ISSN:
1572-9265
Keywords:
Hankel/Toeplitz matrix
;
Structured Total Least Squares
;
displacement rank
;
15A03
;
62P30
;
65F10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) problem when constraints on the matrix structure need to be imposed. Similar to the ordinary TLS approach, the STLS approach can be used to determine the parameter vector of a linear model, given some noisy measurements. In many signal processing applications, the imposition of this matrix structure constraint is necessary for obtaining Maximum Likelihood (ML) estimates of the parameter vector. In this paper we consider the Toeplitz (Hankel) STLS problem (i.e., an STLS problem in which the Toeplitz (Hankel) structure needs to be preserved). A fast implementation of an algorithm for solving this frequently occurring STLS problem is proposed. The increased efficiency is obtained by exploiting the low displacement rank of the involved matrices and the sparsity of the associated generators. The fast implementation is compared to two other implementations of algorithms for solving the Toeplitz (Hankel) STLS problem. The comparison is carried out on a recently proposed speech compression scheme. The numerical results confirm the high efficiency of the newly proposed fast implementation: the straightforward implementations have a complexity of O((m+n)3) and O(m3) whereas the proposed implementation has a complexity of O(mn+n2).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1019116520737
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