68,026 research outputs found
Inverse Problems and Self-similarity in Imaging
This thesis examines the concept of image self-similarity and provides solutions to various associated inverse problems such as resolution enhancement and missing fractal codes.
In general, many real-world inverse problems are ill-posed, mainly because of the lack of existence of a unique solution. The procedure of providing acceptable unique solutions to such problems is known as regularization. The concept of image prior, which has been of crucial importance in image modelling and processing, has also been important in solving inverse problems since it algebraically translates to the regularization procedure.
Indeed, much recent progress in imaging has been due to advances in the formulation and practice of regularization. This, coupled with progress in optimization and numerical analysis, has yielded much improvement in computational methods of solving inverse imaging problems.
Historically, the idea of self-similarity was important in the development of fractal image coding. Here we show that the self-similarity properties of natural images may be used to construct image priors for the purpose of addressing certain inverse problems. Indeed, new trends in the area of non-local image processing have provided a rejuvenated appreciation of image self-similarity and opportunities to explore novel self-similarity-based priors.
We first revisit the concept of fractal-based methods and address some open theoretical problems in the area. This includes formulating a necessary and sufficient condition for the contractivity of the block fractal transform operator. We shall also provide some more generalized formulations of fractal-based self-similarity constraints of an image. These formulations can be developed algebraically and also in terms of the set-based method of Projection Onto Convex Sets (POCS).
We then revisit the traditional inverse problems of single frame image zooming and multi-frame resolution enhancement, also known as super-resolution. Some ideas will be borrowed from newly developed non-local denoising algorithms in order to formulate self-similarity priors. Understanding the role of scale and choice of examples/samples is also important in these proposed models. For this purpose, we perform an extensive series of numerical experiments and analyze the results. These ideas naturally lead to the method of self-examples, which relies on the regularity properties of natural images at different scales, as a means of solving the single-frame image zooming problem.
Furthermore, we propose and investigate a multi-frame super-resolution counterpart which does not require explicit motion estimation among video sequences
Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization
As a powerful statistical image modeling technique, sparse representation has
been successfully used in various image restoration applications. The success
of sparse representation owes to the development of l1-norm optimization
techniques, and the fact that natural images are intrinsically sparse in some
domain. The image restoration quality largely depends on whether the employed
sparse domain can represent well the underlying image. Considering that the
contents can vary significantly across different images or different patches in
a single image, we propose to learn various sets of bases from a pre-collected
dataset of example image patches, and then for a given patch to be processed,
one set of bases are adaptively selected to characterize the local sparse
domain. We further introduce two adaptive regularization terms into the sparse
representation framework. First, a set of autoregressive (AR) models are
learned from the dataset of example image patches. The best fitted AR models to
a given patch are adaptively selected to regularize the image local structures.
Second, the image non-local self-similarity is introduced as another
regularization term. In addition, the sparsity regularization parameter is
adaptively estimated for better image restoration performance. Extensive
experiments on image deblurring and super-resolution validate that by using
adaptive sparse domain selection and adaptive regularization, the proposed
method achieves much better results than many state-of-the-art algorithms in
terms of both PSNR and visual perception.Comment: 35 pages. This paper is under review in IEEE TI
Neural Nearest Neighbors Networks
Non-local methods exploiting the self-similarity of natural signals have been
well studied, for example in image analysis and restoration. Existing
approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed
feature space. The main hurdle in optimizing this feature space w.r.t.
application performance is the non-differentiability of the KNN selection rule.
To overcome this, we propose a continuous deterministic relaxation of KNN
selection that maintains differentiability w.r.t. pairwise distances, but
retains the original KNN as the limit of a temperature parameter approaching
zero. To exploit our relaxation, we propose the neural nearest neighbors block
(N3 block), a novel non-local processing layer that leverages the principle of
self-similarity and can be used as building block in modern neural network
architectures. We show its effectiveness for the set reasoning task of
correspondence classification as well as for image restoration, including image
denoising and single image super-resolution, where we outperform strong
convolutional neural network (CNN) baselines and recent non-local models that
rely on KNN selection in hand-chosen features spaces.Comment: to appear at NIPS*2018, code available at
https://github.com/visinf/n3net
Self-Tuned Deep Super Resolution
Deep learning has been successfully applied to image super resolution (SR).
In this paper, we propose a deep joint super resolution (DJSR) model to exploit
both external and self similarities for SR. A Stacked Denoising Convolutional
Auto Encoder (SDCAE) is first pre-trained on external examples with proper data
augmentations. It is then fine-tuned with multi-scale self examples from each
input, where the reliability of self examples is explicitly taken into account.
We also enhance the model performance by sub-model training and selection. The
DJSR model is extensively evaluated and compared with state-of-the-arts, and
show noticeable performance improvements both quantitatively and perceptually
on a wide range of images
Single image example-based super-resolution using cross-scale patch matching and Markov random field modelling
Example-based super-resolution has become increasingly popular over the last few years for its ability to overcome the limitations of classical multi-frame approach. In this paper we present a new example-based method that uses the input low-resolution image itself as a search space for high-resolution patches by exploiting self-similarity across different resolution scales. Found examples are combined in a high-resolution image by the means of Markov Random Field modelling that forces their global agreement. Additionally, we apply back-projection and steering kernel regression as post-processing techniques. In this way, we are able to produce sharp and artefact-free results that are comparable or better than standard interpolation and state-of-the-art super-resolution techniques
Image Restoration Using Joint Statistical Modeling in Space-Transform Domain
This paper presents a novel strategy for high-fidelity image restoration by
characterizing both local smoothness and nonlocal self-similarity of natural
images in a unified statistical manner. The main contributions are three-folds.
First, from the perspective of image statistics, a joint statistical modeling
(JSM) in an adaptive hybrid space-transform domain is established, which offers
a powerful mechanism of combining local smoothness and nonlocal self-similarity
simultaneously to ensure a more reliable and robust estimation. Second, a new
form of minimization functional for solving image inverse problem is formulated
using JSM under regularization-based framework. Finally, in order to make JSM
tractable and robust, a new Split-Bregman based algorithm is developed to
efficiently solve the above severely underdetermined inverse problem associated
with theoretical proof of convergence. Extensive experiments on image
inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise
removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions
on Circuits System and Video Technology (TCSVT). High resolution pdf version
and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM
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