Non-Iterative Computation of Sparsifiable Solutions to Underdetermined Kronecker Product Linear Systems of Equations
نویسنده
چکیده
The problem of computing sparse (mostly zero) or sparsifiable (by linear transformation) solutions to underdetermined linear systems of equations has applications in compressed sensing and minimumexposure medical imaging. We present a simple, noniterative, low-computational-cost algorithm for computing a sparse solution to an underdetermined linear system of equations. The system matrix is the Kronecker (tensor) product of two matrices, as in separable 2D deconvolution and reconstruction from partial 2D Fourier data, where the image is sparsifiable by a separable 2D wavelet or other transform. Numerical examples and program illustrate the new algorithm. Keywords— Sparse reconstruction Phone: 734-763-9810. Fax: 734-763-1503. Email: [email protected]. EDICS: 2-REST.
منابع مشابه
Location of Non-Zeros in Sparse Solutions of Underdetermined Linear Systems of Equations
The problem of computing sparse (mostly zero) or sparsifiable (by linear transformation) solutions to greatly underdetermined linear systems of equations has applications in compressed sensing. The locations of the nonzero elements in the solution is a much smaller set of variables than the solution itself. We present explicit equations for the relatively few variables that determine these nonz...
متن کاملA Non-Iterative Procedure for Computing Sparse and Sparsifiable Solutions to Slightly Underdetermined Linear Systems of Equations
The problem of computing sparse (mostly zero) solutions to underdetermined linear systems of equations has received much attention recently, due to its applications to compressed sensing. Under mild assumptions, the sparsest solution has minimum-L1norm, and can be computed using linear programming. In some applications (valid deconvolution, singular linear transformations), the linear system is...
متن کاملSolving systems of nonlinear equations using decomposition technique
A systematic way is presented for the construction of multi-step iterative method with frozen Jacobian. The inclusion of an auxiliary function is discussed. The presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of Newton multi-step method. The auxiliary function provides us the way to overcome the singul...
متن کاملThe numerical solution of the pressure Poisson equation for the incompressible Navier-Stokes equations using a quadrilateral spectral multidomain penalty method
We outline the basic features of a spectral multidomain penalty method (SMPM)based solver for the pressure Poisson equation (PPE) with Neumann boundary conditions, as encountered in the time-discretization of the incompressible Navier-Stokes equations. One one hand, the SMPM discretization enables robust under-resolved simulations without sacrificing high accuracy. On the other, the solution of...
متن کاملExact and numerical solutions of linear and non-linear systems of fractional partial differential equations
The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...
متن کامل