5,252 research outputs found
Mathematical approaches to digital color image denoising
Many mathematical models have been designed to remove noise from images. Most of them focus on grey value images with additive artificial noise. Only very few specifically target natural color photos taken by a digital camera with real noise. Noise in natural color photos have special characteristics that are substantially different
from those that have been added artificially.
In this thesis previous denoising models are reviewed. We analyze the strengths and weakness of existing denoising models by showing where they perform well and where they don't. We put special focus on two models: The steering kernel regression model and the non-local model. For Kernel Regression model, an adaptive bilateral
filter is introduced as complementary to enhance it. Also a non-local bilateral filter is proposed as an application of the idea of non-local means filter. Then the idea of cross-channel denoising is proposed in this thesis. It is effective in
denoising monochromatic images by understanding the characteristics of digital noise in natural color images. A non-traditional color space is also introduced specifically for this purpose. The cross-channel paradigm can be applied to most of the exisiting models to greatly improve their performance for denoising natural color images.Ph.D.Committee Chair: Haomin Zhou; Committee Member: Luca Dieci; Committee Member: Ronghua Pan; Committee Member: Sung Ha Kang; Committee Member: Yang Wan
The curvelet transform for image denoising
We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a` trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement
Total variation regularization for manifold-valued data
We consider total variation minimization for manifold valued data. We propose
a cyclic proximal point algorithm and a parallel proximal point algorithm to
minimize TV functionals with -type data terms in the manifold case.
These algorithms are based on iterative geodesic averaging which makes them
easily applicable to a large class of data manifolds. As an application, we
consider denoising images which take their values in a manifold. We apply our
algorithms to diffusion tensor images, interferometric SAR images as well as
sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds
(which includes the data space in diffusion tensor imaging) we show the
convergence of the proposed TV minimizing algorithms to a global minimizer
Rethinking the Pipeline of Demosaicing, Denoising and Super-Resolution
Incomplete color sampling, noise degradation, and limited resolution are the
three key problems that are unavoidable in modern camera systems. Demosaicing
(DM), denoising (DN), and super-resolution (SR) are core components in a
digital image processing pipeline to overcome the three problems above,
respectively. Although each of these problems has been studied actively, the
mixture problem of DM, DN, and SR, which is a higher practical value, lacks
enough attention. Such a mixture problem is usually solved by a sequential
solution (applying each method independently in a fixed order: DM DN
SR), or is simply tackled by an end-to-end network without enough
analysis into interactions among tasks, resulting in an undesired performance
drop in the final image quality. In this paper, we rethink the mixture problem
from a holistic perspective and propose a new image processing pipeline: DN
SR DM. Extensive experiments show that simply modifying the usual
sequential solution by leveraging our proposed pipeline could enhance the image
quality by a large margin. We further adopt the proposed pipeline into an
end-to-end network, and present Trinity Enhancement Network (TENet).
Quantitative and qualitative experiments demonstrate the superiority of our
TENet to the state-of-the-art. Besides, we notice the literature lacks a full
color sampled dataset. To this end, we contribute a new high-quality full color
sampled real-world dataset, namely PixelShift200. Our experiments show the
benefit of the proposed PixelShift200 dataset for raw image processing.Comment: Code is available at: https://github.com/guochengqian/TENe
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
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