An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

Optimal Window and Lattice in Gabor Transform Application to Audio Analysis

This article deals with the use of optimal lattice and optimal window in Discrete Gabor Transform computation. In the case of a generalized Gaussian window, extending earlier contributions, we introduce an additional local window adaptation technique for non-stationary signals. We illustrate our approach and the earlier one by addressing three time-frequency analysis problems to show the improvements achieved by the use of optimal lattice and window: close frequencies distinction, frequency estimation and SNR estimation. The results are presented, when possible, with real world audio signals

ShearLab 3D: Faithful Digital Shearlet Transforms based on Compactly Supported Shearlets

Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably deficient of sparsely approximating and also of analyzing in the sense of, for instance, detecting their direction. Shearlets are a directional representation system extending the wavelet framework, which overcomes those deficiencies. Similar to wavelets, shearlets allow a faithful implementation and fast associated transforms. In this paper, we will introduce a comprehensive carefully documented software package coined ShearLab 3D (www.ShearLab.org) and discuss its algorithmic details. This package provides MATLAB code for a novel faithful algorithmic realization of the 2D and 3D shearlet transform (and their inverses) associated with compactly supported universal shearlet systems incorporating the option of using CUDA. We will present extensive numerical experiments in 2D and 3D concerning denoising, inpainting, and feature extraction, comparing the performance of ShearLab 3D with similar transform-based algorithms such as curvelets, contourlets, or surfacelets. In the spirit of reproducible reseaerch, all scripts are accessible on www.ShearLab.org.Comment: There is another shearlet software package (http://www.mathematik.uni-kl.de/imagepro/members/haeuser/ffst/) by S. H\"auser and G. Steidl. We will include this in a revisio

Perceptually Motivated Wavelet Packet Transform for Bioacoustic Signal Enhancement

A significant and often unavoidable problem in bioacoustic signal processing is the presence of background noise due to an adverse recording environment. This paper proposes a new bioacoustic signal enhancement technique which can be used on a wide range of species. The technique is based on a perceptually scaled wavelet packet decomposition using a species-specific Greenwood scale function. Spectral estimation techniques, similar to those used for human speech enhancement, are used for estimation of clean signal wavelet coefficients under an additive noise model. The new approach is compared to several other techniques, including basic bandpass filtering as well as classical speech enhancement methods such as spectral subtraction, Wiener filtering, and Ephraim–Malah filtering. Vocalizations recorded from several species are used for evaluation, including the ortolan bunting (Emberiza hortulana), rhesus monkey (Macaca mulatta), and humpback whale (Megaptera novaeanglia), with both additive white Gaussian noise and environment recording noise added across a range of signal-to-noise ratios (SNRs). Results, measured by both SNR and segmental SNR of the enhanced wave forms, indicate that the proposed method outperforms other approaches for a wide range of noise conditions

Automatic Conflict Detection in Police Body-Worn Audio

Automatic conflict detection has grown in relevance with the advent of body-worn technology, but existing metrics such as turn-taking and overlap are poor indicators of conflict in police-public interactions. Moreover, standard techniques to compute them fall short when applied to such diversified and noisy contexts. We develop a pipeline catered to this task combining adaptive noise removal, non-speech filtering and new measures of conflict based on the repetition and intensity of phrases in speech. We demonstrate the effectiveness of our approach on body-worn audio data collected by the Los Angeles Police Department.Comment: 5 pages, 2 figures, 1 tabl

Spatiospectral concentration on a sphere

We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere, or, alternatively, of strictly spacelimited functions that are optimally concentrated within the spherical harmonic domain. Such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications, as well as in medical imaging, computer science, cosmology and numerical analysis. The spherical Slepian functions can be found either by solving an algebraic eigenvalue problem in the spectral domain or by solving a Fredholm integral equation in the spatial domain. The associated eigenvalues are a measure of the spatiospectral concentration. When the concentration region is an axisymmetric polar cap the spatiospectral projection operator commutes with a Sturm-Liouville operator; this enables the eigenfunctions to be computed extremely accurately and efficiently, even when their area-bandwidth product, or Shannon number, is large. In the asymptotic limit of a small concentration region and a large spherical harmonic bandwidth the spherical concentration problem approaches its planar equivalent, which exhibits self-similarity when the Shannon number is kept invariant.Comment: 48 pages, 17 figures. Submitted to SIAM Review, August 24th, 200