A fast algorithm of two-level banded Toeplitz systems of linear equations with application to image restoration

Abstract

Abstract:A fast algorithm is proposed for the solution of nm × nm block banded Toeplitz systems with banded Toeplitz blocks (BBTBTB). The algorithm consists of using the idea of embedding a BBTBTB matrix in a m × (n + k) block-triangular Toeplitz matrix. The computational complexity of the proposed algorithm is O(m 2 nlogn + m 3 n + k 3 m 3 ). The validity of the approach is illustrated by an application to image restoration.