| Summary: | Master of Science === Department of Statistics === Diego M. Maldonado === Haiyan Wang === This report addresses some mathematical and statistical techniques
of image processing and their computational implementation.
Fundamental theories have been presented, applied and illustrated
with examples. To make the report as self-contained as possible, key
terminologies have been defined and some classical results and
theorems are stated, in the most part, without proof. Some
algorithms and techniques of image processing have been described
and substantiated with experimentation using MATLAB. Several ways of
estimating original images from noisy image data and their
corresponding risks are discussed. Two image processing concepts
selected to illustrate computational implementation are: "Bayes
classification" and "Wavelet denoising". The discussion of the
latter involves introducing a specialized area of mathematics,
namely, wavelets. A self-contained theory for wavelets is built by
first reviewing basic concepts of Fourier Analysis and then
introducing Multi-resolution Analysis and wavelets. For a better
understanding of Fourier Analysis techniques in image processing,
original solutions to some problems in Fourier Analysis have been
worked out. Finally, implementation of the above-mentioned concepts
are illustrated with examples and MATLAB codes.
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