A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data

Convolutional Gated Recurrent Neural Network Incorporating Spatial Features for Audio Tagging

Environmental audio tagging is a newly proposed task to predict the presence or absence of a specific audio event in a chunk. Deep neural network (DNN) based methods have been successfully adopted for predicting the audio tags in the domestic audio scene. In this paper, we propose to use a convolutional neural network (CNN) to extract robust features from mel-filter banks (MFBs), spectrograms or even raw waveforms for audio tagging. Gated recurrent unit (GRU) based recurrent neural networks (RNNs) are then cascaded to model the long-term temporal structure of the audio signal. To complement the input information, an auxiliary CNN is designed to learn on the spatial features of stereo recordings. We evaluate our proposed methods on Task 4 (audio tagging) of the Detection and Classification of Acoustic Scenes and Events 2016 (DCASE 2016) challenge. Compared with our recent DNN-based method, the proposed structure can reduce the equal error rate (EER) from 0.13 to 0.11 on the development set. The spatial features can further reduce the EER to 0.10. The performance of the end-to-end learning on raw waveforms is also comparable. Finally, on the evaluation set, we get the state-of-the-art performance with 0.12 EER while the performance of the best existing system is 0.15 EER.Comment: Accepted to IJCNN2017, Anchorage, Alaska, US

Stochastic partial differential equation based modelling of large space-time data sets

Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a flexible model class for spatio-temporal processes which is computationally feasible also for large data sets. The Gaussian process defined through the stochastic partial differential equation has in general a nonseparable covariance structure. Furthermore, its parameters can be physically interpreted as explicitly modeling phenomena such as transport and diffusion that occur in many natural processes in diverse fields ranging from environmental sciences to ecology. In order to obtain computationally efficient statistical algorithms we use spectral methods to solve the stochastic partial differential equation. This has the advantage that approximation errors do not accumulate over time, and that in the spectral space the computational cost grows linearly with the dimension, the total computational costs of Bayesian or frequentist inference being dominated by the fast Fourier transform. The proposed model is applied to postprocessing of precipitation forecasts from a numerical weather prediction model for northern Switzerland. In contrast to the raw forecasts from the numerical model, the postprocessed forecasts are calibrated and quantify prediction uncertainty. Moreover, they outperform the raw forecasts, in the sense that they have a lower mean absolute error