arXiv subjects

Laurent Daudet

Publications and source records attributed to Laurent Daudet.

33 records · Page 2Linked to original sources

arXiv2015

Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques

This paper investigates experimental means of measuring the transmission matrix (TM) of a highly scattering medium, with the simplest optical setup. Spatial light modulation is performed by a digital micromirror device (DMD), allowing high rates and high pixel counts but only binary amplitude modulation. We used intensity measurement only, thus avoiding the need for a reference beam. Therefore, the phase of the TM has to be estimated through signal processing techniques of phase retrieval. Here, we compare four different phase retrieval principles on noisy experimental data. We validate our estimations of the TM on three criteria : quality of prediction, distribution of singular values, and quality of focusing. Results indicate that Bayesian phase retrieval algorithms with variational approaches provide a good tradeoff between the computational complexity and the precision of the estimates.

physics.optics↗

arXiv2015

Listening to features

This work explores nonparametric methods which aim at synthesizing audio from low-dimensionnal acoustic features typically used in MIR frameworks. Several issues prevent this task to be straightforwardly achieved. Such features are designed for analysis and not for synthesis, thus favoring high-level description over easily inverted acoustic representation. Whereas some previous studies already considered the problem of synthesizing audio from features such as Mel-Frequency Cepstral Coefficients, they mainly relied on the explicit formula used to compute those features in order to inverse them. Here, we instead adopt a simple blind approach, where arbitrary sets of features can be used during synthesis and where reconstruction is exemplar-based. After testing the approach on a speech synthesis from well known features problem, we apply it to the more complex task of inverting songs from the Million Song Dataset. What makes this task harder is twofold. First, that features are irregularly spaced in the temporal domain according to an onset-based segmentation. Second the exact method used to compute these features is unknown, although the features for new audio can be computed using their API as a black-box. In this paper, we detail these difficulties and present a framework to nonetheless attempting such synthesis by concatenating audio samples from a training dataset, whose features have been computed beforehand. Samples are selected at the segment level, in the feature space with a simple nearest neighbor search. Additionnal constraints can then be defined to enhance the synthesis pertinence. Preliminary experiments are presented using RWC and GTZAN audio datasets to synthesize tracks from the Million Song Dataset.

cs.SD↗

arXiv2014

Imaging With Nature: Compressive Imaging Using a Multiply Scattering Medium

The recent theory of compressive sensing leverages upon the structure of signals to acquire them with much fewer measurements than was previously thought necessary, and certainly well below the traditional Nyquist-Shannon sampling rate. However, most implementations developed to take advantage of this framework revolve around controlling the measurements with carefully engineered material or acquisition sequences. Instead, we use the natural randomness of wave propagation through multiply scattering media as an optimal and instantaneous compressive imaging mechanism. Waves reflected from an object are detected after propagation through a well-characterized complex medium. Each local measurement thus contains global information about the object, yielding a purely analog compressive sensing method. We experimentally demonstrate the effectiveness of the proposed approach for optical imaging by using a 300-micrometer thick layer of white paint as the compressive imaging device. Scattering media are thus promising candidates for designing efficient and compact compressive imagers.

physics.optics↗

arXiv2014

Convex Optimization Approaches for Blind Sensor Calibration using Sparsity

We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. We divide this problem in 3 subproblems with different conditions on the gains, specifially (i) gains with different amplitude and the same phase, (ii) gains with the same amplitude and different phase and (iii) gains with different amplitude and phase. In order to solve the first case, we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. For the second case, we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals. An alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals. Finally for the third case, we propose a formulation that combines the earlier two approaches to solve the problem. The performance of the proposed algorithms is investigated extensively through numerical simulations, which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many (unknown, but sparse) calibrating signals are provided.

cs.IT↗

arXiv2014

Blind Denoising with Random Greedy Pursuits

Denoising methods require some assumptions about the signal of interest and the noise. While most denoising procedures require some knowledge about the noise level, which may be unknown in practice, here we assume that the signal expansion in a given dictionary has a distribution that is more heavy-tailed than the noise. We show how this hypothesis leads to a stopping criterion for greedy pursuit algorithms which is independent from the noise level. Inspired by the success of ensemble methods in machine learning, we propose a strategy to reduce the variance of greedy estimates by averaging pursuits obtained from randomly subsampled dictionaries. We call this denoising procedure Blind Random Pursuit Denoising (BIRD). We offer a generalization to multidimensional signals, with a structured sparse model (S-BIRD). The relevance of this approach is demonstrated on synthetic and experimental MEG signals where, without any parameter tuning, BIRD outperforms state-of-the-art algorithms even when they are informed by the noise level. Code is available to reproduce all experiments.

cs.IT↗

arXiv2014

Sampling and reconstruction of solutions to the Helmholtz equation

We consider the inverse problem of reconstructing general solutions to the Helmholtz equation on some domain $Ω$ from their values at scattered points $x_1,\dots,x_n\subset Ω$. This problem typically arises when sampling acoustic fields with $n$ microphones for the purpose of reconstructing this field over a region of interest $Ω$ contained in a larger domain $D$ in which the acoustic field propagates. In many applied settings, the shape of $D$ and the boundary conditions on its border are unknown. Our reconstruction method is based on the approximation of a general solution $u$ by linear combinations of Fourier-Bessel functions or plane waves. We analyze the convergence of the least-squares estimates to $u$ using these families of functions based on the samples $(u(x_i))_{i=1,\dots,n}$. Our analysis describes the amount of regularization needed to guarantee the convergence of the least squares estimate towards $u$, in terms of a condition that depends on the dimension of the approximation subspace, the sample size $n$ and the distribution of the samples. It reveals the advantage of using non-uniform distributions that have more points on the boundary of $Ω$. Numerical illustrations show that our approach compares favorably with reconstruction methods using other basis functions, and other types of regularization.

math.NA↗

arXiv2014

Balancing Sparsity and Rank Constraints in Quadratic Basis Pursuit

We investigate the methods that simultaneously enforce sparsity and low-rank structure in a matrix as often employed for sparse phase retrieval problems or phase calibration problems in compressive sensing. We propose a new approach for analyzing the trade off between the sparsity and low rank constraints in these approaches which not only helps to provide guidelines to adjust the weights between the aforementioned constraints, but also enables new simulation strategies for evaluating performance. We then provide simulation results for phase retrieval and phase calibration cases both to demonstrate the consistency of the proposed method with other approaches and to evaluate the change of performance with different weights for the sparsity and low rank structure constraints.

math.NA↗

arXiv2013

Source localization in reverberant rooms using sparse modeling and narrowband measurements

We study two cases of acoustic source localization in a reverberant room, from a number of point-wise narrowband measurements. In the first case, the room is perfectly known. We show that using a sparse recovery algorithm with a dictionary of sources computed a priori requires measurements at multiple frequencies. Furthermore, we study the choice of frequencies for these measurements, and show that one should avoid the modal frequencies of the room. In the second case, when the shape and the boundary conditions of the room are unknown, we propose a model of the acoustical field based on the Vekua theory, still allowing the localization of sources, at the cost of an increased number of measurements. Numerical results are given, using simple adaptations of standard sparse recovery methods.

cs.IT↗

arXiv2013

Dictionary Subselection Using an Overcomplete Joint Sparsity Model

Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As this model is often unknown for many classes of the signals, we need to select such a model based on the domain knowledge or using some exemplar signals. This paper presents a new exemplar based approach for the linear model (called the dictionary) selection, for such sparse inverse problems. The problem of dictionary selection, which has also been called the dictionary learning in this setting, is first reformulated as a joint sparsity model. The joint sparsity model here differs from the standard joint sparsity model as it considers an overcompleteness in the representation of each signal, within the range of selected subspaces. The new dictionary selection paradigm is examined with some synthetic and realistic simulations.

cs.LG↗

arXiv2013

Low-complexity computation of plate eigenmodes with Vekua approximations and the Method of Particular Solutions

This paper extends the Method of Particular Solutions (MPS) to the computation of eigenfrequencies and eigenmodes of plates. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This framework also requires a suitable formulation of the boundary conditions. Numerical tests, on two plates with various boundary conditions, demonstrate that the proposed approach provides competitive results with standard numerical schemes such as the Finite Element Method, at reduced complexity, and with large flexibility in the implementation choices.

math.NA↗

arXiv2012

Nearfield Acoustic Holography using sparsity and compressive sampling principles

Regularization of the inverse problem is a complex issue when using Near-field Acoustic Holography (NAH) techniques to identify the vibrating sources. This paper shows that, for convex homogeneous plates with arbitrary boundary conditions, new regularization schemes can be developed, based on the sparsity of the normal velocity of the plate in a well-designed basis, i.e. the possibility to approximate it as a weighted sum of few elementary basis functions. In particular, these new techniques can handle discontinuities of the velocity field at the boundaries, which can be problematic with standard techniques. This comes at the cost of a higher computational complexity to solve the associated optimization problem, though it remains easily tractable with out-of-the-box software. Furthermore, this sparsity framework allows us to take advantage of the concept of Compressive Sampling: under some conditions on the sampling process (here, the design of a random array, which can be numerically and experimentally validated), it is possible to reconstruct the sparse signals with significantly less measurements (i.e., microphones) than classically required. After introducing the different concepts, this paper presents numerical and experimental results of NAH with two plate geometries, and compares the advantages and limitations of these sparsity-based techniques over standard Tikhonov regularization.

physics.data-an↗

arXiv2012

Matching Pursuits with Random Sequential Subdictionaries

Matching pursuits are a class of greedy algorithms commonly used in signal processing, for solving the sparse approximation problem. They rely on an atom selection step that requires the calculation of numerous projections, which can be computationally costly for large dictionaries and burdens their competitiveness in coding applications. We propose using a non adaptive random sequence of subdictionaries in the decomposition process, thus parsing a large dictionary in a probabilistic fashion with no additional projection cost nor parameter estimation. A theoretical modeling based on order statistics is provided, along with experimental evidence showing that the novel algorithm can be efficiently used on sparse approximation problems. An application to audio signal compression with multiscale time-frequency dictionaries is presented, along with a discussion of the complexity and practical implementations.

cs.DS↗

arXiv2012

Informed Source Separation using Iterative Reconstruction

This paper presents a technique for Informed Source Separation (ISS) of a single channel mixture, based on the Multiple Input Spectrogram Inversion method. The reconstruction of the source signals is iterative, alternating between a time- frequency consistency enforcement and a re-mixing constraint. A dual resolution technique is also proposed, for sharper transients reconstruction. The two algorithms are compared to a state-of-the-art Wiener-based ISS technique, on a database of fourteen monophonic mixtures, with standard source separation objective measures. Experimental results show that the proposed algorithms outperform both this reference technique and the oracle Wiener filter by up to 3dB in distortion, at the cost of a significantly heavier computation.

cs.ET↗

arXiv2011

Blind calibration for compressed sensing by convex optimization

We consider the problem of calibrating a compressed sensing measurement system under the assumption that the decalibration consists in unknown gains on each measure. We focus on {\em blind} calibration, using measures performed on a few unknown (but sparse) signals. A naive formulation of this blind calibration problem, using $\ell_{1}$ minimization, is reminiscent of blind source separation and dictionary learning, which are known to be highly non-convex and riddled with local minima. In the considered context, we show that in fact this formulation can be exactly expressed as a convex optimization problem, and can be solved using off-the-shelf algorithms. Numerical simulations demonstrate the effectiveness of the approach even for highly uncalibrated measures, when a sufficient number of (unknown, but sparse) calibrating signals is provided. We observe that the success/failure of the approach seems to obey sharp phase transitions.

math.ST↗

arXiv1995

Secondary Instabilities of Surface Waves on Viscous Fluids in the Faraday Instability

Secondary instabilities of Faraday waves show three regimes: (1) As seen previously, low-viscosity (nu) fluids destabilize first into squares. At higher driving accelerations a, squares show low-frequency modulations corresponding to the motion of phase defects, while theory predicts a stationary transverse amplitude modulation (TAM). (2) High-nu fluids destabilize first to stripes. Stripes then show an oscillatory TAM whose frequency is incommensurate with the driving frequency. At higher a, the TAM undergoes a phase instability. At still higher a, edge dislocations form and fluid droplets are ejected. (3) Intermediate-nu fluids show a complex coexistence of squares and stripes, as well as stationary and oscillatory TAM instabilities of the stripes.

patt-sol↗