Full waveform inversion with extrapolated low frequency data

The availability of low frequency data is an important factor in the success of full waveform inversion (FWI) in the acoustic regime. The low frequencies help determine the kinematically relevant, low-wavenumber components of the velocity model, which are in turn needed to avoid convergence of FWI to spurious local minima. However, acquiring data below 2 or 3 Hz from the field is a challenging and expensive task. In this paper we explore the possibility of synthesizing the low frequencies computationally from high-frequency data, and use the resulting prediction of the missing data to seed the frequency sweep of FWI. As a signal processing problem, bandwidth extension is a very nonlinear and delicate operation. It requires a high-level interpretation of bandlimited seismic records into individual events, each of which is extrapolable to a lower (or higher) frequency band from the non-dispersive nature of the wave propagation model. We propose to use the phase tracking method for the event separation task. The fidelity of the resulting extrapolation method is typically higher in phase than in amplitude. To demonstrate the reliability of bandwidth extension in the context of FWI, we first use the low frequencies in the extrapolated band as data substitute, in order to create the low-wavenumber background velocity model, and then switch to recorded data in the available band for the rest of the iterations. The resulting method, EFWI for short, demonstrates surprising robustness to the inaccuracies in the extrapolated low frequency data. With two synthetic examples calibrated so that regular FWI needs to be initialized at 1 Hz to avoid local minima, we demonstrate that FWI based on an extrapolated [1, 5] Hz band, itself generated from data available in the [5, 15] Hz band, can produce reasonable estimations of the low wavenumber velocity models

Construction of some families of 2-dimensional crystalline representations

We construct explicitly some analytic families of etale (phi,Gamma)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and extend some results (of Deligne, Edixhoven, Fontaine and Serre) on the representations arising from modular forms.Comment: 13 pages, english and french abstract

Chirplet approximation of band-limited, real signals made easy

In this paper we present algorithms for approximating real band-limited signals by multiple Gaussian Chirps. These algorithms do not rely on matching pursuit ideas. They are hierarchial and, at each stage, the number of terms in a given approximation depends only on the number of positive-valued maxima and negative-valued minima of a signed amplitude function characterizing part of the signal. Like the algorithms used in \cite{gre2} and unlike previous methods, our chirplet approximations require neither a complete dictionary of chirps nor complicated multi-dimensional searches to obtain suitable choices of chirp parameters

On a class of intersection graphs

Given a directed graph D = (V,A) we define its intersection graph I(D) = (A,E) to be the graph having A as a node-set and two nodes of I(D) are adjacent if their corresponding arcs share a common node that is the tail of at least one of these arcs. We call these graphs facility location graphs since they arise from the classical uncapacitated facility location problem. In this paper we show that facility location graphs are hard to recognize and they are easy to recognize when the graph is triangle-free. We also determine the complexity of the vertex coloring, the stable set and the facility location problems on that class

Multichannel Speech Separation and Enhancement Using the Convolutive Transfer Function

This paper addresses the problem of speech separation and enhancement from multichannel convolutive and noisy mixtures, \emph{assuming known mixing filters}. We propose to perform the speech separation and enhancement task in the short-time Fourier transform domain, using the convolutive transfer function (CTF) approximation. Compared to time-domain filters, CTF has much less taps, consequently it has less near-common zeros among channels and less computational complexity. The work proposes three speech-source recovery methods, namely: i) the multichannel inverse filtering method, i.e. the multiple input/output inverse theorem (MINT), is exploited in the CTF domain, and for the multi-source case, ii) a beamforming-like multichannel inverse filtering method applying single source MINT and using power minimization, which is suitable whenever the source CTFs are not all known, and iii) a constrained Lasso method, where the sources are recovered by minimizing the $\ell_1$-norm to impose their spectral sparsity, with the constraint that the $\ell_2$-norm fitting cost, between the microphone signals and the mixing model involving the unknown source signals, is less than a tolerance. The noise can be reduced by setting a tolerance onto the noise power. Experiments under various acoustic conditions are carried out to evaluate the three proposed methods. The comparison between them as well as with the baseline methods is presented.Comment: Submitted to IEEE/ACM Transactions on Audio, Speech and Language Processin

Online Localization and Tracking of Multiple Moving Speakers in Reverberant Environments

We address the problem of online localization and tracking of multiple moving speakers in reverberant environments. The paper has the following contributions. We use the direct-path relative transfer function (DP-RTF), an inter-channel feature that encodes acoustic information robust against reverberation, and we propose an online algorithm well suited for estimating DP-RTFs associated with moving audio sources. Another crucial ingredient of the proposed method is its ability to properly assign DP-RTFs to audio-source directions. Towards this goal, we adopt a maximum-likelihood formulation and we propose to use an exponentiated gradient (EG) to efficiently update source-direction estimates starting from their currently available values. The problem of multiple speaker tracking is computationally intractable because the number of possible associations between observed source directions and physical speakers grows exponentially with time. We adopt a Bayesian framework and we propose a variational approximation of the posterior filtering distribution associated with multiple speaker tracking, as well as an efficient variational expectation-maximization (VEM) solver. The proposed online localization and tracking method is thoroughly evaluated using two datasets that contain recordings performed in real environments.Comment: IEEE Journal of Selected Topics in Signal Processing, 201