613 research outputs found
Confidence driven TGV fusion
We introduce a novel model for spatially varying variational data fusion,
driven by point-wise confidence values. The proposed model allows for the joint
estimation of the data and the confidence values based on the spatial coherence
of the data. We discuss the main properties of the introduced model as well as
suitable algorithms for estimating the solution of the corresponding biconvex
minimization problem and their convergence. The performance of the proposed
model is evaluated considering the problem of depth image fusion by using both
synthetic and real data from publicly available datasets
A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational
methods for image recovery problems. In this paper, we extend the NLTV-based
regularization to multicomponent images by taking advantage of the Structure
Tensor (ST) resulting from the gradient of a multicomponent image. The proposed
approach allows us to penalize the non-local variations, jointly for the
different components, through various matrix norms with .
To facilitate the choice of the hyper-parameters, we adopt a constrained convex
optimization approach in which we minimize the data fidelity term subject to a
constraint involving the ST-NLTV regularization. The resulting convex
optimization problem is solved with a novel epigraphical projection method.
This formulation can be efficiently implemented thanks to the flexibility
offered by recent primal-dual proximal algorithms. Experiments are carried out
for multispectral and hyperspectral images. The results demonstrate the
interest of introducing a non-local structure tensor regularization and show
that the proposed approach leads to significant improvements in terms of
convergence speed over current state-of-the-art methods
Polca SARA - Full polarization, direction-dependent calibration and sparse imaging for radio interferometry
New generation of radio interferometers are envisaged to produce high
quality, high dynamic range Stokes images of the observed sky from the
corresponding under-sampled Fourier domain measurements. In practice, these
measurements are contaminated by the instrumental and atmospheric effects that
are well represented by Jones matrices, and are most often varying with
observation direction and time. These effects, usually unknown, act as a
limiting factor in achieving the required imaging performance and thus, their
calibration is crucial. To address this issue, we develop a global algorithm,
named Polca SARA, aiming to perform full polarization, direction-dependent
calibration and sparse imaging by employing a non-convex optimization
technique. In contrast with the existing approaches, the proposed method offers
global convergence guarantees and flexibility to incorporate sophisticated
priors to regularize the imaging as well as the calibration problem. Thus, we
adapt a polarimetric imaging specific method, enforcing the physical
polarization constraint along with a sparsity prior for the sought images. We
perform extensive simulation studies of the proposed algorithm. While
indicating the superior performance of polarization constraint based imaging,
the obtained results also highlight the importance of calibrating for
direction-dependent effects as well as for off-diagonal terms (denoting
polarization leakage) in the associated Jones matrices, without inclusion of
which the imaging quality deteriorates
Templates for Convex Cone Problems with Applications to Sparse Signal Recovery
This paper develops a general framework for solving a variety of convex cone
problems that frequently arise in signal processing, machine learning,
statistics, and other fields. The approach works as follows: first, determine a
conic formulation of the problem; second, determine its dual; third, apply
smoothing; and fourth, solve using an optimal first-order method. A merit of
this approach is its flexibility: for example, all compressed sensing problems
can be solved via this approach. These include models with objective
functionals such as the total-variation norm, ||Wx||_1 where W is arbitrary, or
a combination thereof. In addition, the paper also introduces a number of
technical contributions such as a novel continuation scheme, a novel approach
for controlling the step size, and some new results showing that the smooth and
unsmoothed problems are sometimes formally equivalent. Combined with our
framework, these lead to novel, stable and computationally efficient
algorithms. For instance, our general implementation is competitive with
state-of-the-art methods for solving intensively studied problems such as the
LASSO. Further, numerical experiments show that one can solve the Dantzig
selector problem, for which no efficient large-scale solvers exist, in a few
hundred iterations. Finally, the paper is accompanied with a software release.
This software is not a single, monolithic solver; rather, it is a suite of
programs and routines designed to serve as building blocks for constructing
complete algorithms.Comment: The TFOCS software is available at http://tfocs.stanford.edu This
version has updated reference
Time-Varying Feedback Optimization for Quadratic Programs with Heterogeneous Gradient Step Sizes
Online feedback-based optimization has become a promising framework for
real-time optimization and control of complex engineering systems. This
tutorial paper surveys the recent advances in the field as well as provides
novel convergence results for primal-dual online algorithms with heterogeneous
step sizes for different elements of the gradient. The analysis is performed
for quadratic programs and the approach is illustrated on applications for
adaptive step-size and model-free online algorithms, in the context of optimal
control of modern power systems
Efficient optimization methods for regularized learning: support vector machines and total-variation regularization
Tesis doctoral inédita. Universidad Autónoma de Madrid, Escuela Politécnica Superior, mayo de 201
- …