130 results about "Toeplitz matrix" patented technology

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.

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.