1,380 research outputs found
Quantum polarization tomography of bright squeezed light
We reconstruct the polarization sector of a bright polarization squeezed beam
starting from a complete set of Stokes measurements. Given the symmetry that
underlies the polarization structure of quantum fields, we use the unique SU(2)
Wigner distribution to represent states. In the limit of localized and bright
states, the Wigner function can be approximated by an inverse three-dimensional
Radon transform. We compare this direct reconstruction with the results of a
maximum likelihood estimation, finding an excellent agreement.Comment: 15 pages, 5 figures. Contribution to New Journal of Physics, Focus
Issue on Quantum Tomography. Comments welcom
Multiscale adaptive smoothing models for the hemodynamic response function in fMRI
In the event-related functional magnetic resonance imaging (fMRI) data
analysis, there is an extensive interest in accurately and robustly estimating
the hemodynamic response function (HRF) and its associated statistics (e.g.,
the magnitude and duration of the activation). Most methods to date are
developed in the time domain and they have utilized almost exclusively the
temporal information of fMRI data without accounting for the spatial
information. The aim of this paper is to develop a multiscale adaptive
smoothing model (MASM) in the frequency domain by integrating the spatial and
frequency information to adaptively and accurately estimate HRFs pertaining to
each stimulus sequence across all voxels in a three-dimensional (3D) volume. We
use two sets of simulation studies and a real data set to examine the finite
sample performance of MASM in estimating HRFs. Our real and simulated data
analyses confirm that MASM outperforms several other state-of-the-art methods,
such as the smooth finite impulse response (sFIR) model.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS609 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Sample Complexity of Dictionary Learning and other Matrix Factorizations
Many modern tools in machine learning and signal processing, such as sparse
dictionary learning, principal component analysis (PCA), non-negative matrix
factorization (NMF), -means clustering, etc., rely on the factorization of a
matrix obtained by concatenating high-dimensional vectors from a training
collection. While the idealized task would be to optimize the expected quality
of the factors over the underlying distribution of training vectors, it is
achieved in practice by minimizing an empirical average over the considered
collection. The focus of this paper is to provide sample complexity estimates
to uniformly control how much the empirical average deviates from the expected
cost function. Standard arguments imply that the performance of the empirical
predictor also exhibit such guarantees. The level of genericity of the approach
encompasses several possible constraints on the factors (tensor product
structure, shift-invariance, sparsity \ldots), thus providing a unified
perspective on the sample complexity of several widely used matrix
factorization schemes. The derived generalization bounds behave proportional to
w.r.t.\ the number of samples for the considered matrix
factorization techniques.Comment: to appea
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