TOTAL LEAST SQUARES PROBLEMS - Neural-based Orthogonal Data Fitting: The EXIN Neural Networks - page 2

A complete analysis of the TLS problems can be found in [98], where the
algorithm of [74] is generalized to all cases in which it fails to produce a solution
( nongeneric TLS ). Most of the following theoretical presentation of the TLS
problems is based on [98].
1.2 SOME TLS APPLICATIONS
There are a lot of TLS applications in many fields:
• Time-domain system identification and parameter estimation . This includes
deconvolution techniques: for example, renography [100], transfer function
models [57], estimates of the autoregressive parameters of an ARMA model
from noisy measurements [179], and structural identification [8].
• Identification of state-space models from noisy input-output measurements .
Examples, including the identification of an industrial plant, can be found
in [134] and [135].
• Signal processing . A lot of algorithms have been proposed for the harmonic
retrieval problem: the Pisarenko harmonic decomposition [152], the linear
prediction - based work of Rahman and Yu [158], the ESPRIT (estimation
of signal parameters via rotational invariance techniques) algorithm of
Roy and Kailath [163], and the Procrustes rotations - based ESPRIT
algorithm proposed by Zoltowski and Stavrinides [202]. Zoltowski [201]
also applied TLS to the minimum variance distortionless response (MVDR)
beamforming problem.
• Biomedical signal processing . This includes signal parameter estimates
in the accurate quantification of in vivo magnetic resonance spectroscopy
(MRS) and the quantification of chromophore concentration changes in
neonatal brain [94].
• Image processing . This includes the image reconstruction algorithm for com-
puting images of the interior structure of highly scattering media (optical
tomography) by using the conjugate gradient method [200], a method for
removing noise from digital images corrupted with additive, multiplicative,
and mixed noise [87], and the regularized constrained TLS method for restor-
ing an image distorted by a linear space-invariant point-spread function
which is not exactly known [130].
• Computer vision . This includes disparity-assisted stereo optical flow estima-
tion [102] and robust and reliable motion analysis [24,137].
• Experimental modal analysis . Estimates of the frequency response functions
from measured input forces and response signals are applied to mechanical
structures [162].
• Nonlinear models . The true variables are related to each other nonlinearly
(see [73]).