Gilles Chardon

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.

Near-field acoustic holography using sparse regularization 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, alternative 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 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.

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 blind calibration, using measures performed on a few unknown (but sparse) signals. A naive formulation of this blind calibration problem, using ℓ1 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.

Low Frequency Interpolation of Room Impulse Responses Using Compressed Sensing

Measuring the Room Impulse Responses within a finite 3D spatial domain can require a very large number of measurements with standard uniform sampling. In this paper, we show that, at low frequencies, this sampling can be done with significantly less measurements, using some modal properties of the room. At a given temporal frequency, a plane wave approximation of the acoustic field leads to a sparse approximation, and therefore a compressed sensing framework can be used for its acquisition. This paper describes three different sparse models that can be constructed, and the corresponding estimation algorithms: two models that exploit the structured sparsity of the soundfield, with projections of the modes onto plane waves sharing the same wavenumber, and one that computes a sparse decomposition on a dictionary of independent plane waves with time / space variable separation. These models are compared numerically and experimentally, with an array of 120 microphones irregularly placed within a 2 ×2 ×2 m volume inside a room, with an approximate uniform distribution. One of the most challenging part is the design of estimation algorithms whose computational complexity remains tractable.

A Blind Dereverberation Method for Narrowband Source Localization

Narrowband source localization gets extremely challenging in strong reverberation. When the room is perfectly known, some dictionary-based methods have recently been proposed, allowing source localization with few measurements. In this paper, we first show that, for these methods, the choice of frequencies is important as they fail to localize sources that emit at a frequency near the modal frequencies of the room. A more difficult case, but also important in practice, is when the room geometry and boundary conditions are unknown. In this setup, we introduce a new model for the acoustic soundfield, based on the Vekua theory, that allows a separation of the field into its reverberant and direct source contributions, at the cost of more measurements. This can be used for the design of a dereverberation pre-processing step, suitable for a large variety of standard source localization techniques. We discuss the spatial sampling strategies for the sound field, in order to successfully recover acoustic sources, and the influence of parameters such as number of measurements and model order. This is validated in numerical and experimental tests, that show that this method significantly improves localization in strong reverberant conditions.

Compressively sampling the plenacoustic function

Directly measuring the full set of acoustic impulse responses within a room would require an unreasonably large number of measurements. Considering that the acoustic wavefield is sparse in some dictionaries, Compressed Sensing allows the recovery of the full wavefield with a reduced set of measurements, but raises challenging computational and memory issues. Two practical algorithms are presented and compared: one that exploits the structured sparsity of the soundfield, with projections of the modes onto plane waves sharing the same wavenumber, and one that computes a sparse decomposition on a dictionary of independent plane waves with time/space variable separation.

Perceptual matching pursuit with Gabor dictionaries and time-frequency masking

This paper describes a method to obtain a perceptually relevant sparse representation of a sound signal. Based on matching pursuit (MP) and recent psychoacoustic data on time-frequency masking measured with Gabor atoms, a perceptual matching pursuit (PMP) algorithm is proposed. To obtain a good match between the masking model and the signal representation, a dictionary of Gabor atoms with variable sizes is chosen for MP. In the proposed method, the signal is first decomposed using MP and the masking model is applied on the resulting set of atoms. This allows for isolating the masked components from the residual. Experimental results show that exploiting time-frequency masking allows to remove more atoms than using only spectral masking. Additionally, accounting for masking effects between atoms of different sizes and at different times allows for sparser representations. The objective evaluation of the proposed PMP algorithm indicates imperceptible distortions.

Narrowband source localization in an unknown reverberant environment usingwavefield sparse decomposition

We propose a method for narrowband localization of sources in an unknown reverberant field. A sparse model for the wavefield is introduced, derived from the physical equations. We compare two localization algorithms that take advantage on the structured sparsity naturally present into the model: a greedy iterative scheme, and an ℓ1 minimization method. Both methods are validated in 2D on numerical simulations, and on experimental data with a chaotic-shaped plate. These results, robust with respect to the specific sampling of the field and to noise, show that this approach may be an interesting alternative to traditional approaches of source localization, when a large number of narrowband sensors are deployed.

Optimal subsampling of multichannel damped sinusoids

In this paper, we investigate the optimal ways to sample multichannel impulse responses, composed of a small number of exponentially damped sinusoids, under the constraint that the total number of samples is fixed — for instance with limited storage / computational power. We compute Cramér-Rao bounds for multichannel estimation of the parameters of a damped sinusoid. These bounds provide the length during which the signals should be measured to get the best results, roughly at 2 times the typical decay time of the sinusoid. Due to bandwidth constraints, the signals are best sampled irregularly, and variants of Matching Pursuit and MUSIC adapted to the irregular sampling and multichannel data are compared to the Cramér-Rao bounds. In practical situation, this method leads to savings in terms of memory, data throughput and computational complexity.

Design of Spatial Microphone Arrays for Sound Field Interpolation

This paper presents a design method for microphone arrays with arbitrary geometries. Based on a theoretical analysis and on the magic points method, it allows for the interpolation of a sound field in a generic convex domain with a limited number of microphones on a given frequency band. It is shown that only a few microphones are needed in the interior of the considered domain to ensure a low interpolation error in the frequency band of interest, and that most of the microphones have to be located on the boundary of the domain, with a non-uniform density depending on the shape of the domain. Practical design constraints can be included in the optimization process. Comparisons for some particular array geometries with design methods known from the literature are given, showing that the proposed approach results in lower errors.