In the �eld of image processing, building good representation models for
natural images is crucial for various applications, such as image restora-
tion, sampling, segmentation, etc. Adaptive image representation models
are designed for describing the intrinsic structures of natural images. In
the classical Bayesian inference, this representation is often known as the
prior of the intensity distribution of the input image. Early image priors
have forms such as total variation norm, Markov Random Fields (MRF),
and wavelets. Recently, image priors obtained from machine learning tech-
niques tend to be more adaptive, which aims at capturing the natural image
models via learning from larger databases. In this thesis, we study adaptive
representations of natural images for image restoration.
The purpose of image restoration is to remove the artifacts which degrade
an image. The degradation comes in many forms such as image blurs,
noises, and artifacts from the codec. Take image denoising for an example.
There are several classic representation methods which can generate state-
of-the-art results. The �rst one is the assumption of image self-similarity.
However, this representation has the issue that sometimes the self-similarity
assumption would fail because of high noise levels or unique image contents.
The second one is the wavelet based nonlocal representation, which also has
a problem in that the �xed basis function is not adaptive enough for any
arbitrary type of input images. The third is the sparse coding using over-
complete dictionaries, which does not have the hierarchical structure that is
similar to the one in human visual system and is therefore prone to denoising
artifacts.
My research started from image denoising. Through the thorough review
and evaluation of state-of-the-art denoising methods, it was found that the representation of images is substantially important for the denoising tech-
nique. At the same time, an improvement on one of the nonlocal denoising
method was proposed, which improves the representation of images by the
integration of Gaussian blur, clustering and Rotationally Invariant Block
Matching. Enlightened by the successful application of sparse coding in
compressive sensing, we exploited the image self-similarity by using a sparse
representation based on wavelet coe�cients in a nonlocal and hierarchical
way, which generates competitive results compared to the state-of-the-art
denoising algorithms. Meanwhile, another adaptive local �lter learned by
Genetic Programming (GP) was proposed for e�cient image denoising. In
this work, we employed GP to �nd the optimal representations for local im-
age patches through training on massive datasets, which yields competitive
results compared to state-of-the-art local denoising �lters. After success-
fully dealt with the denoising part, we moved to the parameter estimation
for image degradation models. For instance, image blur identi�cation uses
deep learning, which has recently been proposed as a popular image repre-
sentation approach. This work has also been extended to blur estimation
based on the fact that the second step of the framework has been replaced
with general regression neural network. In a word, in this thesis, spatial cor-
relations, sparse coding, genetic programming, deep learning are explored
as adaptive image representation models for both image restoration and
parameter estimation.
We conclude this thesis by considering methods based on machine learning
to be the best adaptive representations for natural images. We have shown
that they can generate better results than conventional representation mod-
els for the tasks of image denoising and deblurring
