3,429 research outputs found
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Compressive Imaging Using RIP-Compliant CMOS Imager Architecture and Landweber Reconstruction
In this paper, we present a new image sensor architecture for fast and accurate compressive sensing (CS) of natural images. Measurement matrices usually employed in CS CMOS image sensors are recursive pseudo-random binary matrices. We have proved that the restricted isometry property of these matrices is limited by a low sparsity constant. The quality of these matrices is also affected by the non-idealities of pseudo-random number generators (PRNG). To overcome these limitations, we propose a hardware-friendly pseudo-random ternary measurement matrix generated on-chip by means of class III elementary cellular automata (ECA). These ECA present a chaotic behavior that emulates random CS measurement matrices better than other PRNG. We have combined this new architecture with a block-based CS smoothed-projected Landweber reconstruction algorithm. By means of single value decomposition, we have adapted this algorithm to perform fast and precise reconstruction while operating with binary and ternary matrices. Simulations are provided to qualify the approach.Ministerio de Economía y Competitividad TEC2015-66878-C3-1-RJunta de Andalucía TIC 2338-2013Office of Naval Research (USA) N000141410355European Union H2020 76586
Jump-sparse and sparse recovery using Potts functionals
We recover jump-sparse and sparse signals from blurred incomplete data
corrupted by (possibly non-Gaussian) noise using inverse Potts energy
functionals. We obtain analytical results (existence of minimizers, complexity)
on inverse Potts functionals and provide relations to sparsity problems. We
then propose a new optimization method for these functionals which is based on
dynamic programming and the alternating direction method of multipliers (ADMM).
A series of experiments shows that the proposed method yields very satisfactory
jump-sparse and sparse reconstructions, respectively. We highlight the
capability of the method by comparing it with classical and recent approaches
such as TV minimization (jump-sparse signals), orthogonal matching pursuit,
iterative hard thresholding, and iteratively reweighted minimization
(sparse signals)
Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem
In this paper, we develop a Bayesian evidence maximization framework to solve
the sparse non-negative least squares (S-NNLS) problem. We introduce a family
of probability densities referred to as the Rectified Gaussian Scale Mixture
(R- GSM) to model the sparsity enforcing prior distribution for the solution.
The R-GSM prior encompasses a variety of heavy-tailed densities such as the
rectified Laplacian and rectified Student- t distributions with a proper choice
of the mixing density. We utilize the hierarchical representation induced by
the R-GSM prior and develop an evidence maximization framework based on the
Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate
the hyper-parameters and obtain a point estimate for the solution. We refer to
the proposed method as rectified sparse Bayesian learning (R-SBL). We provide
four R- SBL variants that offer a range of options for computational complexity
and the quality of the E-step computation. These methods include the Markov
chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate
message passing and a diagonal approximation. Using numerical experiments, we
show that the proposed R-SBL method outperforms existing S-NNLS solvers in
terms of both signal and support recovery performance, and is also very robust
against the structure of the design matrix.Comment: Under Review by IEEE Transactions on Signal Processin
Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings
We tackle the multi-party speech recovery problem through modeling the
acoustic of the reverberant chambers. Our approach exploits structured sparsity
models to perform room modeling and speech recovery. We propose a scheme for
characterizing the room acoustic from the unknown competing speech sources
relying on localization of the early images of the speakers by sparse
approximation of the spatial spectra of the virtual sources in a free-space
model. The images are then clustered exploiting the low-rank structure of the
spectro-temporal components belonging to each source. This enables us to
identify the early support of the room impulse response function and its unique
map to the room geometry. To further tackle the ambiguity of the reflection
ratios, we propose a novel formulation of the reverberation model and estimate
the absorption coefficients through a convex optimization exploiting joint
sparsity model formulated upon spatio-spectral sparsity of concurrent speech
representation. The acoustic parameters are then incorporated for separating
individual speech signals through either structured sparse recovery or inverse
filtering the acoustic channels. The experiments conducted on real data
recordings demonstrate the effectiveness of the proposed approach for
multi-party speech recovery and recognition.Comment: 31 page
Sketch-based subspace clustering of hyperspectral images
Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images
FASTLens (FAst STatistics for weak Lensing) : Fast method for Weak Lensing Statistics and map making
With increasingly large data sets, weak lensing measurements are able to
measure cosmological parameters with ever greater precision. However this
increased accuracy also places greater demands on the statistical tools used to
extract the available information. To date, the majority of lensing analyses
use the two point-statistics of the cosmic shear field. These can either be
studied directly using the two-point correlation function, or in Fourier space,
using the power spectrum. But analyzing weak lensing data inevitably involves
the masking out of regions or example to remove bright stars from the field.
Masking out the stars is common practice but the gaps in the data need proper
handling. In this paper, we show how an inpainting technique allows us to
properly fill in these gaps with only operations, leading to a new
image from which we can compute straight forwardly and with a very good
accuracy both the pow er spectrum and the bispectrum. We propose then a new
method to compute the bispectrum with a polar FFT algorithm, which has the main
advantage of avoiding any interpolation in the Fourier domain. Finally we
propose a new method for dark matter mass map reconstruction from shear
observations which integrates this new inpainting concept. A range of examples
based on 3D N-body simulations illustrates the results.Comment: Final version accepted by MNRAS. The FASTLens software is available
from the following link : http://irfu.cea.fr/Ast/fastlens.software.ph
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