innovations are described below:· Because of the degradation problem of many chaotic systems,the sampling performance of the sensing matrix constructed by the iterative chaotic sequence is not ideal.Therefore,we propose to establish the chaotic sensing operator by using the chaotic stream generated by the topologically conjugate chaotic system(TCc S).The core idea is firstly to divide one of the two transformations of the TCc S to many sub-zones according to the continuous and invertible function.Then by matching sub-zone rather than adopting real value of an iteration,we can generate an infinite chaotic stream,which overcomes the degradation phenomenon incurred by the limited precision effects.As a result,the proposed approaches can solve the difficulty of realizing random sensing matrices in hardware and software,and also can effectively guarantee the efficiency of the corresponding ICS algorithm.· Considering that the row or column size of traditional binarization sensing matrix is limited,and the density of real-valued chaotic operator is high,we propose the construction of chaotic binary matrices with arbitrary size based on chaotic systems.Then the proposed sensing operator is applied to the ICS algorithm,and the sampling performance of the proposed algorithm is theoretically analyzed.Finally,the numerical analysis shows that the proposed ICS algorithm based on chaotic binary matrices has considerable advantages in terms of the computational complexity,memory cost and hardware implementation,compared with its counterparts.· In order to accelerate the data sampling process,shorten the recovery time and reduce the complexity of the algorithm,a structural chaotic sensing matrix is designed,which combines the merits of both structured random sensing matrix and real-valued chaotic construction.After that,we propose an ICS algorithm based on the proposed structural chaotic sensing operator.Experimental results indicate that the proposed algorithm can effectively shorten the running time of image recovery,and significantly reduce the complexity of data acquisition and reconstruction,which implies that it can surpass the traditional ICS algorithm.· Two typical compressive imaging applications including chaotic single pixel camera and chaotic CS-magnetic resonance imaging,are constructed,which directly solves the shortcomings of the traditional mode in these two kinds of compressive imaging applications,such as unfriendly hardware realization and huge memory demand.It shows the application prospect and potential value of chaotic ICS algorithms for compressive imaging applications.