In oceanography, the acquisition and processing of observations are crucial to improve the understanding of complex oceanic processes. Considering an idealized model of the North Atlantic ocean circulation, we propose to implement a variational data assimilation method optimized by deep learning to reconstruct abrupt changes in ocean circulation, representing Dansgaard-Oeschger climate events. We show that this assimilation method leads to improved reconstruction performances, particularly at low sampling frequencies. Focusing on this difficult latter case, four sampling strategies are studied more specifically. Our experiments highlight that clusters of three consecutive observations regularly sampled leads to a better monitoring of the ocean circulation regime shifts. These results pave the way for further research in optimal ocean observation.

In underwater acoustics, environmental fluctuations can lead to a loss of coherence in sonar arrays. Among the various approaches that can be considered to mitigate their effects, sub-array processing is a popular and intuitive one. However, it naturally results in sub-optimal performance. In this paper, we propose to enhance the approach in two ways. A first improvement is made by linking the parameters of the approach to those of the environment through a canonical correlation analysis. This leads in particular to an environment-informed calibration of the sub-arrays. A second improvement, more classical, is considered by using a sparse regularization on each sub-array processing. We show on real data the relevance of these choices and discuss the perspectives they open.

Considering low-frequency acoustic sources, shallow-water environments act as modal dispersive waveguides. In this context, the signal can be described as a sum of a few modal components, each of them propagating with its own wavenumber. When dealing with broadband sources, wavenumber-frequency (f-k) diagrams constitute popular representations naturally enabling modal separation. Based on a Fourier transform, they require however a large number of sensors to resolve wavenumbers with a high-resolution. This limitation can be overcame by adding some physical priors to the processing method. In the continuation of previous works, we propose here a new grid-free algorithm allowing a super-resolution of the (f-k) diagram by benifiting from the sparse nature of the wavenumber spectrum and embedding the broadband behavior of the wavenumbers within the algorithm. The method is validated on simulated data.

This paper focusses on “safe” screening techniques for the LASSO problem. Motivated by the need for low-complexity algorithms, we propose a new approach, dubbed “joint screening test”, allowing to screen a set of atoms by carrying out one single test. The approach is particularized to two different sets of atoms, respectively expressed as sphere and dome regions. After presenting the mathematical derivations of the tests, we elaborate on their relative effectiveness and discuss the practical use of such procedures.

In this paper, we investigate a new method for phase recovery when prior information on the missing phases is available. In particular, we propose to take into account this information in a generic fashion by means of a multivariate Von Mises distribution. Building on a Bayesian formulation (a Maximum A Posteriori estimation), we show that the problem can be expressed using a Mahalanobis distance and be solved by a lifting optimization procedure.

In this paper we focus on the problem of estimating the directions of arrival (DOA) of a set of incident plane waves. Unlike many previous works, which assume that the received observations are only affected by additive noise, we consider the setup where some phase noise also corrupts the data (as for example observed in atmospheric sound propagation or underwater acoustics). We propose a new methodology to solve this problem in a Bayesian framework by resorting to a variational mean-field approximation. Our simulation results illustrate the benefits of carefully accounting for the phase noise in the DOA estimation process.

Random projections have proven extremely useful in many signal processing and machine learning applications. However, they often require either to store a very large random matrix, or to use a different, structured matrix to reduce the computational and memory costs. Here, we overcome this difficulty by proposing an analog, optical device, that performs the random projections literally at the speed of light without having to store any matrix in memory. This is achieved using the physical properties of multiple coherent scattering of coherent light in random media. We use this device on a simple task of classification with a kernel machine, and we show that, on the MNIST database, the experimental results closely match the theoretical performance of the corresponding kernel. This framework can help make kernel methods practical for applications that have large training sets and/or require real-time prediction. We discuss possible extensions of the method in terms of a class of kernels, speed, memory consumption and different problems.

In this work, we propose a novel procedure for video superresolution, that is, the recovery of a sequence of high-resolution images from its low-resolution counterpart. Our approach is based on a “sequential” model (i.e., each high-resolution frame is supposed to be a displaced version of the preceding one) and considers the use of sparsity-enforcing priors. Both the recovery of the high-resolution images and the motion fields relating them is tackled. This leads to a large-dimensional, nonconvex and nonsmooth problem. We propose an algorithmic framework to address the latter. Our approach relies on fast gradient evaluation methods and modern optimization techniques for nondifferentiable/nonconvex problems. Unlike some other previous works, we show that there exists a provably convergent method with a complexity linear in the problem dimensions. We assess the proposed optimization method on several video benchmarks and emphasize its good performance with respect to the state of the art.

We propose extended coherence-based conditions for exact sparse support recovery using orthogonal matching pursuit and orthogonal least squares. Unlike standard uniform guarantees, we embed some information about the decay of the sparse vector coefficients in our conditions. As a result, the standard condition μ <; 1/(2k - 1) (where μ denotes the mutual coherence and k the sparsity level) can be weakened as soon as the nonzero coefficients obey some decay, both in the noiseless and the bounded-noise scenarios. Furthermore, the resulting condition is approaching μ <; 1/k for strongly decaying sparse signals. Finally, in the noiseless setting, we prove that the proposed conditions, in particular the bound μ <; 1/k, are the tightest achievable guarantees based on mutual coherence.

In this paper, we consider the phase recovery problem, where a complex signal vector has to be estimated from the knowledge of the modulus of its linear projections, from a naive variational Bayesian point of view. In particular, we derive an iterative algorithm following the minimization of the Kullback-Leibler divergence under the mean-field assumption, and show on synthetic data with random projections that this approach leads to an efficient and robust procedure, with a reasonable computational cost.

Following recent contributions in non-linear sparse representations, this work focuses on a particular non-linear model, defined as the nested composition of functions. Recalling that most linear sparse representation algorithms can be straightforwardly extended to non-linear models, we emphasize that their performance highly relies on an efficient computation of the gradient of the objective function. In the particular case of interest, we propose to resort to a well-known technique from the theory of optimal control to evaluate the gradient. This computation is then implemented into the “ℓ1-reweighted” procedure proposed by Candès et al., leading to a non-linear extension of it.

We recently introduced the high-resolution nonnegative matrix factorization (HR-NMF) model for analyzing mixtures of nonstationary signals in the time-frequency domain, and highlighted its capability to both reach high spectral resolution and reconstruct high quality audio signals. In order to estimate the model parameters and the latent components, we proposed to resort to an expectation-maximization (EM) algorithm based on a Kalman filter/smoother. The approach proved to be appropriate for modeling audio signals in applications such as source separation and audio inpainting. However, its computational cost is high, dominated by the Kalman filter/smoother, and may be prohibitive when dealing with high-dimensional signals. In this paper, we consider two different alternatives, using the variational Bayesian EM algorithm and two mean-field approximations. We show that, while significantly reducing the complexity of the estimation, these novel approaches do not alter its quality.

This paper presents a probabilistic framework for the multimodal alignment of dance movements. The approach is based on a Hidden Markov Model (HMM) and considers different feature functions, each corresponding to a particular modality, namely motion features, extracted from depth maps, and audio features, extracted from audio recordings of dancers' steps. We show that this approach allows performing accurate dancer alignment, while constituting a general framework for various multimodal alignment tasks.

Taking advantage of the structures inherent in many sparse decompositions constitutes a promising research axis. In this paper, we address this problem from a Bayesian point of view. We exploit a Boltzmann machine, allowing to take a large variety of structures into account, and focus on the resolution of a joint maximum a posteriori problem. The proposed algorithm, called Structured Bayesian Orthogonal Matching Pursuit (SBOMP), is a structured extension of the Bayesian Orthogonal Matching Pursuit algorithm (BOMP) introduced in our previous work [1]. In numerical tests involving a recovery problem, SBOMP is shown to have good performance over a wide range of sparsity levels while keeping a reasonable computational complexity.

The ever increasing availability of high speed Internet access has led to a leap in technologies that support real-time realistic interaction between humans in online virtual environments. In the context of this work, we wish to realise the vision of an online dance studio where a dance class is to be provided by an expert dance teacher and to be delivered to online students via the web. In this paper we study some of the technical issues that need to be addressed in this challenging scenario. In particular, we describe an automatic dance analysis tool that would be used to evaluate a student's performance and provide him/her with meaningful feedback to aid improvement.

This work addresses the Huawei/3DLife Grand Challenge, presenting a novel method for the analysis of dance movements. The approach focuses on the decomposition of the dance movements into elementary motions. Placing this problem into a probabilistic framework, we propose to exploit Gaussian processes to accurately model the different components of the decomposition. The preliminary results, presented in this paper, are very promising. In particular, two applications are considered, illustrating the relevance of the proposed approach, namely the correction of tracking errors and the smoothing of some movements of the teacher to help toward the dance learning.

In this paper, we consider the problem of dictionary learning for sparse representations. Several algorithms dealing with this problem can be found in the literature. One of them, introduced by Sezer et al. in optimizes a dictionary made up of the union of orthonormal bases. In this paper, we propose a probabilistic interpretation of Sezer's algorithm and suggest a novel optimization procedure based on the EM algorithm. Comparisons of the performance in terms of missed detection rate show a clear superiority of the proposed approach.

This paper proposes a new compression algorithm based on the directional DCT (DDCT) bases introduced in [1]. We first explain how to extend the DDCT concept to rectangular bases and exploit them to build a set of bases using a bintree segmentation. We then use dynamic programming to select a basis from this set according to a rate-distortion criterion. Comparisons in terms of rate-distortion performance are finally made with the current compression standards JPEG and JPEG2000.

In this paper we address the problem of sparse representation (SR) within a Bayesian framework. We assume that the observations are generated from a Bernoulli-Gaussian process and consider the corresponding Bayesian inference problem. Tractable solutions are then proposed based on the “mean-field” approximation and the variational Bayes EM algorithm. The resulting SR algorithms are shown to have a tractable complexity and very good performance over a wide range of sparsity levels. In particular, they significantly improve the critical sparsity upon state-of-the-art SR algorithms.

In this paper, we consider the problem of spatial prediction based on sparse representations. Several algorithms dealing with this problem can be found in the literature. We propose a novel method involving a mixture of sparse representations. We first place this approach into a probabilistic framework and then derive a practical procedure to solve it. Comparisons of the rate-distortion performance show the superiority of the proposed algorithm with regard to other state-of-the-art algorithms.