5,159 research outputs found
First order algorithms in variational image processing
Variational methods in imaging are nowadays developing towards a quite
universal and flexible tool, allowing for highly successful approaches on tasks
like denoising, deblurring, inpainting, segmentation, super-resolution,
disparity, and optical flow estimation. The overall structure of such
approaches is of the form ; where the functional is a data fidelity term also
depending on some input data and measuring the deviation of from such
and is a regularization functional. Moreover is a (often linear)
forward operator modeling the dependence of data on an underlying image, and
is a positive regularization parameter. While is often
smooth and (strictly) convex, the current practice almost exclusively uses
nonsmooth regularization functionals. The majority of successful techniques is
using nonsmooth and convex functionals like the total variation and
generalizations thereof or -norms of coefficients arising from scalar
products with some frame system. The efficient solution of such variational
problems in imaging demands for appropriate algorithms. Taking into account the
specific structure as a sum of two very different terms to be minimized,
splitting algorithms are a quite canonical choice. Consequently this field has
revived the interest in techniques like operator splittings or augmented
Lagrangians. Here we shall provide an overview of methods currently developed
and recent results as well as some computational studies providing a comparison
of different methods and also illustrating their success in applications.Comment: 60 pages, 33 figure
Discriminative Transfer Learning for General Image Restoration
Recently, several discriminative learning approaches have been proposed for
effective image restoration, achieving convincing trade-off between image
quality and computational efficiency. However, these methods require separate
training for each restoration task (e.g., denoising, deblurring, demosaicing)
and problem condition (e.g., noise level of input images). This makes it
time-consuming and difficult to encompass all tasks and conditions during
training. In this paper, we propose a discriminative transfer learning method
that incorporates formal proximal optimization and discriminative learning for
general image restoration. The method requires a single-pass training and
allows for reuse across various problems and conditions while achieving an
efficiency comparable to previous discriminative approaches. Furthermore, after
being trained, our model can be easily transferred to new likelihood terms to
solve untrained tasks, or be combined with existing priors to further improve
image restoration quality
A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal
Unveiling meaningful geophysical information from seismic data requires to
deal with both random and structured "noises". As their amplitude may be
greater than signals of interest (primaries), additional prior information is
especially important in performing efficient signal separation. We address here
the problem of multiple reflections, caused by wave-field bouncing between
layers. Since only approximate models of these phenomena are available, we
propose a flexible framework for time-varying adaptive filtering of seismic
signals, using sparse representations, based on inaccurate templates. We recast
the joint estimation of adaptive filters and primaries in a new convex
variational formulation. This approach allows us to incorporate plausible
knowledge about noise statistics, data sparsity and slow filter variation in
parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a
constrained minimization problem that alleviates standard regularization issues
in finding hyperparameters. The approach demonstrates significantly good
performance in low signal-to-noise ratio conditions, both for simulated and
real field seismic data
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