245 research outputs found
A Framework for Fast Image Deconvolution with Incomplete Observations
In image deconvolution problems, the diagonalization of the underlying
operators by means of the FFT usually yields very large speedups. When there
are incomplete observations (e.g., in the case of unknown boundaries), standard
deconvolution techniques normally involve non-diagonalizable operators,
resulting in rather slow methods, or, otherwise, use inexact convolution
models, resulting in the occurrence of artifacts in the enhanced images. In
this paper, we propose a new deconvolution framework for images with incomplete
observations that allows us to work with diagonalized convolution operators,
and therefore is very fast. We iteratively alternate the estimation of the
unknown pixels and of the deconvolved image, using, e.g., an FFT-based
deconvolution method. This framework is an efficient, high-quality alternative
to existing methods of dealing with the image boundaries, such as edge
tapering. It can be used with any fast deconvolution method. We give an example
in which a state-of-the-art method that assumes periodic boundary conditions is
extended, through the use of this framework, to unknown boundary conditions.
Furthermore, we propose a specific implementation of this framework, based on
the alternating direction method of multipliers (ADMM). We provide a proof of
convergence for the resulting algorithm, which can be seen as a "partial" ADMM,
in which not all variables are dualized. We report experimental comparisons
with other primal-dual methods, where the proposed one performed at the level
of the state of the art. Four different kinds of applications were tested in
the experiments: deconvolution, deconvolution with inpainting, superresolution,
and demosaicing, all with unknown boundaries.Comment: IEEE Trans. Image Process., to be published. 15 pages, 11 figures.
MATLAB code available at
https://github.com/alfaiate/DeconvolutionIncompleteOb
Image Mapping and Object Removal Using ADM in Image Inpainting: Review
Image inpainting is a technology for restoring the damaged parts of an image by referring to the information from the undamaged parts to make the restored image look “complete”, “continuous” and “natural”. Inpainting traditionally has been done by professional restorers. For instance, in the valuable painting such as in the museum world would be carried out by a skilled art conservator or art restorer. But this process is manual so it is time consuming. Digital Image Inpainting tries to imitate this process and perform the Inpainting automatically. The aim of this work is to develop an automatic system that can remove unwanted objects from the image and restore the image in undetectable way. Among various image inpainting algorithms Alternating Direction Method (ADM) is used for image restoration. ADM works well for solving inverse problem. In this paper, various applications of ADM method for image restoration are discussed.
DOI: 10.17762/ijritcc2321-8169.15030
Elimination of Glass Artifacts and Object Segmentation
Many images nowadays are captured from behind the glasses and may have
certain stains discrepancy because of glass and must be processed to make
differentiation between the glass and objects behind it. This research paper
proposes an algorithm to remove the damaged or corrupted part of the image and
make it consistent with other part of the image and to segment objects behind
the glass. The damaged part is removed using total variation inpainting method
and segmentation is done using kmeans clustering, anisotropic diffusion and
watershed transformation. The final output is obtained by interpolation. This
algorithm can be useful to applications in which some part of the images are
corrupted due to data transmission or needs to segment objects from an image
for further processing
Learning the Morphological Diversity
International audienceThis article proposes a new method for image separation into a linear combination of morphological components. Sparsity in global dictionaries is used to extract the cartoon and oscillating content of the image. Complicated texture patterns are extracted by learning adapted local dictionaries that sparsify patches in the image. These global and local sparsity priors together with the data fidelity define a non-convex energy and the separation is obtained as a stationary point of this energy. This variational optimization is extended to solve more general inverse problems such as inpainting. A new adaptive morphological component analysis algorithm is derived to find a stationary point of the energy. Using adapted dictionaries learned from data allows to circumvent some difficulties faced by fixed dictionaries. Numerical results demonstrate that this adaptivity is indeed crucial to capture complex texture patterns
Maximum-a-posteriori estimation with Bayesian confidence regions
Solutions to inverse problems that are ill-conditioned or ill-posed may have
significant intrinsic uncertainty. Unfortunately, analysing and quantifying
this uncertainty is very challenging, particularly in high-dimensional
problems. As a result, while most modern mathematical imaging methods produce
impressive point estimation results, they are generally unable to quantify the
uncertainty in the solutions delivered. This paper presents a new general
methodology for approximating Bayesian high-posterior-density credibility
regions in inverse problems that are convex and potentially very
high-dimensional. The approximations are derived by using recent concentration
of measure results related to information theory for log-concave random
vectors. A remarkable property of the approximations is that they can be
computed very efficiently, even in large-scale problems, by using standard
convex optimisation techniques. In particular, they are available as a
by-product in problems solved by maximum-a-posteriori estimation. The
approximations also have favourable theoretical properties, namely they
outer-bound the true high-posterior-density credibility regions, and they are
stable with respect to model dimension. The proposed methodology is illustrated
on two high-dimensional imaging inverse problems related to tomographic
reconstruction and sparse deconvolution, where the approximations are used to
perform Bayesian hypothesis tests and explore the uncertainty about the
solutions, and where proximal Markov chain Monte Carlo algorithms are used as
benchmark to compute exact credible regions and measure the approximation
error
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
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