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This paper introduces a novel adaptation approach for first-order pre- and de-emphasis filters, an essential tool in many speech and audio codecs to increase coding efficiency and perceived quality. The proposed zero-bit self-adaptation approach differs from classical forward and backward adaptation approaches in that the de-emphasis coefficient is estimated at the receiver, from the decoded pre-emphasized signal. This eliminates the need to transmit information that arises from forward adaptation as well as the signal-filter lag that is inherent in backward adaptation. Evaluation results show that the de-emphasis coefficient can be estimated accurately from the decoded pre-emphasized signal and that the proposed zero-bit self-adaptation approach provides comparable subjective improvement to forward adaptation., Comment: This paper has been accepted by the 47th International Conference on Telecommunications and Signal Processing (TSP 2024)

We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and ii) on the detection of cells containing points that violate the dual constraints. The detection is based on upper-bounds on the dual certificate, in the spirit of branch-and-bound methods. The interest of this approach is that it avoids the use of heuristic approaches to find the maximizers of dual certificates. We prove the convergence of this approach under mild hypotheses and a linear convergence rate under additional non-degeneracy assumptions. These results are confirmed by simple numerical experiments.

In the context of the optimization of Deep Neural Networks, we propose to rescale the learning rate using a new technique of automatic differentiation. This technique relies on the computation of the {\em curvature}, a second order information whose computational complexity is in between the computation of the gradient and the one of the Hessian-vector product. If (1C,1M) represents respectively the computational time and memory footprint of the gradient method, the new technique increase the overall cost to either (1.5C,2M) or (2C,1M). This rescaling has the appealing characteristic of having a natural interpretation, it allows the practitioner to choose between exploration of the parameters set and convergence of the algorithm. The rescaling is adaptive, it depends on the data and on the direction of descent. The numerical experiments highlight the different exploration/convergence regimes.

Data-driven optimization of sampling patterns in MRI has recently received a significant attention.Following recent observations on the combinatorial number of minimizers in off-the-grid optimization, we propose a framework to globally optimize the sampling densities using Bayesian optimization. Using a dimension reduction technique, we optimize the sampling trajectories more than 20 times faster than conventional off-the-grid methods, with a restricted number of training samples. This method -- among other benefits -- discards the need of automatic differentiation.Its performance is slightly worse than state-of-the-art learned trajectories since it reduces the space of admissible trajectories, but comes with significant computational advantages.Other contributions include: i) a careful evaluation of the distance in probability space to generate trajectories ii) a specific training procedure on families of operators for unrolled reconstruction networks and iii) a gradient projection based scheme for trajectory optimization.

A recent trend in the signal/image processing literature is the optimization of Fourier sampling schemes for specific datasets of signals. In this paper, we explain why choosing optimal non Cartesian Fourier sampling patterns is a difficult nonconvex problem by bringing to light two optimization issues. The first one is the existence of a combinatorial number of spurious minimizers for a generic class of signals. The second one is a vanishing gradient effect for the high frequencies. We conclude the paper by showing how using large datasets can mitigate first effect and illustrate experimentally the benefits of using stochastic gradient algorithms with a variable metric.

Reduced cohomology motivates to look at harmonic functions which satisfy certain gradient conditions. If $G$ is a direct product of two infinite groups or a (FC-central)-by-cyclic group, then there are no harmonic functions with gradient in $c_0$ on its Cayley graphs. From this, it follows that a metabelian group $G$ has no harmonic functions with gradient in $\ell^p$. Furthermore, under a radial isoperimetric condition, groups whose isoperimetric profile is bounded by power of logarithms also have no harmonic functions with gradient in $\ell^p$., Comment: 39 pages, updated references

In this paper we introduce CorticalFlow, a new geometric deep-learning model that, given a 3-dimensional image, learns to deform a reference template towards a targeted object. To conserve the template mesh's topological properties, we train our model over a set of diffeomorphic transformations. This new implementation of a flow Ordinary Differential Equation (ODE) framework benefits from a small GPU memory footprint, allowing the generation of surfaces with several hundred thousand vertices. To reduce topological errors introduced by its discrete resolution, we derive numeric conditions which improve the manifoldness of the predicted triangle mesh. To exhibit the utility of CorticalFlow, we demonstrate its performance for the challenging task of brain cortical surface reconstruction. In contrast to current state-of-the-art, CorticalFlow produces superior surfaces while reducing the computation time from nine and a half minutes to one second. More significantly, CorticalFlow enforces the generation of anatomically plausible surfaces; the absence of which has been a major impediment restricting the clinical relevance of such surface reconstruction methods.

This paper presents a new neural speech compression method that is practical in the sense that it operates at low bitrate, introduces a low latency, is compatible in computational complexity with current mobile devices, and provides a subjective quality that is comparable to that of standard mobile-telephony codecs. Other recently proposed neural vocoders also have the ability to operate at low bitrate. However, they do not produce the same level of subjective quality as standard codecs. On the other hand, standard codecs rely on objective and short-term metrics such as the segmental signal-to-noise ratio that correlate only weakly with perception. Furthermore, standard codecs are less efficient than unsupervised neural networks at capturing speech attributes, especially long-term ones. The proposed method combines a cognitive-coding encoder that extracts an interpretable unsupervised hierarchical representation with a multi stage decoder that has a GAN-based architecture. We observe that this method is very robust to the quantization of representation features. An AB test was conducted on a subset of the Harvard sentences that are commonly used to evaluate standard mobile-telephony codecs. The results show that the proposed method outperforms the standard AMR-WB codec in terms of delay, bitrate and subjective quality.

This paper proposes a novel approach for speech signal prediction based on a recurrent neural network (RNN). Unlike existing RNN-based predictors, which operate on parametric features and are trained offline on a large collection of such features, the proposed predictor operates directly on speech samples and is trained online on the recent past of the speech signal. Optionally, the network can be pre-trained offline to speed-up convergence at start-up. The proposed predictor is a single end-to-end network that captures all sorts of dependencies between samples, and therefore has the potential to outperform classical linear/non-linear and short-term/long-term speech predictor structures. We apply it to the packet loss concealment (PLC) problem and show that it outperforms the standard ITU G.711 Appendix I PLC technique.

Conventional feature-based classification methods do not apply well to automatic recognition of speech emotions, mostly because the precise set of spectral and prosodic features that is required to identify the emotional state of a speaker has not been determined yet. This paper presents a method that operates directly on the speech signal, thus avoiding the problematic step of feature extraction. Furthermore, this method combines the strengths of the classical source-filter model of human speech production with those of the recently introduced liquid state machine (LSM), a biologically-inspired spiking neural network (SNN). The source and vocal tract components of the speech signal are first separated and converted into perceptually relevant spectral representations. These representations are then processed separately by two reservoirs of neurons. The output of each reservoir is reduced in dimensionality and fed to a final classifier. This method is shown to provide very good classification performance on the Berlin Database of Emotional Speech (Emo-DB). This seems a very promising framework for solving efficiently many other problems in speech processing.

We propose an approach for cognitive coding of speech by unsupervised extraction of contextual representations in two hierarchical levels of abstraction. Speech attributes such as phoneme identity that last one hundred milliseconds or less are captured in the lower level of abstraction, while speech attributes such as speaker identity and emotion that persist up to one second are captured in the higher level of abstraction. This decomposition is achieved by a two-stage neural network, with a lower and an upper stage operating at different time scales. Both stages are trained to predict the content of the signal in their respective latent spaces. A top-down pathway between stages further improves the predictive capability of the network. With an application in speech compression in mind, we investigate the effect of dimensionality reduction and low bitrate quantization on the extracted representations. The performance measured on the LibriSpeech and EmoV-DB datasets reaches, and for some speech attributes even exceeds, that of state-of-the-art approaches.

We propose a novel learning based algorithm to generate efficient and physically plausible sampling patterns in MRI. This method has a few advantages compared to recent learning based approaches: i) it works off-the-grid and ii) allows to handle arbitrary physical constraints. These two features allow for much more versatility in the sampling patterns that can take advantage of all the degrees of freedom offered by an MRI scanner. The method consists in a high dimensional optimization of a cost function defined implicitly by an algorithm. We propose various numerical tools to address this numerical challenge.

Balancing square and rectangular tables by rotation has been a interesting way to illustrate the intermediate value theorem. The aim of this note is to show that the balancing act but with non-rectangular tables can be a nice application of the ergodic theorem (or more generally, invariant measures)., Comment: 5 pages

We give lower and upper bounds for the separation profile (introduced by Benjamini, Schramm & Tim\'ar) for various graphs using the isoperimetric profile, growth and Hilbertian compression. For graphs which have polynomial isoperimetry and growth, we show that the separation profile $\mathrm{Sep}(n)$ is also bounded by powers of $n$. For many amenable groups, we show a lower bound in $n/ \log(n)^a$ and, for any group which has a non-trivial compression exponent in an $L^p$-space, an upper bound in $n/ \log(n)^b$. We show that solvable groups of exponential growth cannot have a separation profile bounded above by a sublinear power function. In an appendix, we introduce the notion of local separation, with applications for percolation clusters of $ \mathbb{Z}^{d} $ and graphs which have polynomial isoperimetry and growth., Comment: 41 pages

Critical nets in $\mathbb{R}^k$ (sometimes called geodesic nets) are embedded graph with the property that their embedding is a critical point of the total (edge) length functional and under the constraint that certain 1-valent vertices (leaves) have a fixed position. In contrast to what happens on generic manifolds, we show that, if n is the number of 1-valent vertices, the total length of the edges not incident with a 1-valent vertex is bounded by rn (where r is the outer radius), the degree of any vertex is bounded by n and that the number of edges (and hence the number of vertices) is bounded by nl where l is related to the combinatorial diameter of the graph., Comment: 19 pages, 1 figure

In this paper we compute the Hausdorff distance between sets of continuous curves and sets of piecewise constant or linear discretizations. These sets are Sobolev balls given by the continuous or discrete $L^p$-norm of the derivatives. We detail the suitable discretization or smoothing procedure which are preservative in the sense of these norms. Finally we exhibit the link between Eulerian numbers and the uniformly space knots B-spline used for smoothing.

We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space M($\Omega$) of Radon measures on a subset $\Omega$ of R d. Our main result states that under some regularity conditions, the method eventually converges linearly. Additionally, we prove that continuously optimizing the amplitudes of positions of the target measure will succeed at a linear rate with a good initialization. Finally, we propose to combine the two approaches into an alternating method and discuss the comparative advantages of this approach.

We establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be understood as the \textit{atoms} of the regularizer. We then explicit that general principle by using a few popular applications. In particular, we relate it to the common wisdom that total gradient variation minimization favors the reconstruction of piecewise constant images., Comment: in Proceedings of iTWIST'18, Paper-ID: 30, Marseille, France, November, 21-23, 2018

We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and elements of the extreme rays of the regularizer level sets. An extension to a broader class of quasi-convex regularizers is also discussed. As a side result, we characterize the minimizers of the total gradient variation, which was still an unresolved problem.

This paper deals with the 3/4-discrete 2-Wasserstein optimal transport between two measures, where one is supported by a set of segment and the other one is supported by a set of Dirac masses. We select the most suitable optimization procedure that computes the optimal transport and provide numerical examples of approximation of cloud data by segments.

We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are a natural generalization of previous results revolving around the generation of blue-noise point distributions, such as Lloyd's algorithm or more advanced techniques based on power diagrams. We analyze the convergence properties and propose new approaches to accelerate the generation of point distributions. We also design new algorithms to project curves onto spaces of curves with bounded length and curvature or speed and acceleration. We illustrate the algorithm's interest through applications in advanced sampling theory, non-photorealistic rendering and path planning.

The Graetz problem is a convection-diffusion equation in a pipe invariant along a direction. The contribution of the present work is to propose a mathematical analysis of the Neumann, Robin and periodic boundary condition on the boundary of a semi-infinite pipe. The solution in the 3D space of the original problem is reduced to eigenproblems in the 2D section of the pipe. The set of solutions is described, its structure depends on the type of boundary condition and of the sign of the total flow of the fluid. This analysis is the cornerstone of numerical methods to solve Graetz problem in finite pipes, semi infinite pipes and exchangers of arbitrary cross section. Numerical test-cases illustrate the capabilities of these methods to provide solutions in various configurations.

This paper aims at determining under which conditions the semi-discrete optimal transport is twice differentiable with respect to the parameters of the discrete measure and exhibits numerical applications. The discussion focuses on minimal conditions on the background measure to ensure differentiability. We provide numerical illustrations in stippling and blue noise problems.

The aim of the current paper is to explore the implications on the group $G$ of the non-vanishing of the cohomology in degree one of one of its representation $\pi$, given some mixing conditions on $\pi$. In one direction, harmonic cocycles are used to show that the FC-centre should be finite (for mildly mixing unitary representations). Next, for any subgroup $H

We introduce the notion of connection thickness of spheres in a Cayley graph, related to dead-ends and their retreat depth. It was well-known that connection thickness is bounded for finitely presented one-ended groups. We compute that for natural generating sets of lamplighter groups on a line or on a tree, connection thickness is linear or logarithmic respectively. We show that it depends strongly on the generating set. We give an example where the metric induced at the (finite) thickness of connection gives diameter of order $n^2$ to the sphere of radius $n$. We also discuss the rarity of dead-ends and the relationships of connection thickness with cut sets in percolation theory and with almost-convexity. Finally, we present a list of open questions about spheres in Cayley graphs., Comment: 42 pages

The aim of this note is to show that lamplighter graphs where the space graph is infinite and at most two-ended and the lamp graph is at most two-ended do not admit harmonic functions with gradients in $\ell^p$ (\ie finite $p$-energy) for any $p\in [1,\infty[$ except constants (and, equivalently, that their reduced $\ell^p$ cohomology is trivial in degree one). Using similar arguments, it is also shown that many direct products of graphs (including all direct products of Cayley graphs) do not admit non-constant harmonic function with gradient in $\ell^p$. The proof relies on a theorem of Thomassen on spanning lines in squares of graphs., Comment: 6 pages

Let $\mathcal{T}_{q+1}$ be the $(q+1)$-regular tree and let $G$ be a group of automorphisms acting transitively on the vertices and on the boundary of $\mathcal{T}_{q+1}$. We give an upper bound for the growth of cocycles with values in any unitary representation of the group $G$. This bound is optimal by projecting the Haagerup cocycle onto an appropriate subspace of $\ell^{2}(E)$. We also obtain a description of functions conditionally of negative type which are unbounded.