687 research outputs found
Variational Image Segmentation Model Coupled with Image Restoration Achievements
Image segmentation and image restoration are two important topics in image
processing with great achievements. In this paper, we propose a new multiphase
segmentation model by combining image restoration and image segmentation
models. Utilizing image restoration aspects, the proposed segmentation model
can effectively and robustly tackle high noisy images, blurry images, images
with missing pixels, and vector-valued images. In particular, one of the most
important segmentation models, the piecewise constant Mumford-Shah model, can
be extended easily in this way to segment gray and vector-valued images
corrupted for example by noise, blur or missing pixels after coupling a new
data fidelity term which comes from image restoration topics. It can be solved
efficiently using the alternating minimization algorithm, and we prove the
convergence of this algorithm with three variables under mild condition.
Experiments on many synthetic and real-world images demonstrate that our method
gives better segmentation results in comparison to others state-of-the-art
segmentation models especially for blurry images and images with missing pixels
values.Comment: 23 page
CT Image Reconstruction by Spatial-Radon Domain Data-Driven Tight Frame Regularization
This paper proposes a spatial-Radon domain CT image reconstruction model
based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model
combines the idea of joint image and Radon domain inpainting model of
\cite{Dong2013X} and that of the data-driven tight frames for image denoising
\cite{cai2014data}. It is different from existing models in that both CT image
and its corresponding high quality projection image are reconstructed
simultaneously using sparsity priors by tight frames that are adaptively
learned from the data to provide optimal sparse approximations. An alternative
minimization algorithm is designed to solve the proposed model which is
nonsmooth and nonconvex. Convergence analysis of the algorithm is provided.
Numerical experiments showed that the SRD-DDTF model is superior to the model
by \cite{Dong2013X} especially in recovering some subtle structures in the
images
Sparse Representation on Graphs by Tight Wavelet Frames and Applications
In this paper, we introduce a new (constructive) characterization of tight
wavelet frames on non-flat domains in both continuum setting, i.e. on
manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet
frame transforms can be computed and how they can be effectively used to
process graph data. We start with defining the quasi-affine systems on a given
manifold \cM that is formed by generalized dilations and shifts of a finite
collection of wavelet functions .
We further require that is generated by some refinable function
with mask . We present the condition needed for the masks so that the associated quasi-affine system generated by is a
tight frame for L_2(\cM). Then, we discuss how the transition from the
continuum (manifolds) to the discrete setting (graphs) can be naturally done.
In order for the proposed discrete tight wavelet frame transforms to be useful
in applications, we show how the transforms can be computed efficiently and
accurately by proposing the fast tight wavelet frame transforms for graph data
(WFTG). Finally, we consider two specific applications of the proposed WFTG:
graph data denoising and semi-supervised clustering. Utilizing the sparse
representation provided by the WFTG, we propose -norm based
optimization models on graphs for denoising and semi-supervised clustering. On
one hand, our numerical results show significant advantage of the WFTG over the
spectral graph wavelet transform (SGWT) by [1] for both applications. On the
other hand, numerical experiments on two real data sets show that the proposed
semi-supervised clustering model using the WFTG is overall competitive with the
state-of-the-art methods developed in the literature of high-dimensional data
classification, and is superior to some of these methods
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