This monograph deals with approximation and noise cancellation of dyn-
ical systems which include linear and nonlinear input/output
relationships. It also deal with approximation and noise cancellation of
two dimensional arrays. It will be of special interest to researchers,
engineers and graduate students who have specialized in ?ltering theory
and system theory and d- ital images. This monograph is composed of two
parts. Part I and Part II will deal with approximation and noise
cancellation of dynamical systems or digital images respectively. From
noiseless or noisy data, reduction will be made. A method which reduces
model information or noise was proposed in the reference vol. 376 in
LNCIS [Hasegawa, 2008]. Using this method will allow model description
to be treated as noise reduction or model reduction without having to
bother, for example, with solving many partial di?er- tial equations.
This monograph will propose a new and easy method which produces the
same results as the method treated in the reference. As proof of its
advantageous e?ect, this monograph provides a new law in the sense of
numerical experiments. The new and easy method is executed using the
algebraic calculations without solving partial di?erential equations.
For our purpose,
manyactualexamplesofmodelinformationandnoisereductionwill also be
provided. Using the analysis of state space approach, the model
reduction problem may have become a major theme of technology after 1966
for emphasizing e?ciency in the ?elds of control, economy, numerical
analysis, and others
