2,724 research outputs found
Fast Image Recovery Using Variable Splitting and Constrained Optimization
We propose a new fast algorithm for solving one of the standard formulations
of image restoration and reconstruction which consists of an unconstrained
optimization problem where the objective includes an data-fidelity
term and a non-smooth regularizer. This formulation allows both wavelet-based
(with orthogonal or frame-based representations) regularization or
total-variation regularization. Our approach is based on a variable splitting
to obtain an equivalent constrained optimization formulation, which is then
addressed with an augmented Lagrangian method. The proposed algorithm is an
instance of the so-called "alternating direction method of multipliers", for
which convergence has been proved. Experiments on a set of image restoration
and reconstruction benchmark problems show that the proposed algorithm is
faster than the current state of the art methods.Comment: Submitted; 11 pages, 7 figures, 6 table
Distributed and parallel sparse convex optimization for radio interferometry with PURIFY
Next generation radio interferometric telescopes are entering an era of big
data with extremely large data sets. While these telescopes can observe the sky
in higher sensitivity and resolution than before, computational challenges in
image reconstruction need to be overcome to realize the potential of
forthcoming telescopes. New methods in sparse image reconstruction and convex
optimization techniques (cf. compressive sensing) have shown to produce higher
fidelity reconstructions of simulations and real observations than traditional
methods. This article presents distributed and parallel algorithms and
implementations to perform sparse image reconstruction, with significant
practical considerations that are important for implementing these algorithms
for Big Data. We benchmark the algorithms presented, showing that they are
considerably faster than their serial equivalents. We then pre-sample gridding
kernels to scale the distributed algorithms to larger data sizes, showing
application times for 1 Gb to 2.4 Tb data sets over 25 to 100 nodes for up to
50 billion visibilities, and find that the run-times for the distributed
algorithms range from 100 milliseconds to 3 minutes per iteration. This work
presents an important step in working towards computationally scalable and
efficient algorithms and implementations that are needed to image observations
of both extended and compact sources from next generation radio interferometers
such as the SKA. The algorithms are implemented in the latest versions of the
SOPT (https://github.com/astro-informatics/sopt) and PURIFY
(https://github.com/astro-informatics/purify) software packages {(Versions
3.1.0)}, which have been released alongside of this article.Comment: 25 pages, 5 figure
Multiscale Adaptive Representation of Signals: I. The Basic Framework
We introduce a framework for designing multi-scale, adaptive, shift-invariant
frames and bi-frames for representing signals. The new framework, called
AdaFrame, improves over dictionary learning-based techniques in terms of
computational efficiency at inference time. It improves classical multi-scale
basis such as wavelet frames in terms of coding efficiency. It provides an
attractive alternative to dictionary learning-based techniques for low level
signal processing tasks, such as compression and denoising, as well as high
level tasks, such as feature extraction for object recognition. Connections
with deep convolutional networks are also discussed. In particular, the
proposed framework reveals a drawback in the commonly used approach for
visualizing the activations of the intermediate layers in convolutional
networks, and suggests a natural alternative
An Efficient Algorithm for Video Super-Resolution Based On a Sequential Model
In this work, we propose a novel procedure for video super-resolution, that
is the recovery of a sequence of high-resolution images from its low-resolution
counterpart. Our approach is based on a "sequential" model (i.e., each
high-resolution frame is supposed to be a displaced version of the preceding
one) and considers the use of sparsity-enforcing priors. Both the recovery of
the high-resolution images and the motion fields relating them is tackled. This
leads to a large-dimensional, non-convex and non-smooth problem. We propose an
algorithmic framework to address the latter. Our approach relies on fast
gradient evaluation methods and modern optimization techniques for
non-differentiable/non-convex problems. Unlike some other previous works, we
show that there exists a provably-convergent method with a complexity linear in
the problem dimensions. We assess the proposed optimization method on {several
video benchmarks and emphasize its good performance with respect to the state
of the art.}Comment: 37 pages, SIAM Journal on Imaging Sciences, 201
Spatio-temporal wavelet regularization for parallel MRI reconstruction: application to functional MRI
Parallel MRI is a fast imaging technique that enables the acquisition of
highly resolved images in space or/and in time. The performance of parallel
imaging strongly depends on the reconstruction algorithm, which can proceed
either in the original k-space (GRAPPA, SMASH) or in the image domain
(SENSE-like methods). To improve the performance of the widely used SENSE
algorithm, 2D- or slice-specific regularization in the wavelet domain has been
deeply investigated. In this paper, we extend this approach using 3D-wavelet
representations in order to handle all slices together and address
reconstruction artifacts which propagate across adjacent slices. The gain
induced by such extension (3D-Unconstrained Wavelet Regularized -SENSE:
3D-UWR-SENSE) is validated on anatomical image reconstruction where no temporal
acquisition is considered. Another important extension accounts for temporal
correlations that exist between successive scans in functional MRI (fMRI). In
addition to the case of 2D+t acquisition schemes addressed by some other
methods like kt-FOCUSS, our approach allows us to deal with 3D+t acquisition
schemes which are widely used in neuroimaging. The resulting 3D-UWR-SENSE and
4D-UWR-SENSE reconstruction schemes are fully unsupervised in the sense that
all regularization parameters are estimated in the maximum likelihood sense on
a reference scan. The gain induced by such extensions is illustrated on both
anatomical and functional image reconstruction, and also measured in terms of
statistical sensitivity for the 4D-UWR-SENSE approach during a fast
event-related fMRI protocol. Our 4D-UWR-SENSE algorithm outperforms the SENSE
reconstruction at the subject and group levels (15 subjects) for different
contrasts of interest (eg, motor or computation tasks) and using different
parallel acceleration factors (R=2 and R=4) on 2x2x3mm3 EPI images.Comment: arXiv admin note: substantial text overlap with arXiv:1103.353
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