2,029 research outputs found
Learning to Invert: Signal Recovery via Deep Convolutional Networks
The promise of compressive sensing (CS) has been offset by two significant
challenges. First, real-world data is not exactly sparse in a fixed basis.
Second, current high-performance recovery algorithms are slow to converge,
which limits CS to either non-real-time applications or scenarios where massive
back-end computing is available. In this paper, we attack both of these
challenges head-on by developing a new signal recovery framework we call {\em
DeepInverse} that learns the inverse transformation from measurement vectors to
signals using a {\em deep convolutional network}. When trained on a set of
representative images, the network learns both a representation for the signals
(addressing challenge one) and an inverse map approximating a greedy or convex
recovery algorithm (addressing challenge two). Our experiments indicate that
the DeepInverse network closely approximates the solution produced by
state-of-the-art CS recovery algorithms yet is hundreds of times faster in run
time. The tradeoff for the ultrafast run time is a computationally intensive,
off-line training procedure typical to deep networks. However, the training
needs to be completed only once, which makes the approach attractive for a host
of sparse recovery problems.Comment: Accepted at The 42nd IEEE International Conference on Acoustics,
Speech and Signal Processin
DeepCodec: Adaptive Sensing and Recovery via Deep Convolutional Neural Networks
In this paper we develop a novel computational sensing framework for sensing
and recovering structured signals. When trained on a set of representative
signals, our framework learns to take undersampled measurements and recover
signals from them using a deep convolutional neural network. In other words, it
learns a transformation from the original signals to a near-optimal number of
undersampled measurements and the inverse transformation from measurements to
signals. This is in contrast to traditional compressive sensing (CS) systems
that use random linear measurements and convex optimization or iterative
algorithms for signal recovery. We compare our new framework with
-minimization from the phase transition point of view and demonstrate
that it outperforms -minimization in the regions of phase transition
plot where -minimization cannot recover the exact solution. In
addition, we experimentally demonstrate how learning measurements enhances the
overall recovery performance, speeds up training of recovery framework, and
leads to having fewer parameters to learn
Quantum Dynamics in a Time-dependent Hard-Wall Spherical Trap
Exact solution of the Schr\"{o}dinger equation is given for a particle inside
a hard sphere whose wall is moving with a constant velocity. Numerical
computations are presented for both contracting and expanding spheres. The
propagator is constructed and compared with the propagator of a particle in an
infinite square well with one wall in uniform motion.Comment: 6 pages, 4 figures, Accepted by Europhys. Let
A Deep Learning Approach to Structured Signal Recovery
In this paper, we develop a new framework for sensing and recovering
structured signals. In contrast to compressive sensing (CS) systems that employ
linear measurements, sparse representations, and computationally complex
convex/greedy algorithms, we introduce a deep learning framework that supports
both linear and mildly nonlinear measurements, that learns a structured
representation from training data, and that efficiently computes a signal
estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an
unsupervised feature learner. SDA enables us to capture statistical
dependencies between the different elements of certain signals and improve
signal recovery performance as compared to the CS approach
Quantum effective force in an expanding infinite square-well potential and Bohmian perspective
The Schr\"{o}dinger equation is solved for the case of a particle confined to
a small region of a box with infinite walls. If walls of the well are moved,
then, due to an effective quantum nonlocal interaction with the boundary, even
though the particle is nowhere near the walls, it will be affected. It is shown
that this force apart from a minus sign is equal to the expectation value of
the gradient of the quantum potential for vanishing at the walls boundary
condition. Variation of this force with time is studied. A selection of Bohmian
trajectories of the confined particle is also computed.Comment: 7 figures, Accepted by Physica Script
Exoplanets prediction in multiplanetary systems
We present the results of a search for additional exoplanets in allmultiplanetary systems discovered to date, employing a logarithmic spacing between planets in our Solar System known as the Titius-Bode (TB) relation. We use theMarkov Chain Monte Carlo method and separately analyse 229 multiplanetary systems that house at least three or more confirmed planets. We find that the planets in similar to 53% of these systems adhere to a logarithmic spacing relation remarkably better than the Solar System planets. Using the TB relation, we predict the presence of 426 additional exoplanets in 229 multiplanetary systems, of which 197 candidates are discovered by interpolation and 229 by extrapolation. Altogether, 47 predicted planets are located within the habitable zone of their host stars, and 5 of the 47 planets have a maximum mass limit of 0.1-2 M-circle plus and a maximum radius lower than 1.25 R-circle plus. Our results and prediction of additional planets agree with previous studies' predictions; however, we improve the uncertainties in the orbital period measurement for the predicted planets significantly.Peer reviewe
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