9,537 research outputs found
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
Local Behavior of Sparse Analysis Regularization: Applications to Risk Estimation
In this paper, we aim at recovering an unknown signal x0 from noisy
L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear
operator and w accounts for some noise. To regularize such an ill-posed inverse
problem, we impose an analysis sparsity prior. More precisely, the recovery is
cast as a convex optimization program where the objective is the sum of a
quadratic data fidelity term and a regularization term formed of the L1-norm of
the correlations between the sought after signal and atoms in a given
(generally overcomplete) dictionary. The L1-sparsity analysis prior is weighted
by a regularization parameter lambda>0. In this paper, we prove that any
minimizers of this problem is a piecewise-affine function of the observations y
and the regularization parameter lambda. As a byproduct, we exploit these
properties to get an objectively guided choice of lambda. In particular, we
develop an extension of the Generalized Stein Unbiased Risk Estimator (GSURE)
and show that it is an unbiased and reliable estimator of an appropriately
defined risk. The latter encompasses special cases such as the prediction risk,
the projection risk and the estimation risk. We apply these risk estimators to
the special case of L1-sparsity analysis regularization. We also discuss
implementation issues and propose fast algorithms to solve the L1 analysis
minimization problem and to compute the associated GSURE. We finally illustrate
the applicability of our framework to parameter(s) selection on several imaging
problems
- …