25 research outputs found
PyHST2: an hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities
We present the PyHST2 code which is in service at ESRF for phase-contrast and
absorption tomography. This code has been engineered to sustain the high data
flow typical of the third generation synchrotron facilities (10 terabytes per
experiment) by adopting a distributed and pipelined architecture. The code
implements, beside a default filtered backprojection reconstruction, iterative
reconstruction techniques with a-priori knowledge. These latter are used to
improve the reconstruction quality or in order to reduce the required data
volume and reach a given quality goal. The implemented a-priori knowledge
techniques are based on the total variation penalisation and a new recently
found convex functional which is based on overlapping patches.
We give details of the different methods and their implementations while the
code is distributed under free license.
We provide methods for estimating, in the absence of ground-truth data, the
optimal parameters values for a-priori techniques
Total Variation meets Sparsity: statistical learning with segmenting penalties
International audiencePrediction from medical images is a valuable aid to diagnosis. For instance, anatomical MR images can reveal certain disease conditions, while their functional counterparts can predict neuropsychi-atric phenotypes. However, a physician will not rely on predictions by black-box models: understanding the anatomical or functional features that underpin decision is critical. Generally, the weight vectors of clas-sifiers are not easily amenable to such an examination: Often there is no apparent structure. Indeed, this is not only a prediction task, but also an inverse problem that calls for adequate regularization. We address this challenge by introducing a convex region-selecting penalty. Our penalty combines total-variation regularization, enforcing spatial conti-guity, and 1 regularization, enforcing sparsity, into one group: Voxels are either active with non-zero spatial derivative or zero with inactive spatial derivative. This leads to segmenting contiguous spatial regions (inside which the signal can vary freely) against a background of zeros. Such segmentation of medical images in a target-informed manner is an important analysis tool. On several prediction problems from brain MRI, the penalty shows good segmentation. Given the size of medical images, computational efficiency is key. Keeping this in mind, we contribute an efficient optimization scheme that brings significant computational gains
An optimal subgradient algorithm for large-scale convex optimization in simple domains
This paper shows that the optimal subgradient algorithm, OSGA, proposed in
\cite{NeuO} can be used for solving structured large-scale convex constrained
optimization problems. Only first-order information is required, and the
optimal complexity bounds for both smooth and nonsmooth problems are attained.
More specifically, we consider two classes of problems: (i) a convex objective
with a simple closed convex domain, where the orthogonal projection on this
feasible domain is efficiently available; (ii) a convex objective with a simple
convex functional constraint. If we equip OSGA with an appropriate
prox-function, the OSGA subproblem can be solved either in a closed form or by
a simple iterative scheme, which is especially important for large-scale
problems. We report numerical results for some applications to show the
efficiency of the proposed scheme. A software package implementing OSGA for
above domains is available
Handling convexity-like constraints in variational problems
We provide a general framework to construct finite dimensional approximations
of the space of convex functions, which also applies to the space of c-convex
functions and to the space of support functions of convex bodies. We give
estimates of the distance between the approximation space and the admissible
set. This framework applies to the approximation of convex functions by
piecewise linear functions on a mesh of the domain and by other
finite-dimensional spaces such as tensor-product splines. We show how these
discretizations are well suited for the numerical solution of problems of
calculus of variations under convexity constraints. Our implementation relies
on proximal algorithms, and can be easily parallelized, thus making it
applicable to large scale problems in dimension two and three. We illustrate
the versatility and the efficiency of our approach on the numerical solution of
three problems in calculus of variation : 3D denoising, the principal agent
problem, and optimization within the class of convex bodies.Comment: 23 page
Distributed solution of stochastic optimal control problems on GPUs
Stochastic optimal control problems arise in many applications and are, in principle, large-scale involving up to millions of decision variables. Their applicability in control applications is often limited by the availability of algorithms that can solve them efficiently and within the sampling time of the controlled system.
In this paper we propose a dual accelerated proximal gradient algorithm which is amenable to parallelization and demonstrate that its GPU implementation affords high speed-up values (with respect to a CPU implementation) and greatly outperforms well-established commercial optimizers such as Gurobi
Solving Multiple-Block Separable Convex Minimization Problems Using Two-Block Alternating Direction Method of Multipliers
In this paper, we consider solving multiple-block separable convex
minimization problems using alternating direction method of multipliers (ADMM).
Motivated by the fact that the existing convergence theory for ADMM is mostly
limited to the two-block case, we analyze in this paper, both theoretically and
numerically, a new strategy that first transforms a multi-block problem into an
equivalent two-block problem (either in the primal domain or in the dual
domain) and then solves it using the standard two-block ADMM. In particular, we
derive convergence results for this two-block ADMM approach to solve
multi-block separable convex minimization problems, including an improved
O(1/\epsilon) iteration complexity result. Moreover, we compare the numerical
efficiency of this approach with the standard multi-block ADMM on several
separable convex minimization problems which include basis pursuit, robust
principal component analysis and latent variable Gaussian graphical model
selection. The numerical results show that the multiple-block ADMM, although
lacks theoretical convergence guarantees, typically outperforms two-block
ADMMs
Designing Gabor windows using convex optimization
Redundant Gabor frames admit an infinite number of dual frames, yet only the
canonical dual Gabor system, constructed from the minimal l2-norm dual window,
is widely used. This window function however, might lack desirable properties,
e.g. good time-frequency concentration, small support or smoothness. We employ
convex optimization methods to design dual windows satisfying the Wexler-Raz
equations and optimizing various constraints. Numerical experiments suggest
that alternate dual windows with considerably improved features can be found
Revisiting Synthesis Model of Sparse Audio Declipper
The state of the art in audio declipping has currently been achieved by SPADE
(SParse Audio DEclipper) algorithm by Kiti\'c et al. Until now, the
synthesis/sparse variant, S-SPADE, has been considered significantly slower
than its analysis/cosparse counterpart, A-SPADE. It turns out that the opposite
is true: by exploiting a recent projection lemma, individual iterations of both
algorithms can be made equally computationally expensive, while S-SPADE tends
to require considerably fewer iterations to converge. In this paper, the two
algorithms are compared across a range of parameters such as the window length,
window overlap and redundancy of the transform. The experiments show that
although S-SPADE typically converges faster, the average performance in terms
of restoration quality is not superior to A-SPADE
Data-proximal complementary -TV reconstruction for limited data CT
In a number of tomographic applications, data cannot be fully acquired,
resulting in a severely underdetermined image reconstruction. In such cases,
conventional methods lead to reconstructions with significant artifacts. To
overcome these artifacts, regularization methods are applied that incorporate
additional information. An important example is TV reconstruction, which is
known to be efficient at compensating for missing data and reducing
reconstruction artifacts. At the same time, however, tomographic data is also
contaminated by noise, which poses an additional challenge. The use of a single
regularizer must therefore account for both the missing data and the noise.
However, a particular regularizer may not be ideal for both tasks. For example,
the TV regularizer is a poor choice for noise reduction across multiple scales,
in which case curvelet regularization methods are well suited. To
address this issue, in this paper we introduce a novel variational
regularization framework that combines the advantages of different
regularizers. The basic idea of our framework is to perform reconstruction in
two stages, where the first stage mainly aims at accurate reconstruction in the
presence of noise, and the second stage aims at artifact reduction. Both
reconstruction stages are connected by a data proximity condition. The proposed
method is implemented and tested for limited-view CT using a combined
curvelet-TV approach. We define and implement a curvelet transform adapted to
the limited-view problem and illustrate the advantages of our approach in
numerical experiments