3,933 research outputs found
Task adapted reconstruction for inverse problems
The paper considers the problem of performing a task defined on a model
parameter that is only observed indirectly through noisy data in an ill-posed
inverse problem. A key aspect is to formalize the steps of reconstruction and
task as appropriate estimators (non-randomized decision rules) in statistical
estimation problems. The implementation makes use of (deep) neural networks to
provide a differentiable parametrization of the family of estimators for both
steps. These networks are combined and jointly trained against suitable
supervised training data in order to minimize a joint differentiable loss
function, resulting in an end-to-end task adapted reconstruction method. The
suggested framework is generic, yet adaptable, with a plug-and-play structure
for adjusting both the inverse problem and the task at hand. More precisely,
the data model (forward operator and statistical model of the noise) associated
with the inverse problem is exchangeable, e.g., by using neural network
architecture given by a learned iterative method. Furthermore, any task that is
encodable as a trainable neural network can be used. The approach is
demonstrated on joint tomographic image reconstruction, classification and
joint tomographic image reconstruction segmentation
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
Learning Deep CNN Denoiser Prior for Image Restoration
Model-based optimization methods and discriminative learning methods have
been the two dominant strategies for solving various inverse problems in
low-level vision. Typically, those two kinds of methods have their respective
merits and drawbacks, e.g., model-based optimization methods are flexible for
handling different inverse problems but are usually time-consuming with
sophisticated priors for the purpose of good performance; in the meanwhile,
discriminative learning methods have fast testing speed but their application
range is greatly restricted by the specialized task. Recent works have revealed
that, with the aid of variable splitting techniques, denoiser prior can be
plugged in as a modular part of model-based optimization methods to solve other
inverse problems (e.g., deblurring). Such an integration induces considerable
advantage when the denoiser is obtained via discriminative learning. However,
the study of integration with fast discriminative denoiser prior is still
lacking. To this end, this paper aims to train a set of fast and effective CNN
(convolutional neural network) denoisers and integrate them into model-based
optimization method to solve other inverse problems. Experimental results
demonstrate that the learned set of denoisers not only achieve promising
Gaussian denoising results but also can be used as prior to deliver good
performance for various low-level vision applications.Comment: Accepted to CVPR 2017. Code: https://github.com/cszn/ircn
Bregman Cost for Non-Gaussian Noise
One of the tasks of the Bayesian inverse problem is to find a good estimate
based on the posterior probability density. The most common point estimators
are the conditional mean (CM) and maximum a posteriori (MAP) estimates, which
correspond to the mean and the mode of the posterior, respectively. From a
theoretical point of view it has been argued that the MAP estimate is only in
an asymptotic sense a Bayes estimator for the uniform cost function, while the
CM estimate is a Bayes estimator for the means squared cost function. Recently,
it has been proven that the MAP estimate is a proper Bayes estimator for the
Bregman cost if the image is corrupted by Gaussian noise. In this work we
extend this result to other noise models with log-concave likelihood density,
by introducing two related Bregman cost functions for which the CM and the MAP
estimates are proper Bayes estimators. Moreover, we also prove that the CM
estimate outperforms the MAP estimate, when the error is measured in a certain
Bregman distance, a result previously unknown also in the case of additive
Gaussian noise
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