46,170 research outputs found
Combining synchrosqueezed wave packet transform with optimization for crystal image analysis
We develop a variational optimization method for crystal analysis in atomic
resolution images, which uses information from a 2D synchrosqueezed transform
(SST) as input. The synchrosqueezed transform is applied to extract initial
information from atomic crystal images: crystal defects, rotations and the
gradient of elastic deformation. The deformation gradient estimate is then
improved outside the identified defect region via a variational approach, to
obtain more robust results agreeing better with the physical constraints. The
variational model is optimized by a nonlinear projected conjugate gradient
method. Both examples of images from computer simulations and imaging
experiments are analyzed, with results demonstrating the effectiveness of the
proposed method
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
An algorithm for constrained one-step inversion of spectral CT data
We develop a primal-dual algorithm that allows for one-step inversion of
spectral CT transmission photon counts data to a basis map decomposition. The
algorithm allows for image constraints to be enforced on the basis maps during
the inversion. The derivation of the algorithm makes use of a local upper
bounding quadratic approximation to generate descent steps for non-convex
spectral CT data discrepancy terms, combined with a new convex-concave
optimization algorithm. Convergence of the algorithm is demonstrated on
simulated spectral CT data. Simulations with noise and anthropomorphic phantoms
show examples of how to employ the constrained one-step algorithm for spectral
CT data.Comment: Submitted to Physics in Medicine and Biolog
A dual framework for low-rank tensor completion
One of the popular approaches for low-rank tensor completion is to use the
latent trace norm regularization. However, most existing works in this
direction learn a sparse combination of tensors. In this work, we fill this gap
by proposing a variant of the latent trace norm that helps in learning a
non-sparse combination of tensors. We develop a dual framework for solving the
low-rank tensor completion problem. We first show a novel characterization of
the dual solution space with an interesting factorization of the optimal
solution. Overall, the optimal solution is shown to lie on a Cartesian product
of Riemannian manifolds. Furthermore, we exploit the versatile Riemannian
optimization framework for proposing computationally efficient trust region
algorithm. The experiments illustrate the efficacy of the proposed algorithm on
several real-world datasets across applications.Comment: Aceepted to appear in Advances of Nueral Information Processing
Systems (NIPS), 2018. A shorter version appeared in the NIPS workshop on
Synergies in Geometric Data Analysis 201
Non-negative mixtures
This is the author's accepted pre-print of the article, first published as M. D. Plumbley, A. Cichocki and R. Bro. Non-negative mixtures. In P. Comon and C. Jutten (Ed), Handbook of Blind Source Separation: Independent Component Analysis and Applications. Chapter 13, pp. 515-547. Academic Press, Feb 2010. ISBN 978-0-12-374726-6 DOI: 10.1016/B978-0-12-374726-6.00018-7file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.2
- …