854 research outputs found
Sparse Poisson Noisy Image Deblurring
International audienceDeblurring noisy Poisson images has recently been subject of an increasingly amount of works in many areas such as astronomy or biological imaging. In this paper, we focus on confocal microscopy which is a very popular technique for 3D imaging of biological living specimens which gives images with a very good resolution (several hundreds of nanometers), even though degraded by both blur and Poisson noise. Deconvolution methods have been proposed to reduce these degradations and we focus in this paper on techniques which promote the introduction of explicit prior on the solution. One difficulty of these techniques is to set the value of the parameter which weights the trade-off between the data term and the regularizing term. Actually, only few works have been devoted to the research of an automatic selection of this regularizing parameter when considering Poisson noise so it is often set manually such that it gives the best visual results. We present here two recent methods to estimate this regularizing parameter and we first propose an improvement of these estimators which takes advantage of confocal images. Following these estimators, we secondly propose to express the problem of Poisson noisy images deconvolution as the minimization of a new constrained problem. The proposed constrained formulation is well suited to this application domain since it is directly expressed using the anti log-likelihood of the Poisson distribution and therefore does not require any approximation. We show how to solve the unconstrained and constrained problem using the recent Alternating Direction technique and we present results on synthetic and real data using well-known priors such as Total Variation and wavelet transforms. Among these wavelet transforms, we specially focus on the Dual-Tree Complex Wavelet transform and on the dictionary composed of Curvelets and undecimated wavelet transform
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
A new steplength selection for scaled gradient methods with application to image deblurring
Gradient methods are frequently used in large scale image deblurring problems
since they avoid the onerous computation of the Hessian matrix of the objective
function. Second order information is typically sought by a clever choice of
the steplength parameter defining the descent direction, as in the case of the
well-known Barzilai and Borwein rules. In a recent paper, a strategy for the
steplength selection approximating the inverse of some eigenvalues of the
Hessian matrix has been proposed for gradient methods applied to unconstrained
minimization problems. In the quadratic case, this approach is based on a
Lanczos process applied every m iterations to the matrix of the most recent m
back gradients but the idea can be extended to a general objective function. In
this paper we extend this rule to the case of scaled gradient projection
methods applied to non-negatively constrained minimization problems, and we
test the effectiveness of the proposed strategy in image deblurring problems in
both the presence and the absence of an explicit edge-preserving regularization
term
New convergence results for the scaled gradient projection method
The aim of this paper is to deepen the convergence analysis of the scaled
gradient projection (SGP) method, proposed by Bonettini et al. in a recent
paper for constrained smooth optimization. The main feature of SGP is the
presence of a variable scaling matrix multiplying the gradient, which may
change at each iteration. In the last few years, an extensive numerical
experimentation showed that SGP equipped with a suitable choice of the scaling
matrix is a very effective tool for solving large scale variational problems
arising in image and signal processing. In spite of the very reliable numerical
results observed, only a weak, though very general, convergence theorem is
provided, establishing that any limit point of the sequence generated by SGP is
stationary. Here, under the only assumption that the objective function is
convex and that a solution exists, we prove that the sequence generated by SGP
converges to a minimum point, if the scaling matrices sequence satisfies a
simple and implementable condition. Moreover, assuming that the gradient of the
objective function is Lipschitz continuous, we are also able to prove the
O(1/k) convergence rate with respect to the objective function values. Finally,
we present the results of a numerical experience on some relevant image
restoration problems, showing that the proposed scaling matrix selection rule
performs well also from the computational point of view
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