Robust Watermarking Algorithm for Medical Images Based on Non-Subsampled Shearlet Transform and Schur Decomposition

With the development of digitalization in healthcare,more and more information is delivered and stored in digital form,facilitating people’s lives significantly.In the meanwhile,privacy leakage and security issues come along with it.Zero watermarking can solve this problem well.To protect the security of medical information and improve the algorithm’s robustness,this paper proposes a robust watermarking algorithm for medical images based on Non-Subsampled Shearlet Transform(NSST)and Schur decomposition.Firstly,the low-frequency subband image of the original medical image is obtained by NSST and chunked.Secondly,the Schur decomposition of low-frequency blocks to get stable values,extracting the maximum absolute value of the diagonal elements of the upper triangle matrix after the Schur decom-position of each low-frequency block and constructing the transition matrix from it.Then,the mean of the matrix is compared to each element’s value,creating a feature matrix by combining perceptual hashing,and selecting 32 bits as the feature sequence.Finally,the feature vector is exclusive OR(XOR)operated with the encrypted watermark information to get the zero watermark and complete registration with a third-party copyright certification center.Experimental data show that the Normalized Correlation(NC)values of watermarks extracted in random carrier medical images are above 0.5,with higher robustness than traditional algorithms,especially against geometric attacks and achieve watermark information invisibility without altering the carrier medical image.

Joint eigenvalue estimation by balanced simultaneous Schur decomposition

The problem of joint eigenvalue estimation for the non-defective commuting set of matrices A is addressed. A procedure revealing the joint eigenstructure by simultaneous diagonalization of. A with simultaneous Schur decomposition （SSD） and balance procedure alternately is proposed for performance considerations and also for overcoming the convergence difficulties of previous methods based only on simultaneous Schur form and unitary transformations, it is shown that the SSD procedure can be well incorporated with the balancing algorithm in a pingpong manner, i. e., each optimizes a cost function and at the same time serves as an acceleration procedure for the other. Under mild assumptions, the convergence of the two cost functions alternately optimized, i. e., the norm of A and the norm of the left-lower part of A is proved. Numerical experiments are conducted in a multi-dimensional harmonic retrieval application and suggest that the presented method converges considerably faster than the methods based on only unitary transformation for matrices which are not near to normality.

Studying turbulence structure near the wall in hydrodynamic flows:An approach based on the Schur decomposition of the velocity gradient tensor

The Schur decomposition of the velocity gradient tensor(VGT)is an alternative to the classical Cauchy-Stokes decomposition into rotation rate and strain rate components.Recently,there have been several strands of work that have employed this decomposition to examine the physics of turbulence dynamics,including approaches that combine the Schur and Cauchy-Stokes formalisms.These are briefly reviewed before the latter approach is set out.This partitions the rotation rate and strain rate tensors into normal/local and non-normal/non-local contributions.We then study the relation between the VGT dynamics and ejection-sweep events in a channel flow boundary-layer.We show that the sweeps in particular exhibit novel behaviour compared with either the other quadrants,or the flow in general,with a much-reduced contribution to the dynamics from the non-normal terms above the viscous sub-layer.In particular,the reduction in the production term that is the interaction between the non-normality and the normal straining reduces in the log-layer as a consequence of an absence of alignment between the non-normal vorticity and the strain rate eigenvectors.There have been early forays into using the Schur transform approach for subgrid-scale modelling in large-eddy simulation(LES)and this would appear to be an exciting way forward.

Application of Zero-Watermarking for Medical Image in Intelligent Sensor Network Security

The field of healthcare is considered to be the most promising application of intelligent sensor networks.However,the security and privacy protection ofmedical images collected by intelligent sensor networks is a hot problem that has attracted more and more attention.Fortunately,digital watermarking provides an effective method to solve this problem.In order to improve the robustness of the medical image watermarking scheme,in this paper,we propose a novel zero-watermarking algorithm with the integer wavelet transform(IWT),Schur decomposition and image block energy.Specifically,we first use IWT to extract low-frequency information and divide them into non-overlapping blocks,then we decompose the sub-blocks by Schur decomposition.After that,the feature matrix is constructed according to the relationship between the image block energy and the whole image energy.At the same time,we encrypt watermarking with the logistic chaotic position scrambling.Finally,the zero-watermarking is obtained by XOR operation with the encrypted watermarking.Three indexes of peak signal-to-noise ratio,normalization coefficient(NC)and the bit error rate(BER)are used to evaluate the robustness of the algorithm.According to the experimental results,most of the NC values are around 0.9 under various attacks,while the BER values are very close to 0.These experimental results show that the proposed algorithm is more robust than the existing zero-watermarking methods,which indicates it is more suitable for medical image privacy and security protection.

A projection method and Kronecker product preconditioner for solving Sylvester tensor equations

The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor format,which needs less flops and storage than the standard projection method.The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product(NKP) preconditioner,which is easy to construct and is able to accelerate the convergence of the iterative solver.Numerical experiments are presented to show good performance of the approaches.

Homogeneous wavelets and framelets with the refinable structure

Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.