%AChen, Zixuan [School of Mathematical Sciences Dalian University of Technology Dalian China]%ANagy, James [Department of Mathematics Emory University Atlanta Georgia]%AXi, Yuanzhe [Department of Mathematics Emory University Atlanta Georgia]%AYu, Bo [School of Mathematical Sciences Dalian University of Technology Dalian China]%BJournal Name: Numerical Linear Algebra with Applications; Journal Volume: 27; Journal Issue: 2; Related Information: CHORUS Timestamp: 2023-09-02 02:54:41
%D2019%IWiley Blackwell (John Wiley & Sons); None
%JJournal Name: Numerical Linear Algebra with Applications; Journal Volume: 27; Journal Issue: 2; Related Information: CHORUS Timestamp: 2023-09-02 02:54:41
%K
%MOSTI ID: 10453564
%PMedium: X
%TStructured FISTA for image restoration
%XSummary
In this paper, we propose an efficient numerical scheme for solving some large‐scale ill‐posed linear inverse problems arising from image restoration. In order to accelerate the computation, two different hidden structures are exploited. First, the coefficient matrix is approximated as the sum of a small number of Kronecker products. This procedure not only introduces one more level of parallelism into the computation but also enables the usage of computationally intensive matrix–matrix multiplications in the subsequent optimization procedure. We then derive the corresponding Tikhonov regularized minimization model and extend the fast iterative shrinkage‐thresholding algorithm (FISTA) to solve the resulting optimization problem. Because the matrices appearing in the Kronecker product approximation are all structured matrices (Toeplitz, Hankel, etc.), we can further exploit their fast matrix–vector multiplication algorithms at each iteration. The proposed algorithm is thus calledstructuredFISTA (sFISTA). In particular, we show that the approximation error introduced by sFISTA is well under control and sFISTA can reach the same image restoration accuracy level as FISTA. Finally, both the theoretical complexity analysis and some numerical results are provided to demonstrate the efficiency of sFISTA.

%0Journal Article