Subjects: Computer Science >> Computer Application Technology submitted time 2023-02-15 Cooperative journals: 《桂林电子科技大学学报》
Abstract： Aiming at the situation of uneven graph frequency distribution, a design method of non-uniform graph filter banks
is proposed. Firstly, according to the property of graph frequency distribution, the non-uniform analysis filter of well frequency
selection characteristics and well sparse property in vertex domain is need to be designed. The method of it is that design
the non-polynomial form filter with low order by approximating the polynomial form with high order. Secondly, given
the non-uniform analysis filter and sub-band signal, the reconstruction problem could be formulated a least square problem.
To avoid the high calculation cost of matrix inverse in this optimization when graph is with large scale, a precondition gradient
descent method is proposed to solve this problem and which can be implemented in distributed manner. Numerical results
show that the non-uniform graph filter banks proposed in this paper can achieve perfect reconstruction and have well
frequency selection characteristic and localized property in vertex domain. Compared with existing iteration methods, the
proposed algorithm has the faster convergence rate and lower calculation cost.
Subjects: Computer Science >> Computer Application Technology submitted time 2023-02-15 Cooperative journals: 《桂林电子科技大学学报》
Abstract： Critically sampled graph filter banks with spectral domain sampling requires to perform eigendecomposition of the
Laplacian matrix, which leads to high computational complexity. To solve this problem, an improved Jacobi algorithm is
proposed to approximate the eigenmatrix of the framework to reduce the computational complexity. In this algorithm, the
approximate solution of eigenmatrix is formulated into a constrained optimization problem, whose objective function is the
approximation error of Laplacian matrix, and the constraint function is the sparse orthogonality of the approximate eigenmatrix.
Theoretical and simulation experiments show that using the approximate feature matrix in the filter banks will not destroy
its perfect reconstruction conditions. Compared with the existing critically sampled graph filter banks with spectral domain
sampling, the improved algorithm reduces the computational complexity while maintaining good denoise performance.
Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science submitted time 2023-02-14 Cooperative journals: 《桂林电子科技大学学报》
Abstract： The reconstruction problem of spatio-temporal signals can be cast as recovering differential smooth time-varying
graph signals. For the optimization problem, the existing distributed algorithm based on gradient descent method shows
slow convergence when the condition number of the Hessian matrix of the problem is large which leads to a large reconstruction
error when the maximum iteration number is limited in an observation interval. Therefore, an online distributed reconstruction
algorithm based on approximate Newton's method is proposed in the paper, whose principle is to decompose the
original optimization problem into a series of local problems on subgraphs through subgraph decomposition and find these
solutions, and then obtain the approximate global optimal solution via fusion average of local solutions between each subgraph.
According to the gap between the approximate solution and the actual one, it can be proved that the decompostion
and fusion matrix obtained in this way is sparse and can be regarded as the approximate Hessian inverse. Hence, the algorithm
replaces the approximate matrix into the classical Newton iterative formula which can be implemented in a distributed
manner due to the structural sparsity of the approximate matrix. Simulation results show that the proposed algorithm has
faster convergence rate and smaller reconstruction error, and requires less communication cost compared with the existing
algorithm.
Subjects: Information Science and Systems Science >> Systematic Application of Information Technology submitted time 2022-09-27 Cooperative journals: 《桂林电子科技大学学报》
Abstract： Classification that assigns label for pixel in HSI dataset is an important pre-processed method in hyperspectral image (HSI) processing, label information is useful for application such as recognition and exploration. A graph based semisupervised classification method is proposed to tackle problems of large data volume, high data dimension, and small known sample size in HSI classification task. Dataset was modeled with graph for dimensional reducing, then the task is formulated as an unconstrained optimization problem in this method. Matrix inverse is inevitable for solving such problem, and complexity would increase with large scale. In order to avoid large scale matrix inversion, a quasi-Newton method which approximates inversion operation according to decomposition of Hessian matrix is used, such method can be implemented in distributed manner. Simulations demonstrate that, compared with existing methods, proposed algorithm has lower complexity and higher accuracy in large scale and multi-class HSI classification task.
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