Sparse Solutions to Underdetermined Kronecker Product Systems ∗

نویسندگان

  • Sadegh Jokar
  • Volker Mehrmann
چکیده

Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. For the mutual incoherence we also discuss results for sums of Kronecker products.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Non-Iterative Computation of Sparsifiable Solutions to Underdetermined Kronecker Product Linear Systems of Equations

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 ...

متن کامل

Fe b 20 09 Sparse representation of solutions of Kronecker product systems ∗

Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. For the mutual incoherence we also discuss results for sums of Kronecker products.

متن کامل

Hierarchical restricted isometry property for Kronecker product measurements

Hierarchically sparse signals and Kronecker product structured measurements arise naturally in a variety of applications. The simplest example of a hierarchical sparsity structure is two-level (s, σ)-hierarchical sparsity which features s-block-sparse signals with σ-sparse blocks. For a large class of algorithms recovery guarantees can be derived based on the restricted isometry property (RIP) ...

متن کامل

A 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 کامل

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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009