Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field

Nonlinear approximation with nonstationary Gabor frames

We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that the concept of painless nonorthogonal expansions generalizes to the nonstationary case, providing perfect reconstruction and an FFT based implementation for compactly supported window functions sampled at a certain density. It is also known that for some signal classes, NSGFs with flexible time resolution tend to provide sparser expansions than can be obtained with classical Gabor frames. In this article we show, for the continuous case, that sparseness of a nonstationary Gabor expansion is equivalent to smoothness in an associated decomposition space. In this way we characterize signals with sparse expansions relative to NSGFs with flexible time resolution. Based on this characterization we prove an upper bound on the approximation error occurring when thresholding the coefficients of the corresponding frame expansions. We complement the theoretical results with numerical experiments, estimating the rate of approximation obtained from thresholding the coefficients of both stationary and nonstationary Gabor expansions.Comment: 19 pages, 2 figure

Scattering of dipole-mode vector solitons: Theory and experiment

We study, both theoretically and experimentally, the scattering properties of optical dipole-mode vector solitons - radially asymmetric composite self-trapped optical beams. First, we analyze the soliton collisions in an isotropic two-component model with a saturable nonlinearity and demonstrate that in many cases the scattering dynamics of the dipole-mode solitons allows us to classify them as ``molecules of light'' - extremely robust spatially localized objects which survive a wide range of interactions and display many properties of composite states with a rotational degree of freedom. Next, we study the composite solitons in an anisotropic nonlinear model that describes photorefractive nonlinearities, and also present a number of experimental verifications of our analysis.Comment: 8 pages + 4 pages of figure

Gravitational wave detection with single-laser atom interferometers

We present a new general design approach of a broad-band detector of gravitational radiation that relies on two atom interferometers separated by a distance L. In this scheme, only one arm and one laser will be used for operating the two atom interferometers. We consider atoms in the atom interferometers not only as perfect inertial reference sensors, but also as highly stable clocks. Atomic coherence is intrinsically stable and can be many orders of magnitude more stable than a laser. The unique one-laser configuration allows us to then apply time-delay interferometry to the responses of the two atom interferometers, thereby canceling the laser phase fluctuations while preserving the gravitational wave signal in the resulting data set. Our approach appears very promising. We plan to investigate further its practicality and detailed sensitivity analysis.Comment: Paper submitted to General Relativity and Gravitation as part of the prceedings of the International Workshop on Gravitational Waves Detection with Atom Interferometry (Florence, February 2009)

Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Studies of Vibrational Properties in Ga Stabilized d-Pu by Extended X-ray Absorption Fine Structure

Temperature dependent extended x-ray absorption fine structure (EXAFS) spectra were measured for a 3.3 at% Ga stabilized Pu alloy over the range T= 20 - 300 K at both the Ga K-edge and the Pu L_III-edge. The temperature dependence of the pair-distance distribution widths, \sigma(T) was accurately modeled using a correlated-Debye model for the lattice vibrational properties, suggesting Debye-like behavior in this material. We obtain pair- specific correlated-Debye temperatures, \Theta_cD, of 110.7 +/- 1.7 K and 202.6 +/- 3.7 K, for the Pu-Pu and Ga-Pu pairs, respectively. These results represent the first unambiguous determination of Ga-specific vibrational properties in PuGa alloys, and indicate the Ga-Pu bonds are significantly stronger than the Pu-Pu bonds. This effect has important implications for lattice stabilization mechanisms in these alloys.Comment: 7 pages, 4 figures, Phys. Rev. B in pres