129 results about "Toeplitz matrix" patented technology

The invention provides a signal DOA estimation method. The method supposes that an unknown noise covariance matrix has a symmetrical Toeplitz matrix character; according to the difference conception of the traditional covariance matrix, an imaginary number j is introduced so that the newly constructed covariance matrix changes into a central Hermitian matrix, thereby, the character decomposition can obtain the same DOA as the incident signal numbers. The method greatly reduces the number of the antenna array element required by estimating the signal wave arrival direction, and a wave crest is only formed in the wave arrival direction of the real signal. The method can reduce cost greatly in the practical application.

The invention discloses an evaluation method of the undetermined wave arrival direction of a non-uniform array. The problem of quite high computing complexity in the prior art is mainly solved. The evaluation method comprises steps of firstly constructing a virtual array by use of a covariance matrix for receiving array data; then obtaining observation data of a difference synthesis array by use of data of whole virtual array elements; then carrying out decorrelation by constructing a Toeplitz matrix used for observing data to replace the traditional space smooth operation and evaluating subspace of signals and noise; and at last using the subspace of the noise to construct a polynomial about a MUSIC spectrum and using the solution of the polynomial to evaluate wave arrival direction. Thus, angle grid searching with many computations is avoided; evaluation precision which is higher than that of the traditional SS-MUSIC algorithm can be obtained in a quite low computation complexity; and the evaluation method can be used for evaluating target directions.

The invention provides a seismic data reconstruction method based on a matrix reduced rank, and the method comprises the steps: obtaining a quadruple Toeplitz matrix built through the seismic frequency slicing data, and storing a part of rows and columns of elements of the quadruple Toeplitz matrix, so as to express the quadruple Toeplitz matrix, wherein the part of rows and columns of elements of the quadruple Toeplitz matrix comprises all different elements of the quadruple Toeplitz matrix; carrying out the reduced-rank processing of the quadruple Toeplitz matrix expressed by the part of rows and columns of elements of the quadruple Toeplitz matrix through employing a random QR reduced-rank decomposition algorithm, so as to carry out the reduced-rank processing of the quadruple Toeplitz matrix; solving the mean value of the diagonal elements of the quadruple Toeplitz matrix through a no-expansion averaging algorithm after reduced-rank processing, and obtaining the reconstruction data of the seismic frequency slicing data; carrying out the Fourier inversion of the reconstruction data of the seismic frequency slicing data, and obtaining the time domain seismic reconstruction data which is used for oil gas exploration. The method can reduce the data storage size and calculation burden, and does not reduce the reconstruction quality.

The invention discloses a verifiable and secure privacy amplification method based on quantum key distribution. The method comprises the steps of S1, generating an initial random number string W, respectively generating random number strings K<mis,A> and K<mis,B> by two communication parties (Alice and Bob) in a base comparison process of quantum key distribution, and combining the two random number strings into a random number string W=[<Kmis,A>, K<mis,B>] by the Alice; S2, verifying randomness, after an error correction phase of the quantum key distribution is finished, estimating the minimum entropy lower limit of the W relative to an attacker Eve, wherein H<min>(W|E) is greater than or equal to 1-H<2>(e); S3, calculating a final secure key length N<f>; S4, extracting a perfect random string W*, through adoption of a partial pre-shared secure key of the two communication parties, constructing a Toeplitz matrix H<R>, and extracting the perfect random number string W* from the W according to the H<R>; S5, negotiating a universal hash function H<PA> through a public channel according to the W*; and S6, respectively carrying out hash operation on error corrected key strings by the two communication parties according to the H<PA>, and generating a final secure key. The method has the advantages of verifiability, security, easy realization and simplification of quantum key distribution system design and realization.

The present invention relates to a narrowband near field signal source positioning method under non-uniform noise. The method comprises the steps of firstly utilizing a principal back-diagonal element for receiving an estimated value of a data array covariance matrix to eliminate the distance unknown quantity, constructing a toeplitz structure matrix, and transforming the non-uniform noise into the uniform noise; then using a direction of arrival estimation method to estimate the information source direction information on the constructed toeplitz matrix; finally, utilizing a second back-diagonal element for receiving the data array covariance matrix and the estimated value in a direction of arrival to construct the toeplitz structure matrix only containing the distance unknown quantity, and using the toeplitz structure matrix to obtain the estimated value of a narrowband near field signal source distance. The narrowband near field signal source positioning method under the non-uniform noise of the present invention effectively solves the problem that the noise is non-uniform when a near field signal source is positioned, is simple to calculate, and has good estimation performances both on the direction of arrival and the distance.

A method of computing an inversion (X) of a nearly Toeplitz n by n matrix (A). A perturbation matrix (E) is first determined such that the sum of the nearly Toeplitz matrix (A) and the perturbation matrix (E) is a Toeplitz matrix (T). The inversion is solved by solving the equation X=T−1(B+EX), where B is a vector or matrix of dimension n by m. An initial estimate X(0) is selected and estimates of the inversion X are iteratively computed through the recursion X(n−1)=T−1(B+EX(n)). The initial estimate X(0) may be equal to an inversion (T−1) of the Toeplitz matrix (T). The present invention may be utilized in a radio receiver to efficiently compute (1) a least-squares (LS) channel estimate, (2) minimum mean squared error (MMSE) prefilter coefficients for a decision feedback equalizer (DFE), or (3) an autoregressive (AR) noise-spectrum estimation from a finite number of observed noise samples.

A coded image system enables a user to recover an object scene from an encoded image. The coded the image system comprises: a physical object scene; an encoding logic creating an encoded image, the encoding logic including a programmable aperture mask spaced a distance away from the physical object scene to encode the encoded image via a doubly-Toeplitz matrix, the doubly-Toeplitz matrix including two one-dimensional vectors; and a decoding logic operatively coupled to the programmable aperture mask to decode the encoded image recovering a visual representation of the object scene from the encoded image.

The invention discloses a method for restoring a motion blurred image based on a total variational model and a neutral network, which mainly solves the problem existing in the prior method that the image cannot be accurately restored. The implementation process comprises the following steps of: (1) constructing a Toeplitz matrix; (2) working out gradients in horizontal and vertical directions; (3) initializing the neutral network; (4) working out a neuron output; (5) working out the output of the neutral network; (6) working out a first variation delta E1 of a network energy function; (7) if the neurons are completely updated, jumping to the step (4); otherwise, jumping to a step (8); (8) if the set iterations are reached, outputting a restoration result, otherwise jumping to a step (9); (9) working out a restoration error; (10) if the restoration error is smaller than the set error, outputting the restoration result, otherwise jumping to a step (11); (11) working out the current input bias matrix; (12) working out a second variation delta E2 of the network energy function; and (13) if the summation of the delta E1 and the delta E2 is less than 0, jumping to a step (2); if the summation of the delta E1 and the delta E2 is more than or equal to 0, jumping to the step (3); and if the delta E1 is equal to 0, outputting the restoration result. The method can obtain relatively accurate restored images, and be applied to the restoration of motion blurred images.

Disclosed in the present invention is a verifiable and secure privacy amplification method for quantum key distribution, comprising the steps of: S1. generating an initial random number string W, two communication parties (Alice and Bob) respectively generating random number strings Kmis,A and Kmis,B during the basis comparison process of quantum key distribution, and then Alice merging the two random number strings into a random number string W = [Kmis,A, Kmis,B]; S2. performing randomness verification: after an error correction stage of quantum key distribution ends, estimating the lower limit of the minimum entropy Hmin(W|E) ≥ 1-H2(e) of W with respect to an attacker Eve; S3. calculating a final security key length Nf; S4. extracting a perfect random string W*: by pre-sharing part of the security key between the two communication parties, constructing a Toeplitz matrix HR, and extracting a perfect random number string W* from W according to HR; S5. issuing a negotiation-size universal hash function HPA according to W*; and S6. the two communication parties respectively performing, according to HPA, a hash operation on the error-corrected key string, so as to generate a final security key. The present invention has advantages such as being verifiable and secure, being easy to implement, and being able to simplify the design and implementation of a quantum key distribution system.

A set of image-space data is reconstructed from a set of k-space data. The set of image-space data is generated by minimizing a cost functional by an iterative non-linear conjugate gradient process. The iterative process may be accelerated by introducing k-space weighting to the cost functional. With proper choice of k-space weighting, a block-Toeplitz matrix is generated which permits use of Fast Fourier Transform techniques. An image is rendered from the set of image-space data.

The invention discloses an under-channel direction finding system based on Toeplitz matrix recovery. The system comprises a uniform linear array containing M omnidirectional antennas, a P-channel receiver, P-1 multipath radio frequency change-over switches, a synchronous time sequence controller, a signal acquisition processor and a spectrum estimation direction finding module. The method comprises the following steps: designing a switching mode of the multi-channel radio frequency selector switch, so that antenna array elements can be gated in a time-sharing manner; establishing a mathematical model of gating antenna array element receiving signals; calculating a covariance matrix of gating array element receiving signals; according to the Toeplitz characteristics of the covariance matrixof the uniform linear array, obtaining a covariance matrix corresponding the whole array by recovery through each calculated covariance matrix; and according to the recovered covariance matrix, carrying DOA estimation by using a covariance-based algorithm. According to the method, the characteristics of the Toeplitz matrix are utilized, the overall covariance can be recovered only by calculatingthe sub-covariance, the complexity is low, and physical hardware is easy to implement.

The invention discloses a sparse array DOA estimation method based on a PD-ALM algorithm. The method comprises the following steps: rearranging sampling data obtained by each snapshot of a sparse array into a toeplitz matrix xT; constructing a matrix filling model based on rank minimization, and filling the matrix xT by using the PD-ALM algorithm to obtain a full matrix x 'T, wherein the first rowof data of the matrix x' T being the sampling data after the single snapshot completion; forming a data matrix X' by all the snapshot complemented sampling data; and finally, performing DOA estimation on the data matrix X' by using a DOA estimation algorithm. According to the PD-ALM algorithm provided by the invention, a penalty decomposition method is adopted to directly solve the rank minimization problem; when the method is applied to the sparse array, the received data matrix of the full array can be well recovered under the conditions that the number of array elements is relatively small, the number of interference sources is large and the array is sparse, so that the wave direction is estimated more accurately, and the direction finding performance of the sparse array is improved.

The invention discloses a compressed sensing time-domain channel estimation method for a wavelet transform modulation system. The method comprises the steps of selecting a suitable wavelet base function based on a channel estimation condition, adopting time-domain block-type pilot insertion, performing IDWT on a signal to finish modulation, building a measurement matrix by adopting a standard Toeplitz matrix, performing time-domain channel estimation by using a compressed sensing technology, and adopting Fourier transform after channel impulse response estimation to simplify a channel solutionprocess. For a wavelet transform modulation system, ICI (Inter-Carrier Interference) and ISI (Inter-Symbol Interference) of each sub-channel can be removed efficiently by utilizing the wavelet base function, and the channel estimation accuracy is improved; the number of measurement values required by channel estimation is reduced by adopting the compressed sensing time-domain channel estimation,and the calculation complexity and cost are reduced; the data signal part is solved by adopting the FFT, so that massive operation caused by wavelet change is avoided, limitations caused by wavelet transform is overcome, and the wavelet transform modulation system is enabled to have a wider application scope.