87,294 research outputs found
Robust 1-Bit Compressed Sensing via Hinge Loss Minimization
This work theoretically studies the problem of estimating a structured
high-dimensional signal from noisy -bit Gaussian
measurements. Our recovery approach is based on a simple convex program which
uses the hinge loss function as data fidelity term. While such a risk
minimization strategy is very natural to learn binary output models, such as in
classification, its capacity to estimate a specific signal vector is largely
unexplored. A major difficulty is that the hinge loss is just piecewise linear,
so that its "curvature energy" is concentrated in a single point. This is
substantially different from other popular loss functions considered in signal
estimation, e.g., the square or logistic loss, which are at least locally
strongly convex. It is therefore somewhat unexpected that we can still prove
very similar types of recovery guarantees for the hinge loss estimator, even in
the presence of strong noise. More specifically, our non-asymptotic error
bounds show that stable and robust reconstruction of can be achieved with
the optimal oversampling rate in terms of the number of
measurements . Moreover, we permit a wide class of structural assumptions on
the ground truth signal, in the sense that can belong to an arbitrary
bounded convex set . The proofs of our main results
rely on some recent advances in statistical learning theory due to Mendelson.
In particular, we invoke an adapted version of Mendelson's small ball method
that allows us to establish a quadratic lower bound on the error of the first
order Taylor approximation of the empirical hinge loss function
Deducing effective light transport parameters in optically thin systems
We present an extensive Monte Carlo study on light transport in optically
thin slabs, addressing both axial and transverse propagation. We completely
characterize the so-called ballistic-to-diffusive transition, notably in terms
of the spatial variance of the transmitted/reflected profile. We test the
validity of the prediction cast by diffusion theory, that the spatial variance
should grow independently of absorption and, to a first approximation, of the
sample thickness and refractive index contrast. Based on a large set of
simulated data, we build a freely available look-up table routine allowing
reliable and precise determination of the microscopic transport parameters
starting from robust observables which are independent of absolute intensity
measurements. We also present the Monte Carlo software package that was
developed for the purpose of this study
Robust 1-bit compressed sensing and sparse logistic regression: A convex programming approach
This paper develops theoretical results regarding noisy 1-bit compressed
sensing and sparse binomial regression. We show that a single convex program
gives an accurate estimate of the signal, or coefficient vector, for both of
these models. We demonstrate that an s-sparse signal in R^n can be accurately
estimated from m = O(slog(n/s)) single-bit measurements using a simple convex
program. This remains true even if each measurement bit is flipped with
probability nearly 1/2. Worst-case (adversarial) noise can also be accounted
for, and uniform results that hold for all sparse inputs are derived as well.
In the terminology of sparse logistic regression, we show that O(slog(n/s))
Bernoulli trials are sufficient to estimate a coefficient vector in R^n which
is approximately s-sparse. Moreover, the same convex program works for
virtually all generalized linear models, in which the link function may be
unknown. To our knowledge, these are the first results that tie together the
theory of sparse logistic regression to 1-bit compressed sensing. Our results
apply to general signal structures aside from sparsity; one only needs to know
the size of the set K where signals reside. The size is given by the mean width
of K, a computable quantity whose square serves as a robust extension of the
dimension.Comment: 25 pages, 1 figure, error fixed in Lemma 4.
Tunable superlattice p-i-n photodetectors: characteristics, theory, and application
Extended measurements and theory on the recently developed monolithic wavelength demultiplexer consisting of voltage-tunable superlattice p-i-n photodetectors in a waveguide confirmation are discussed. It is shown that the device is able to demultiplex and detect two optical signals with a wavelength separation of 20 nm directly into different electrical channels at a data rate of 1 Gb/s and with a crosstalk attenuation varying between 20 and 28 dB, depending on the polarization. The minimum acceptable crosstalk attenuation at a data rate of 100 Mb/s is determined to be 10 dB. The feasibility of using the device as a polarization angle sensor for linearly polarized light is also demonstrated. A theory for the emission of photogenerated carriers out of the quantum wells is included, since this is potentially a speed limiting mechanism in these detectors. It is shown that a theory of thermally assisted tunneling by polar optical phonon interaction is able to predict emission times consistent with the observed temporal response
Optimization of InP APDs for high-speed lightwave systems
Calculations based on a rigorous analytical model are carried out to optimize the width of the indium phosphide avalanche region in high-speed direct-detection avalanche photodiode-based optical receivers. The model includes the effects of intersymbol interference (ISI), tunneling current, avalanche noise, and its correlation with the stochastic avalanche duration, as well as dead space. A minimum receiver sensitivity of -28 dBm is predicted at an optimal width of 0.18 mu m and an optimal gain of approximately 13, for a 10 Gb/s communication system, assuming a Johnson noise level of 629 noise electrons per bit. The interplay among the factors controlling the optimum sensitivity is confirmed. Results show that for a given transmission speed, as the device width decreases below an optimum value, increased tunneling current outweighs avalanche noise reduction due to dead space, resulting in an increase in receiver sensitivity. As the device width increases above its optimum value, the receiver sensitivity increases as device bandwidth decreases, causing ISI to dominate avalanche noise and tunneling current shot noise
Enhancing capacity of coherent optical information storage and transfer in a Bose-Einstein condensate
Coherent optical information storage capacity of an atomic Bose-Einstein
condensate is examined. Theory of slow light propagation in atomic clouds is
generalized to short pulse regime by taking into account group velocity
dispersion. It is shown that the number of stored pulses in the condensate can
be optimized for a particular coupling laser power, temperature and interatomic
interaction strength. Analytical results are derived for semi-ideal model of
the condensate using effective uniform density zone approximation. Detailed
numerical simulations are also performed. It is found that axial density
profile of the condensate protects the pulse against the group velocity
dispersion. Furthermore, taking into account finite radial size of the
condensate, multi-mode light propagation in atomic Bose-Einstein condensate is
investigated. The number of modes that can be supported by a condensate is
found. Single mode condition is determined as a function of experimentally
accessible parameters including trap size, temperature, condensate number
density and scattering length. Quantum coherent atom-light interaction schemes
are proposed for enhancing multi-mode light propagation effects.Comment: 12pages. Laser Physics, in pres
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