Adaptive Measurement Network for CS Image Reconstruction

Conventional compressive sensing (CS) reconstruction is very slow for its characteristic of solving an optimization problem. Convolu- tional neural network can realize fast processing while achieving compa- rable results. While CS image recovery with high quality not only de- pends on good reconstruction algorithms, but also good measurements. In this paper, we propose an adaptive measurement network in which measurement is obtained by learning. The new network consists of a fully-connected layer and ReconNet. The fully-connected layer which has low-dimension output acts as measurement. We train the fully-connected layer and ReconNet simultaneously and obtain adaptive measurement. Because the adaptive measurement fits dataset better, in contrast with random Gaussian measurement matrix, under the same measuremen- t rate, it can extract the information of scene more efficiently and get better reconstruction results. Experiments show that the new network outperforms the original one.Comment: 11pages,8figure

Restricted Isometries for Partial Random Circulant Matrices

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisition process that proceeds by convolution with a random pulse followed by (nonrandom) subsampling. At present, the theoretical analysis of this measurement technique is lacking. This paper demonstrates that the $s$th order restricted isometry constant is small when the number $m$ of samples satisfies $m \gtrsim (s \log n)^{3/2}$, where $n$ is the length of the pulse. This bound improves on previous estimates, which exhibit quadratic scaling

New heterodontosaurid remains from the Canadon Asfalto Formation: cursoriality and the functional importance of the pes in small heterodontosaurids

New ornithischian remains reported here (MPEF-PV 3826) include two complete metatarsi with associated phalanges and caudal vertebrae, from the late Toarcian levels of the Canadon Asfalto Formation. We conclude that these fossil remains represent a bipedal heterodontosaurid but lack diagnostic characters to identify them at the species level, although they probably represent remains of Manidens condorensis, known from the same locality. Histological features suggest a subadult ontogenetic stage for the individual. A cluster analysis based on pedal measurements identifies similarities of this specimen with heterodontosaurid taxa and the inclusion of the new material in a phylogenetic analysis with expanded character sampling on pedal remains confirms the described specimen as a heterodontosaurid. Finally, uncommon features of the digits (length proportions among nonungual phalanges of digit III, and claw features) are also quantitatively compared to several ornithischians, theropods, and birds, suggesting that this may represent a bipedal cursorial heterodontosaurid with gracile and grasping feet and long digits. In particular, the elongated non-terminal pedal phalanges and morphology of digit III resemble features present in arboreal birds, a unique condition found so far among ornithischians

Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

Aminoacid zwitterions in solution : Geometric, energetic, and vibrational analysis using density functional theory-continuum model calculations

Glycine and alanine aminoacids chemistry in solution is explored using a hybrid three parameters density functional (B3PW91) together with a continuum model. Geometries, energies, and vibrational spectra of glycine and alanine zwitterions are studied at the B3PW91/6-31+G∗∗ level and the results compared with those obtained at the HF and MP2/6-31+G∗∗ levels. Solvents effects are incorporated by means of an ellipsoidal cavity model with a multipolar expansion (up to sixth order) of the solute’s electrostatic potential. Our results confirm the validity of the B3PW91 functional for studying aminoacid chemistry in solution. Taking into account the more favorable scaling behavior of density functional techniques with respect to correlated ab initio methods these studies could be extended to larger [email protected] ; [email protected]

Compressed sensing imaging techniques for radio interferometry

Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or compressible signals. We propose new generic imaging techniques based on convex optimization for global minimization problems defined in this context. The versatility of the framework notably allows introduction of specific prior information on the signals, which offers the possibility of significant improvements of reconstruction relative to the standard local matching pursuit algorithm CLEAN used in radio astronomy. We illustrate the potential of the approach by studying reconstruction performances on simulations of two different kinds of signals observed with very generic interferometric configurations. The first kind is an intensity field of compact astrophysical objects. The second kind is the imprint of cosmic strings in the temperature field of the cosmic microwave background radiation, of particular interest for cosmology.Comment: 10 pages, 1 figure. Version 2 matches version accepted for publication in MNRAS. Changes includes: writing corrections, clarifications of arguments, figure update, and a new subsection 4.1 commenting on the exact compliance of radio interferometric measurements with compressed sensin

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

Wisdom of groups promotes cooperation in evolutionary social dilemmas

Whether or not to change strategy depends not only on the personal success of each individual, but also on the success of others. Using this as motivation, we study the evolution of cooperation in games that describe social dilemmas, where the propensity to adopt a different strategy depends both on individual fitness as well as on the strategies of neighbors. Regardless of whether the evolutionary process is governed by pairwise or group interactions, we show that plugging into the "wisdom of groups" strongly promotes cooperative behavior. The more the wider knowledge is taken into account the more the evolution of defectors is impaired. We explain this by revealing a dynamically decelerated invasion process, by means of which interfaces separating different domains remain smooth and defectors therefore become unable to efficiently invade cooperators. This in turn invigorates spatial reciprocity and establishes decentralized decision making as very beneficial for resolving social dilemmas.Comment: 8 two-column pages, 7 figures; accepted for publication in Scientific Report