415 research outputs found
SPATIALLY VARYING BLUR RECOVERY. Diagonal Approximations in the Wavelet Domain
Restoration of images degraded by spatially varying blurs is an issue of increasing importance. Many new optical systems allow to know the system point spread function at some random locations, by using microscopic luminescent structures. Given a set of impulse responses, we propose a fast and efficient algorithm to reconstruct the blurring operator in the whole image domain. Our method consists in finding an approximation of the integral operator by operators diagonal in the wavelet domain. Interestingly, this method complexity scales linearly with the image size. It is thus applicable to large 3D problems. We show that this approach might outperform previously proposed strategies such as linear interpolations (Nagy and O'Leary, 1998) or separable approximations (Zhang et al., 2007). We provide various theoretical and numerical results in order to justify the proposed methods. We also show preliminary deblurring results illustrating the relevance of our formalism
Distributed Deblurring of Large Images of Wide Field-Of-View
Image deblurring is an economic way to reduce certain degradations (blur and
noise) in acquired images. Thus, it has become essential tool in high
resolution imaging in many applications, e.g., astronomy, microscopy or
computational photography. In applications such as astronomy and satellite
imaging, the size of acquired images can be extremely large (up to gigapixels)
covering wide field-of-view suffering from shift-variant blur. Most of the
existing image deblurring techniques are designed and implemented to work
efficiently on centralized computing system having multiple processors and a
shared memory. Thus, the largest image that can be handle is limited by the
size of the physical memory available on the system. In this paper, we propose
a distributed nonblind image deblurring algorithm in which several connected
processing nodes (with reasonable computational resources) process
simultaneously different portions of a large image while maintaining certain
coherency among them to finally obtain a single crisp image. Unlike the
existing centralized techniques, image deblurring in distributed fashion raises
several issues. To tackle these issues, we consider certain approximations that
trade-offs between the quality of deblurred image and the computational
resources required to achieve it. The experimental results show that our
algorithm produces the similar quality of images as the existing centralized
techniques while allowing distribution, and thus being cost effective for
extremely large images.Comment: 16 pages, 10 figures, submitted to IEEE Trans. on Image Processin
Recent Progress in Image Deblurring
This paper comprehensively reviews the recent development of image
deblurring, including non-blind/blind, spatially invariant/variant deblurring
techniques. Indeed, these techniques share the same objective of inferring a
latent sharp image from one or several corresponding blurry images, while the
blind deblurring techniques are also required to derive an accurate blur
kernel. Considering the critical role of image restoration in modern imaging
systems to provide high-quality images under complex environments such as
motion, undesirable lighting conditions, and imperfect system components, image
deblurring has attracted growing attention in recent years. From the viewpoint
of how to handle the ill-posedness which is a crucial issue in deblurring
tasks, existing methods can be grouped into five categories: Bayesian inference
framework, variational methods, sparse representation-based methods,
homography-based modeling, and region-based methods. In spite of achieving a
certain level of development, image deblurring, especially the blind case, is
limited in its success by complex application conditions which make the blur
kernel hard to obtain and be spatially variant. We provide a holistic
understanding and deep insight into image deblurring in this review. An
analysis of the empirical evidence for representative methods, practical
issues, as well as a discussion of promising future directions are also
presented.Comment: 53 pages, 17 figure
Point spread function approximation of high rank Hessians with locally supported non-negative integral kernels
We present an efficient matrix-free point spread function (PSF) method for
approximating operators that have locally supported non-negative integral
kernels. The method computes impulse responses of the operator at scattered
points, and interpolates these impulse responses to approximate integral kernel
entries. Impulse responses are computed by applying the operator to Dirac comb
batches of point sources, which are chosen by solving an ellipsoid packing
problem. Evaluation of kernel entries allows us to construct a hierarchical
matrix (H-matrix) approximation of the operator. Further matrix computations
are performed with H-matrix methods. We use the method to build preconditioners
for the Hessian operator in two inverse problems governed by partial
differential equations (PDEs): inversion for the basal friction coefficient in
an ice sheet flow problem and for the initial condition in an
advective-diffusive transport problem. While for many ill-posed inverse
problems the Hessian of the data misfit term exhibits a low rank structure, and
hence a low rank approximation is suitable, for many problems of practical
interest the numerical rank of the Hessian is still large. But Hessian impulse
responses typically become more local as the numerical rank increases, which
benefits the PSF method. Numerical results reveal that the PSF preconditioner
clusters the spectrum of the preconditioned Hessian near one, yielding roughly
5x-10x reductions in the required number of PDE solves, as compared to
regularization preconditioning and no preconditioning. We also present a
numerical study for the influence of various parameters (that control the shape
of the impulse responses) on the effectiveness of the advection-diffusion
Hessian approximation. The results show that the PSF-based preconditioners are
able to form good approximations of high-rank Hessians using a small number of
operator applications
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Image Restoration
This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with
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