11,272 research outputs found
Learning Dictionaries with Bounded Self-Coherence
Sparse coding in learned dictionaries has been established as a successful
approach for signal denoising, source separation and solving inverse problems
in general. A dictionary learning method adapts an initial dictionary to a
particular signal class by iteratively computing an approximate factorization
of a training data matrix into a dictionary and a sparse coding matrix. The
learned dictionary is characterized by two properties: the coherence of the
dictionary to observations of the signal class, and the self-coherence of the
dictionary atoms. A high coherence to the signal class enables the sparse
coding of signal observations with a small approximation error, while a low
self-coherence of the atoms guarantees atom recovery and a more rapid residual
error decay rate for the sparse coding algorithm. The two goals of high signal
coherence and low self-coherence are typically in conflict, therefore one seeks
a trade-off between them, depending on the application. We present a dictionary
learning method with an effective control over the self-coherence of the
trained dictionary, enabling a trade-off between maximizing the sparsity of
codings and approximating an equiangular tight frame.Comment: 4 pages, 2 figures; IEEE Signal Processing Letters, vol. 19, no. 12,
201
Determining the Mass of Kepler-78b With Nonparametric Gaussian Process Estimation
Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and
orbits a young, active K dwarf every 8 hours. The mass of Kepler-78b has been
independently reported by two teams based on radial velocity measurements using
the HIRES and HARPS-N spectrographs. Due to the active nature of the host star,
a stellar activity model is required to distinguish and isolate the planetary
signal in radial velocity data. Whereas previous studies tested parametric
stellar activity models, we modeled this system using nonparametric Gaussian
process (GP) regression. We produced a GP regression of relevant Kepler
photometry. We then use the posterior parameter distribution for our
photometric fit as a prior for our simultaneous GP + Keplerian orbit models of
the radial velocity datasets. We tested three simple kernel functions for our
GP regressions. Based on a Bayesian likelihood analysis, we selected a
quasi-periodic kernel model with GP hyperparameters coupled between the two RV
datasets, giving a Doppler amplitude of 1.86 0.25 m s and
supporting our belief that the correlated noise we are modeling is
astrophysical. The corresponding mass of 1.87 M
is consistent with that measured in previous studies, and more robust due to
our nonparametric signal estimation. Based on our mass and the radius
measurement from transit photometry, Kepler-78b has a bulk density of
6.0 g cm. We estimate that Kepler-78b is 3226% iron
using a two-component rock-iron model. This is consistent with an Earth-like
composition, with uncertainty spanning Moon-like to Mercury-like compositions.Comment: 10 pages, 5 figures, accepted to ApJ 6/16/201
An evaluation of intrusive instrumental intelligibility metrics
Instrumental intelligibility metrics are commonly used as an alternative to
listening tests. This paper evaluates 12 monaural intrusive intelligibility
metrics: SII, HEGP, CSII, HASPI, NCM, QSTI, STOI, ESTOI, MIKNN, SIMI, SIIB, and
. In addition, this paper investigates the ability of
intelligibility metrics to generalize to new types of distortions and analyzes
why the top performing metrics have high performance. The intelligibility data
were obtained from 11 listening tests described in the literature. The stimuli
included Dutch, Danish, and English speech that was distorted by additive
noise, reverberation, competing talkers, pre-processing enhancement, and
post-processing enhancement. SIIB and HASPI had the highest performance
achieving a correlation with listening test scores on average of
and , respectively. The high performance of SIIB may, in part, be
the result of SIIBs developers having access to all the intelligibility data
considered in the evaluation. The results show that intelligibility metrics
tend to perform poorly on data sets that were not used during their
development. By modifying the original implementations of SIIB and STOI, the
advantage of reducing statistical dependencies between input features is
demonstrated. Additionally, the paper presents a new version of SIIB called
, which has similar performance to SIIB and HASPI,
but takes less time to compute by two orders of magnitude.Comment: Published in IEEE/ACM Transactions on Audio, Speech, and Language
Processing, 201
Compressive Time Delay Estimation Using Interpolation
Time delay estimation has long been an active area of research. In this work,
we show that compressive sensing with interpolation may be used to achieve good
estimation precision while lowering the sampling frequency. We propose an
Interpolating Band-Excluded Orthogonal Matching Pursuit algorithm that uses one
of two interpolation functions to estimate the time delay parameter. The
numerical results show that interpolation improves estimation precision and
that compressive sensing provides an elegant tradeoff that may lower the
required sampling frequency while still attaining a desired estimation
performance.Comment: 5 pages, 2 figures, technical report supporting 1 page submission for
GlobalSIP 201
Entangled-photon Fourier optics
Entangled photons, generated by spontaneous parametric down-conversion from a
second-order nonlinear crystal, present a rich potential for imaging and
image-processing applications. Since this source is an example of a three-wave
mixing process, there is more flexibility in the choices of illumination and
detection wavelengths and in the placement of object(s) to be imaged. Moreover,
this source is entangled, a fact that allows for imaging configurations and
capabilities that cannot be achieved using classical sources of light. In this
paper we examine a number of imaging and image-processing configurations that
can be realized using this source. The formalism that we utilize facilitates
the determination of the dependence of imaging resolution on the physical
parameters of the optical arrangement.Comment: 41 pages, 12 figures, accepted for publication in J. Opt. Soc. Am.
Analysis of Dynamic Brain Imaging Data
Modern imaging techniques for probing brain function, including functional
Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging,
and magnetoencephalography, generate large data sets with complex content. In
this paper we develop appropriate techniques of analysis and visualization of
such imaging data, in order to separate the signal from the noise, as well as
to characterize the signal. The techniques developed fall into the general
category of multivariate time series analysis, and in particular we extensively
use the multitaper framework of spectral analysis. We develop specific
protocols for the analysis of fMRI, optical imaging and MEG data, and
illustrate the techniques by applications to real data sets generated by these
imaging modalities. In general, the analysis protocols involve two distinct
stages: `noise' characterization and suppression, and `signal' characterization
and visualization. An important general conclusion of our study is the utility
of a frequency-based representation, with short, moving analysis windows to
account for non-stationarity in the data. Of particular note are (a) the
development of a decomposition technique (`space-frequency singular value
decomposition') that is shown to be a useful means of characterizing the image
data, and (b) the development of an algorithm, based on multitaper methods, for
the removal of approximately periodic physiological artifacts arising from
cardiac and respiratory sources.Comment: 40 pages; 26 figures with subparts including 3 figures as .gif files.
Originally submitted to the neuro-sys archive which was never publicly
announced (was 9804003
Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals
There are three equivalent ways of representing two jointly observed
real-valued signals: as a bivariate vector signal, as a single complex-valued
signal, or as two analytic signals known as the rotary components. Each
representation has unique advantages depending on the system of interest and
the application goals. In this paper we provide a joint framework for all three
representations in the context of frequency-domain stochastic modeling. This
framework allows us to extend many established statistical procedures for
bivariate vector time series to complex-valued and rotary representations.
These include procedures for parametrically modeling signal coherence,
estimating model parameters using the Whittle likelihood, performing
semi-parametric modeling, and choosing between classes of nested models using
model choice. We also provide a new method of testing for impropriety in
complex-valued signals, which tests for noncircular or anisotropic second-order
statistical structure when the signal is represented in the complex plane.
Finally, we demonstrate the usefulness of our methodology in capturing the
anisotropic structure of signals observed from fluid dynamic simulations of
turbulence.Comment: To appear in IEEE Transactions on Signal Processin
Frequency dependence of signal power and spatial reach of the local field potential
The first recording of electrical potential from brain activity was reported
already in 1875, but still the interpretation of the signal is debated. To take
full advantage of the new generation of microelectrodes with hundreds or even
thousands of electrode contacts, an accurate quantitative link between what is
measured and the underlying neural circuit activity is needed. Here we address
the question of how the observed frequency dependence of recorded local field
potentials (LFPs) should be interpreted. By use of a well-established
biophysical modeling scheme, combined with detailed reconstructed neuronal
morphologies, we find that correlations in the synaptic inputs onto a
population of pyramidal cells may significantly boost the low-frequency
components of the generated LFP. We further find that these low-frequency
components may be less `local' than the high-frequency LFP components in the
sense that (1) the size of signal-generation region of the LFP recorded at an
electrode is larger and (2) that the LFP generated by a synaptically activated
population spreads further outside the population edge due to volume
conduction
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