An Efficient Algorithm for Video Super-Resolution Based On a Sequential Model

In this work, we propose a novel procedure for video super-resolution, 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, non-convex and non-smooth problem. We propose an algorithmic framework to address the latter. Our approach relies on fast gradient evaluation methods and modern optimization techniques for non-differentiable/non-convex 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.}Comment: 37 pages, SIAM Journal on Imaging Sciences, 201

Relaxed Recovery Conditions for OMP/OLS by Exploiting both Coherence and Decay

We propose extended coherence-based conditions for exact sparse support recovery using orthogonal matching pursuit (OMP) and orthogonal least squares (OLS). 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 $\mu<1/(2k-1)$ (where $\mu$ denotes the mutual coherence and $k$ the sparsity level) can be weakened as soon as the non-zero coefficients obey some decay, both in the noiseless and the bounded-noise scenarios. Furthermore, the resulting condition is approaching $\mu<1/k$ for strongly decaying sparse signals. Finally, in the noiseless setting, we prove that the proposed conditions, in particular the bound $\mu<1/k$, are the tightest achievable guarantees based on mutual coherence

Phase recovery from a Bayesian point of view: the variational approach

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 good computational cost.Comment: To appear in the proceedings of IEEE Int'l Conference on Acoustics, Speech and Signal Processing (ICASSP

Approximate Message Passing with Restricted Boltzmann Machine Priors

Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple iid priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance

Soft Bayesian Pursuit Algorithm for Sparse Representations

International audienceThis paper deals with sparse representations within a Bayesian framework. For a Bernoulli-Gaussian model, we here propose a method based on a mean-field approximation to estimate the support of the signal. In numerical tests involving a recovery problem, the resulting algorithm is shown to have good performance over a wide range of sparsity levels, compared to various state-of-the-art algorithms

VON MISES PRIOR FOR PHASE-NOISY DOA ESTIMATION: THE VITAMIN ALGORITHM

International audienceSound waves in the ocean are affected by the space and time variabilities of the propagation medium. These fluctuations, mainly caused by internal waves such as tides and gyres, can lead to a loss of phase information in measured wave-fronts, and make hardly predictable the true location of a source. As a consequence, the performance of classical direction of arrival (DOA) estimation algorithms are significantly degraded. An important literature addresses this issue by considering either the phase as non-informative or the environment as a noise with no physical information. In this work, we propose to introduce a phase prior inspired by random fluctuation theories. This prior is combined with a sparsity assumption on the number of expected DOAs and exploited within a Bayesian framework. The contributions of such an approach are twofold: by the use of suitable prior information (small number of DOAs and phase distortion), it allows an estimation of DOAs from a single snapshot , while simultaneously providing a posterior estimation of the mean fluctuations of the propagation medium. Bayesian inference can be performed in different ways. Among the different possible procedures, we chose here to resort to a Bethe approximation and a message-passing approach recently considered in compressive sensing setups. The resulting algorithm places in the continuation of our previous works. The main improvement lies in the proba-bilistic model used to describe the phase distortion. Here we use a Multivariate Von Mises distribution, more suitable to directional statistics and still fitting the simplified theory of phase fluctuation. Numerical experiments with synthetic datasets show that the proposed algorithm , dubbed as VITAMIN for ``Von mIses swepT Approximate Message passINg'', presents interesting performance compared to other state-of-the-art algorithms. In particular, in the considered experiments, VITAMIN behaves well regarding its robustness to additive noise and phase fluctuations

Sparse representations in nested non-linear models

International audienceFollowing recent contributions in non-linear sparse represen-tations, 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 straight-forwardly 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 estimate the gradient. This computation is then implemented into the optimization procedure proposed byCan es et al., leading to a non-linear extension of it

Soft Bayesian Pursuit Algorithm for Sparse Representations

International audienceThis paper deals with sparse representations within a Bayesian framework. For a Bernoulli-Gaussian model, we here propose a method based on a mean-field approximation to estimate the support of the signal. In numerical tests involving a recovery problem, the resulting algorithm is shown to have good performance over a wide range of sparsity levels, compared to various state-of-the-art algorithms