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 $\ell_1$-minimization from the phase transition point of view and demonstrate that it outperforms $\ell_1$-minimization in the regions of phase transition plot where $\ell_1$-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