During situations involving dangerous activities, such as armed robbery in public areas, surveillance systems often exhibit delays or inefficiencies in their prompt responding. To obviate the necessity for human invol...
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We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong...
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We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multiparameter regularization over the single parameter regularization.
In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarant...
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In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ1/2) for Tikhonov-Browder regularization, where δ denotes the noise level of the data perturbation.
This paper introduces a novel approach to store speech words after cutting the signals and decomposing them through Mallat’s decompostion algorithm, and generate a speech phrase by connecting such word data and recon...
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This paper presents a method for image compression. First, selecting some scattered data points on some lines of a plane to construct an interpolating spline surface approach to the image, then, one kind of wavelets f...
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In noise removal by the approach of regularization, the regularization parameter is global. Constructing the variational model min (Formula Presented) is in some wavelets space. Through the wavelets pyramidal decompos...
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The orthogonality in Hilbert spaces is extended to the general Banach spaces and a concrete shift-invariant orthogonal family in L^1(R) is constructed. The corresponding projection approximation theorems and the algor...
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The orthogonality in Hilbert spaces is extended to the general Banach spaces and a concrete shift-invariant orthogonal family in L^1(R) is constructed. The corresponding projection approximation theorems and the algorithms for signal decomposition and reconstruction are established.
In this paper we establish a high order finite volume method for the fourth order singular perturbation *** conjunction with the optimal meshes,the numerical solutions resulting from the method have optimal convergenc...
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In this paper we establish a high order finite volume method for the fourth order singular perturbation *** conjunction with the optimal meshes,the numerical solutions resulting from the method have optimal convergence *** experiments are presented to verify our theoretical estimates.
The focus of this paper is on the relationship between accuracy of multivariate refinable vector and vector cascade algorithm. We show that, if the vector cascade algorithm (1.5) with isotropic dilation converges to a...
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The focus of this paper is on the relationship between accuracy of multivariate refinable vector and vector cascade algorithm. We show that, if the vector cascade algorithm (1.5) with isotropic dilation converges to a vector-valued function with regularity, then the initial function must satisfy the Strang-Fix conditions.
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