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135 results about "Circulant matrix" patented technology

In linear algebra, a circulant matrix is a special kind of Toeplitz matrix where each row vector is rotated one element to the right relative to the preceding row vector. In numerical analysis, circulant matrices are important because they are diagonalized by a discrete Fourier transform, and hence linear equations that contain them may be quickly solved using a fast Fourier transform. They can be interpreted analytically as the integral kernel of a convolution operator on the cyclic group Cₙ and hence frequently appear in formal descriptions of spatially invariant linear operations.

Image Reconstruction Methods Based on Block Circulant System Matrices

An iterative image reconstruction method used with an imaging system that generates projection data, the method comprises: collecting the projection data; choosing a polar or cylindrical image definition comprising a polar or cylindrical grid representation and a number of basis functions positioned according to the polar or cylindrical grid so that the number of basis functions at different radius positions of the polar or cylindrical image grid is a factor of a number of in-plane symmetries between lines of response along which the projection data are measured by the imaging system; obtaining a system probability matrix that relates each of the projection data to each basis function of the polar or cylindrical image definition; restructuring the system probability matrix into a block circulant matrix and converting the system probability matrix in the Fourier domain; storing the projection data into a measurement data vector; providing an initial polar or cylindrical image estimate; for each iteration; recalculating the polar or cylindrical image estimate according to an iterative solver based on forward and back projection operations with the system probability matrix in the Fourier domain; and converting the polar or cylindrical image estimate into a Cartesian image representation to thereby obtain a reconstructed image.
Owner:SOCPRA SCI SANTE & HUMAINES S E C

Image reconstruction methods based on block circulant system matrices

An iterative image reconstruction method used with an imaging system that generates projection data, the method comprises: collecting the projection data; choosing a polar or cylindrical image definition comprising a polar or cylindrical grid representation and a number of basis functions positioned according to the polar or cylindrical grid so that the number of basis functions at different radius positions of the polar or cylindrical image grid is a factor of a number of in-plane symmetries between lines of response along which the projection data are measured by the imaging system; obtaining a system probability matrix that relates each of the projection data to each basis function of the polar or cylindrical image definition; restructuring the system probability matrix into a block circulant matrix and converting the system probability matrix in the Fourier domain; storing the projection data into a measurement data vector; providing an initial polar or cylindrical image estimate; for each iteration; recalculating the polar or cylindrical image estimate according to an iterative solver based on forward and back projection operations with the system probability matrix in the Fourier domain; and converting the polar or cylindrical image estimate into a Cartesian image representation to thereby obtain a reconstructed image.
Owner:SOCPRA SCI SANTE & HUMAINES S E C

Circulant matrix transformation based and ciphertext computation supportive encryption method

The invention discloses a circulant matrix transformation based and ciphertext computation supportive encryption method. The method includes the steps: firstly, encrypting original data by means of converting the original data into vectors, then converting the vectors into a circulant matrix and encrypting through a key matrix to obtain an encrypted outsourcing matrix; secondly, encrypting computational parameters by means of converting the computational parameters into vectors, then converting the vectors into a circulant matrix and encrypting through a key matrix to obtain an encrypted computational parameter matrix; thirdly, performing arithmetic operation of an encrypting matrix to obtain an encrypted operation result; fourthly, decrypting the encrypted operation result through the key matrix to obtain a circulant matrix, and then selecting one line / column of the circulant matrix to be added to obtain a plaintext of the operation result. The method is particularly suitable for outsourcing storage and computation of confidential data in a cloud computing environment, and can be used for protecting the confidential data of persons or enterprises; the method is supportive to four-rule hybrid operation of infinite addition, subtraction, multiplication and division of encrypted numerical data.
Owner:XI AN JIAOTONG UNIV

Approximation optimization and signal acquisition reconstruction method for 0-1 sparse cyclic matrix

The invention discloses an approximation optimization and signal acquisition reconstruction method for a 0-1 sparse cyclic matrix, belongs to the technical field for the design and optimization of measurement matrix in compressive sensing, and provides a posteriori optimizing method which is easy to implement by hardware and can ensure signal reconstruction effect, wherein the 0-1 sparse cyclic matrix is adopted in the measurement stage, and a Gaussian matrix is adopted in the reconstruction stage. The method comprises the following steps: orthonormalizing the row vector and unitizing the column vector of the measurement matrix obtained by the i-1th iteration by the ith iteration; and optimizing the 0-1 sparse cyclic matrix by taking the maximum value of the absolute value of the correlated coefficient between each row and column vector, the convergence stability of each row vector module and the row and column number of each row and column subjected to Gaussian distribution as the criteria. The posteriori optimization of the measured data and measured matrix is completed by solving a transition matrix and an approximate matrix. The method establishes the foundation for the compressive sensing to be practical from the theoretical study.
Owner:GUANGXI UNIVERSITY OF TECHNOLOGY

Multi-mechanism mixed recurrent neural network model compression method

The invention discloses a multi-mechanism mixed recurrent neural network model compression method. The multi-mechanism mixed recurrent neural network model compression method comprises A, carrying outcirculant matrix restriction: restricting a part of parameter matrixes in the recurrent neural network into circulant matrixes, and updating a backward gradient propagation algorithm to enable the network to carry out batch training of the circulant matrixes, B, carrying out forward activation function approximation: replacing a non-linear activation function with a hardware-friendly linear function during the forward operation process, and keeping the backward gradient updating process unchanged; C, carrying out hybrid quantization: employing different quantification mechanisms for differentparameters according to the error tolerance difference between different parameters in the recurrent neural network; and D, employing a secondary training mechanism: dividing network model training into two phases including initial training and repeated training. Each phase places particular emphasis on a different model compression method, interaction between different model compression methodsis well avoided, and precision loss brought by the model compression method is reduced to the maximum extent. According to the invention, a plurality of model compression mechanisms are employed to compress the recurrent neural network model, model parameters can be greatly reduced, and the multi-mechanism mixed recurrent neural network model compression method is suitable for a memory-limited andlow-delay embedded system needing to use the recurrent neural network, and has good innovativeness and a good application prospect.
Owner:南京风兴科技有限公司
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