Range-azimuth imaging of ground targets via frequency-modulated continuous wave(FMCW)radar is crucial for effective target detection.However,when the pitch of the moving array constructed during motion exceeds the phy...Range-azimuth imaging of ground targets via frequency-modulated continuous wave(FMCW)radar is crucial for effective target detection.However,when the pitch of the moving array constructed during motion exceeds the physical array aperture,azimuth ambiguity occurs,making range-azimuth imaging on a moving platform challenging.To address this issue,we theoretically analyze azimuth ambiguity generation in sparse motion arrays and propose a dual-aperture adaptive processing(DAAP)method for suppressing azimuth ambiguity.This method combines spatial multiple-input multiple-output(MIMO)arrays with sparse motion arrays to achieve high-resolution range-azimuth imaging.In addition,an adaptive QR decomposition denoising method for sparse array signals based on iterative low-rank matrix approximation(LRMA)and regularized QR is proposed to preprocess sparse motion array signals.Simulations and experiments show that on a two-transmitter-four-receiver array,the signal-to-noise ratio(SNR)of the sparse motion array signal after noise suppression via adaptive QR decomposition can exceed 0 dB,and the azimuth ambiguity signal ratio(AASR)can be reduced to below-20 dB.展开更多
Ghost imaging(GI)offers great potential with respect to conventional imaging techniques.However,there are still some obstacles for reconstructing images with high quality,especially in the case that the orthogonal mea...Ghost imaging(GI)offers great potential with respect to conventional imaging techniques.However,there are still some obstacles for reconstructing images with high quality,especially in the case that the orthogonal measurement matrix is impossible to construct.In this paper,we propose a new scheme based on the orthogonal-triangular(QR)decomposition,named QR decomposition ghost imaging(QRGI)to reconstruct a better image with good quality.In the scheme,we can change the randomly non-orthogonal measurement matrix into orthonormal matrix by performing QR decomposition in two cases.(1)When the random measurement matrix is square,it can be firstly decomposed into an orthogonal matrix Q and an upper triangular matrix R.Then let the off-diagonal values of R equal to 0.0,the diagonal elements of R equal to a constant k,where k is the average of all values of the main diagonal,so the resulting measurement matrix can be obtained.(2)When the random measurement matrix is with full rank,we firstly compute its transpose,and followed with above QR operation.Finally,the image of the object can be reconstructed by correlating the new measurement matrix and corresponding bucket values.Both experimental and simulation results verify the feasibility of the proposed QRGI scheme.Moreover,the results also show that the proposed QRGI scheme could improve the imaging quality comparing to traditional GI(TGI)and differential GI(DGI).Besides,in comparison with the singular value decomposition ghost imaging(SVDGI),the imaging quality and the reconstruction time by using QRGI are similar to those by using SVDGI,while the computing time(the time consuming on the light patterns computation)is substantially shortened.展开更多
A fast algorithm FBTQ is presented which computes the QR factorization a block-Toeplitz matrix A (A∈R) in O(mns3) multiplications. We prove that the QR decomposition of A and the inverse Cholesky decomposition can be...A fast algorithm FBTQ is presented which computes the QR factorization a block-Toeplitz matrix A (A∈R) in O(mns3) multiplications. We prove that the QR decomposition of A and the inverse Cholesky decomposition can be computed in parallel using the sametransformation.We also prove that some kind of Toeplltz-block matrices can he transformed into the corresponding block-Toeplitz matrices.展开更多
The purpose of this work is to present an effective tool for computing different QR-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 20...The purpose of this work is to present an effective tool for computing different QR-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 2006) is used. This transform is fast, has a unique algorithm for any length of the input vector/signal and can be used with different complex basic 2 × 2 transforms. The DsiHT is zeroing all components of the input signal while moving or heaping the energy of the signal to one component, for instance the first one. We describe three different types of QR-decompositions that use the basic transforms with the T, G, and M-type complex matrices we introduce, as well as without matrices but using analytical formulas. We also present the mixed QR-decomposition, when different type DsiHTs are used in different stages of the algorithm. The number of such decompositions is greater than 3<sup>(N-1)</sup>, for an N × N complex matrix. Examples of the QR-decomposition are described in detail for the 4 × 4 and 6 × 6 complex matrices and compared with the known method of Householder transforms. The precision of the QR-decompositions of N × N matrices, when N are 6, 13, 17, 19, 21, 40, 64, 100, 128, 201, 256, and 400 is also compared. The MATLAB-based scripts of the codes for QR-decompositions by the described DsiHTs are given.展开更多
基金supported by the National Natural Science Foundation of China under Grant 62301051.
文摘Range-azimuth imaging of ground targets via frequency-modulated continuous wave(FMCW)radar is crucial for effective target detection.However,when the pitch of the moving array constructed during motion exceeds the physical array aperture,azimuth ambiguity occurs,making range-azimuth imaging on a moving platform challenging.To address this issue,we theoretically analyze azimuth ambiguity generation in sparse motion arrays and propose a dual-aperture adaptive processing(DAAP)method for suppressing azimuth ambiguity.This method combines spatial multiple-input multiple-output(MIMO)arrays with sparse motion arrays to achieve high-resolution range-azimuth imaging.In addition,an adaptive QR decomposition denoising method for sparse array signals based on iterative low-rank matrix approximation(LRMA)and regularized QR is proposed to preprocess sparse motion array signals.Simulations and experiments show that on a two-transmitter-four-receiver array,the signal-to-noise ratio(SNR)of the sparse motion array signal after noise suppression via adaptive QR decomposition can exceed 0 dB,and the azimuth ambiguity signal ratio(AASR)can be reduced to below-20 dB.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61871234 and 62001249)the Postgraduate Research&Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX200729)+1 种基金Natural Science Research Project of Higher Education of Jiangsu Province,China(Grant No.20KJB510030)Research project of NanJing Tech University Pujiang Institute(Grant No.njpj2020-1-02)。
文摘Ghost imaging(GI)offers great potential with respect to conventional imaging techniques.However,there are still some obstacles for reconstructing images with high quality,especially in the case that the orthogonal measurement matrix is impossible to construct.In this paper,we propose a new scheme based on the orthogonal-triangular(QR)decomposition,named QR decomposition ghost imaging(QRGI)to reconstruct a better image with good quality.In the scheme,we can change the randomly non-orthogonal measurement matrix into orthonormal matrix by performing QR decomposition in two cases.(1)When the random measurement matrix is square,it can be firstly decomposed into an orthogonal matrix Q and an upper triangular matrix R.Then let the off-diagonal values of R equal to 0.0,the diagonal elements of R equal to a constant k,where k is the average of all values of the main diagonal,so the resulting measurement matrix can be obtained.(2)When the random measurement matrix is with full rank,we firstly compute its transpose,and followed with above QR operation.Finally,the image of the object can be reconstructed by correlating the new measurement matrix and corresponding bucket values.Both experimental and simulation results verify the feasibility of the proposed QRGI scheme.Moreover,the results also show that the proposed QRGI scheme could improve the imaging quality comparing to traditional GI(TGI)and differential GI(DGI).Besides,in comparison with the singular value decomposition ghost imaging(SVDGI),the imaging quality and the reconstruction time by using QRGI are similar to those by using SVDGI,while the computing time(the time consuming on the light patterns computation)is substantially shortened.
文摘A fast algorithm FBTQ is presented which computes the QR factorization a block-Toeplitz matrix A (A∈R) in O(mns3) multiplications. We prove that the QR decomposition of A and the inverse Cholesky decomposition can be computed in parallel using the sametransformation.We also prove that some kind of Toeplltz-block matrices can he transformed into the corresponding block-Toeplitz matrices.
文摘The purpose of this work is to present an effective tool for computing different QR-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 2006) is used. This transform is fast, has a unique algorithm for any length of the input vector/signal and can be used with different complex basic 2 × 2 transforms. The DsiHT is zeroing all components of the input signal while moving or heaping the energy of the signal to one component, for instance the first one. We describe three different types of QR-decompositions that use the basic transforms with the T, G, and M-type complex matrices we introduce, as well as without matrices but using analytical formulas. We also present the mixed QR-decomposition, when different type DsiHTs are used in different stages of the algorithm. The number of such decompositions is greater than 3<sup>(N-1)</sup>, for an N × N complex matrix. Examples of the QR-decomposition are described in detail for the 4 × 4 and 6 × 6 complex matrices and compared with the known method of Householder transforms. The precision of the QR-decompositions of N × N matrices, when N are 6, 13, 17, 19, 21, 40, 64, 100, 128, 201, 256, and 400 is also compared. The MATLAB-based scripts of the codes for QR-decompositions by the described DsiHTs are given.
