46 results about "K matrix" patented technology

In a method and apparatus for accelerated spiral-coded imaging (scanning k-space with a spiral trajectory) in magnetic resonance tomography, the user-defined sequence forming the basis of the spiral scanning is modified such that the k-matrix forming the basis of the sequence is scanned only in a sub-region, the sub-region being defined by a symmetrical shortening on both sides of the k-space matrix in a first direction as well as by a one-sided shortening of the k-space matrix in a second direction orthogonal to the first direction.

In a method for magnetic resonance imaging, by combined switching of radio-frequency excitation pulses, slice selection gradient pulses, phase-coding gradient pulses and readout gradient pulses, a matrix in the k-space is scanned row-by-row and transformed using a Fourier transformation into a matrix in the spatial domain, with the polarity of the slice selection gradient being inverted during the scanning of the k-matrix, allowing elimination of the ambiguity artifact.

In a method and apparatus for accelerated spiral-coded imaging in magnetic resonance tomography using spiral-shaped k-space sampling, the underlying k-matrix is under-sampled such that an additional spiral is obtained by point mirroring of the measured values at the center of the k-matrix. This additional spiral forms a complete data set of the k-matrix together with the first spiral for imaging the output information.

A method of registering and modeling a deformable shape in a digitized image is provided, comprising the steps of providing a measurement matrix W of N measurements of P points of a D-dimensional deformable shape, determining a basis number K for the N measurements, wherein K<N, and selecting K measurements of said measurement matrix W as a basis set, decomposing said measurement matrix W into a matrix product M×∃B, wherein M is a proposed scaled rotation matrix and B is a proposed basis matrix, computing a matrix Qk defined byMi⁢Qk⁢MjT={ID×D,i=j=k0D×D,(i,j)∈Φ,where Φ stands for {(i, j)|i=1, . . . , K; j=1, . . . , N, iγk}, which represents an ambiguity matrix transforming the proposed scaled rotation matrix and the proposed basis matrix into a true scaled rotation matrix and a true basis matrix; decomposing the matrix Qk into gkgkT, for k=1, . . . , K, wherein gk is a column of a D∃K%D∃K matrix G; and recovering the true scaled rotation matrix from M×∃G and the true basis matrix from G−1×∃B.

Systems and methods that facilitate dimensional transformations of data points are disclosed. In particular, the subject invention provides for a system and methodology that simplifies dimensional transformations while mitigating variations of a distance property between pairs of points. A set of n data points in d dimensional space is represented as an n×d input matrix, where d also corresponds to the number of attributes per data point. A transformed matrix represents the n data points in a lower dimensionality k after being mapped. The transformed matrix is an n×k matrix, where k is the number of attributes per data point and is less than d. The transformed matrix is obtained by multiplying the input matrix by a suitable projection matrix. The projection matrix is generated by randomly populating the entries of the matrix with binary or ternary values according to a probability distribution. Unlike previous methods, the projection matrix is formed without obtaining an independent sample from a Gaussian distribution for each entry in the projection matrix, without applying a linear algebraic technique to generate the projection matrix and without employing arbitrary floating point numbers. Processes and / or algorithms can utilize the reduced transformed matrix instead of the larger input matrix to facilitate computational efficiency and data compression.

The present invention relates to a method for calculating the scanning path of the k-matrix, under given boundary conditions for the examination of a subject by means of a magnetic resonance tomography apparatus having a gradient amplifier with appertaining gradient coils, an input-display terminal, a sequence controller and a system computer as well as an analog-to-digital converter. The method has the following steps: entering the boundary conditions into the sequence controller or into the system computer via the input-display terminal; calculating the sampling path of the k-matrix taking the boundary conditions into consideration by the sequence controller or the system computer; and determining the gradient current curves by the sequence controller or the system computer that lead to a scanning along the previously calculated scanning path when applied to the corresponding gradient coils with utilization of the ADC.

The soil-water coupled analysis program of the invention computes a global L matrix and a modified global L matrix regarding a volume change rate of a soil skeleton over time, a global H matrix regarding a water permeability of soil, a global M matrix regarding a mass, and a global K matrix regarding a tangent stiffness of the soil skeleton, based on input settings of soils, such as clay, intermediate soil, and sand, to respective elements of a soil foundation, input settings of a solid soil model, and input settings of analysis conditions (steps S140 to S165). The soil-water coupled analysis program formulates a global tangent stiffness equation (simultaneous linear equations) using all these computed matrixes and determines an unknown ‘jerk field’ and a ‘pore water pressure field’ under given boundary conditions, for example, a given deformation condition and a given stress rate condition (step S170). This enables highly-accurate dynamic and static analyses in soil foundations of various soils from sand to intermediate soils and clay.

The invention relates to a method for online detection of the concentration of electrolyte of an all vanadium redox flow battery. A divalent vanadium V (II) system, a trivalent vanadium V (III) system and a tetravalent vanadium V (IV) system are analyzed by the aid of ultraviolet and visible spectrophotometry, a divalent vanadium V (II) and trivalent vanadium V (III) mixed system and a trivalent vanadium V (III) and tetravalent vanadium V (IV) mixed system are analyzed by the aid of a K matrix method, and a curve equation of the concentration of the vanadium with various valence states and absorbance in the systems is deduced. The concentration of vanadium ions with various valence states in a test sample can be rapidly detected only by substituting absorbance data of the test sample with unknown concentration in the electrolyte of the vanadium battery into the absorbance-concentration curve equation measured and deduced by the method, and accuracy of the method is proved as compared with a national standard method. The method has a huge application prospect in terms of dynamically monitoring valence changes of the electrolyte of the vanadium ions and simultaneously, qualitatively and quantitatively checking the vanadium electrolyte with mixed valence states.