21 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
Discrete-Continuous ADMM for Transductive Inference in Higher-Order MRFs
This paper introduces a novel algorithm for transductive inference in
higher-order MRFs, where the unary energies are parameterized by a variable
classifier. The considered task is posed as a joint optimization problem in the
continuous classifier parameters and the discrete label variables. In contrast
to prior approaches such as convex relaxations, we propose an advantageous
decoupling of the objective function into discrete and continuous subproblems
and a novel, efficient optimization method related to ADMM. This approach
preserves integrality of the discrete label variables and guarantees global
convergence to a critical point. We demonstrate the advantages of our approach
in several experiments including video object segmentation on the DAVIS data
set and interactive image segmentation
Acceleration of the PDHGM on strongly convex subspaces
We propose several variants of the primal-dual method due to Chambolle and
Pock. Without requiring full strong convexity of the objective functions, our
methods are accelerated on subspaces with strong convexity. This yields mixed
rates, with respect to initialisation and with respect to
the dual sequence, and the residual part of the primal sequence. We demonstrate
the efficacy of the proposed methods on image processing problems lacking
strong convexity, such as total generalised variation denoising and total
variation deblurring
A nonsmooth primal-dual method with simultaneous adaptive PDE constraint solver
We introduce an efficient first-order primal-dual method for the solution of
nonsmooth PDE-constrained optimization problems. We achieve this efficiency
through not solving the PDE or its linearisation on each iteration of the
optimization method. Instead, we run the method in parallel with a simple
conventional linear system solver (Jacobi, Gauss-Seidel, conjugate gradients),
always taking only one step of the linear system solver for each step of the
optimization method. The control parameter is updated on each iteration as
determined by the optimization method. We prove linear convergence under a
second-order growth condition, and numerically demonstrate the performance on a
variety of PDEs related to inverse problems involving boundary measurements
Preconditioned ADMM with nonlinear operator constraint
We are presenting a modification of the well-known Alternating Direction
Method of Multipliers (ADMM) algorithm with additional preconditioning that
aims at solving convex optimisation problems with nonlinear operator
constraints. Connections to the recently developed Nonlinear Primal-Dual Hybrid
Gradient Method (NL-PDHGM) are presented, and the algorithm is demonstrated to
handle the nonlinear inverse problem of parallel Magnetic Resonance Imaging
(MRI)
Block-proximal methods with spatially adapted acceleration
We study and develop (stochastic) primal--dual block-coordinate descent
methods for convex problems based on the method due to Chambolle and Pock. Our
methods have known convergence rates for the iterates and the ergodic gap:
if each block is strongly convex, if no convexity is
present, and more generally a mixed rate for strongly convex
blocks, if only some blocks are strongly convex. Additional novelties of our
methods include blockwise-adapted step lengths and acceleration, as well as the
ability to update both the primal and dual variables randomly in blocks under a
very light compatibility condition. In other words, these variants of our
methods are doubly-stochastic. We test the proposed methods on various image
processing problems, where we employ pixelwise-adapted acceleration