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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fast Magnetic Resonance Imaging and Inverse Problems
快速 磁共振成像 逆问题
2023/4/17
磁共振成像是目前医学成像技术中功能最强大，技术门槛最复杂的技术之一。然而，相对其他成像模态较为缓慢的采集速度（较长的扫描时间）制约了磁共振成像在临床上的广泛应用。借助采样样本的数量与扫描时间的正比关系，通过减少采集的数据量（稀疏采样）来缩短磁共振采集时间是磁共振成像领域的重要途径，而从高度欠采样的数据中重建出高质量的图像可以近似为一个病态反问题，对这一问题的求解是快速磁共振成像领域的研究热点。本次...
Inverse-moment chiral sum rules
Inverse moment chiral perturbation theory double line the isospin hypercharged vector propagators
2014/12/23
A general class of inverse-moment sum rules was previously derived by the authors in a chiral perturbation theory (ChPT) study at two-loop order of the isospin and hypercharge vector-current propagato...
A Direct Sampling Method for Inverse Scattering Using Far-Field Data
Direct Sampling Method Inverse Scattering Using Far-Field Data Mathematical Physics
2012/6/21
This work is concerned with a direct sampling method (DSM) for inverse acoustic scattering problems using far-field data. The method characterizes some unknown obstacles, inhomogeneous media or cracks...
Solving the inverse problem of high numerical aperture focusing using Slepian-type vector fields
High numerical aperture focusing Vector diffraction theory Inverse problem Slepian’s concentration problem
2012/5/29
A technique using vector Slepian harmonics and multipole fields is presented for a general treatment of the inverse problem of high numerical aperture focusing. A prescribed intensity distribution or ...
Inverse scattering transform for the Degasperis-Procesi equation: a Riemann-Hilbert approach
Degasperis–Procesi equation Camassa–Holm equation inverse scattering trans-form Riemann–Hilbert problem asymptotics
2011/10/10
Abstract: We present the inverse scattering transform approach to the Cauchy problem on the line for the Degasperis-Procesi equation $u_{txx}-2u_x+2u_xu_{xx}+uu_{xxx}=0$ in the form of an associated R...
State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing
Magnetoencephalography source localization Kalman filter fixed interval smoother
2011/8/17
Abstract: Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a ch...
Inverse Ising inference using all the data
Inverse Ising inference data logistic regression
2011/8/17
Abstract: We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation f...
Global Uniqueness for an Inverse Stochastic Hyperbolic Equation with Three Unknowns
Global uniqueness inverse stochastic hyperbolic equation Carleman estimate three unknowns
2011/9/13
Abstract: This paper is addressed to an inverse stochastic hyperbolic equation with three unknowns, i.e., a source term, an initial displacement and an initial velocity. The global uniqueness is prove...
On the determinant formula in the inverse scattering procedure with a partially known steplike potential
Marchenko inverse scattering Schrodinger operator Titchmarsh-Weyl m− function
2011/9/13
Abstract: We are concerned with the inverse scattering problem for the full line Schr\"odinger operator $-\partial_x^2+q(x)$ with a steplike potential $q$ a priori known on $\Reals_+=(0,\infty)$. Assu...
On direct inverse of Stokes, Helmholtz and Laplacian operators in view of time-stepper-based Newton and Arnoldi solvers in incompressible CFD
Stoke Helmholtz Laplacian operators time-stepper-based Newton Arnoldi solvers incompressible CFD
2011/8/4
Abstract: Factorization of the incompressible Stokes operator linking pressure and velocity is revisited. The main purpose is to use the inverse of the Stokes operator with a large time step as a prec...
Direct and Inverse Computation of Jacobi Matrices of Infinite Homogeneous Affine I.F.S
Jacobi Matrices Orthogonal Polynomials Singular Continuous Measures Iterated Function Systems Gaussian–I.F.S. Quadratures
2011/7/28
Abstract: We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of t...
Inverse problems for Jacobi operators II: Mass perturbations of semi-infinite mass-spring systems
Infinite mass-spring system Jacobi matrices Two-spectra inverse problem
2011/7/26
Abstract: We consider an inverse spectral problem for infinite linear mass-spring systems with different configurations obtained by changing the first mass. We give results on the reconstruction of th...
The uniqueness in the inverse problem for transmission eigenvalues for the spherically-symmetric variable-speed wave equation
transmission eigenvalues inverse spectral problem variable-speed wave equation
2011/7/26
The uniqueness in the inverse problem for transmission eigenvalues for the spherically-symmetric variable-speed wave equation.
Anisotropic Inverse Cascade toward Zonal Flow in Magnetically Confined Plasmas
Magnetically Confined Plasmas Anisotropic Inverse Cascade toward Zonal Flow
2011/9/1
We propose a new mechanism for the generation of zonal flows in magnetically confined plasmas,complementing previous theories based on a modulational instability. We derive a new conservation law that...
Inverse quantum Zeno effect and power laws in a model chiral molecule
Inverse quantum Zeno power laws model chiral molecule
2010/11/8
We consider a chiral molecule modeled by two sets of rotational internal energy levels of different parity and degenerate ground states coupled by a constant interaction. By assuming that the collisio...