Optimization Guarantees for ISTA and ADMM Based Unfolded Networks

Recently, unfolding techniques have been widely utilized to solve the inverse problems in various applications. In this paper, we study optimization guarantees for two popular unfolded networks, i.e., unfolded networks derived from iterative soft thresholding algorithms (ISTA) and derived from Alternating Direction Method of Multipliers (ADMM). Our guarantees–leveraging the Polyak-Lojasiewicz* (PL*) condition–state that the training (empirical) loss decreases to zero with the increase in the number of gradient descent epochs provided that the number of training samples is less than some threshold that depends on various quantities underlying the desired information processing task. Our guarantees also show that this threshold is larger for unfolded ISTA in comparison to unfolded ADMM, suggesting that there are certain regimes of number of training samples where the training error of unfolded ADMM does not converge to zero whereas the training error of unfolded ISTA does. A number of numerical results are provided backing up our theoretical findings

REST: Robust lEarned Shrinkage-Thresholding Network Taming Inverse Problems with Model Mismatch

We consider compressive sensing problems with model mismatch where one wishes to recover a sparse high-dimensional vector from low-dimensional observations subject to uncertainty in the measurement operator. In particular, we design a new robust deep neural network architecture by applying algorithm unfolding techniques to a robust version of the underlying recovery problem. Our proposed network –named Robust lErned Shrinkage-Thresholding (REST) –exhibits additional features including enlarged number of parameters and normalization processing compared to state-of-the-art deep architecture Learned Iterative Shrinkage-Thresholding Algorithm (LISTA), leading to the reliable recovery of the signal under sample-wise varying model mismatch. Our proposed network is also shown to outperform LISTA in compressive sensing problems under sample-wise varying model mismatch

Image Separation with Side Information: A Connected Auto-Encoders Based Approach

X-radiography (X-ray imaging) is a widely used imaging technique in art investigation. It can provide information about the condition of a painting as well as insights into an artist’s techniques and working methods, often revealing hidden information invisible to the naked eye. X-radiograpy of double-sided paintings results in a mixed X-ray image and this paper deals with the problem of separating this mixed image. Using the visible color images (RGB images) from each side of the painting, we propose a new Neural Network architecture, based upon ’connected’ auto-encoders, designed to separate the mixed X-ray image into two simulated X-ray images corresponding to each side. This connected auto-encoders architecture is such that the encoders are based on convolutional learned iterative shrinkage thresholding algorithms (CLISTA) designed using algorithm unrolling techniques, whereas the decoders consist of simple linear convolutional layers; the encoders extract sparse codes from the visible image of the front and rear paintings and mixed X-ray image, whereas the decoders reproduce both the original RGB images and the mixed X-ray image. The learning algorithm operates in a totally self-supervised fashion without requiring a sample set that contains both the mixed X-ray images and the separated ones. The methodology was tested on images from the double-sided wing panels of the Ghent Altarpiece , painted in 1432 by the brothers Hubert and Jan van Eyck. These tests show that the proposed approach outperforms other state-of-the-art X-ray image separation methods for art investigation applications

Probing Shadowed Nuclear Sea with Massive Gauge Bosons in the Future Heavy-Ion Collisions

The production of the massive bosons $Z^0$ and $W^{\pm}$ could provide an excellent tool to study cold nuclear matter effects and the modifications of nuclear parton distribution functions (nPDFs) relative to parton distribution functions (PDFs) of a free proton in high energy nuclear reactions at the LHC as well as in heavy-ion collisions (HIC) with much higher center-of mass energies available in the future colliders. In this paper we calculate the rapidity and transverse momentum distributions of the vector boson and their nuclear modification factors in p+Pb collisions at $\sqrt{s_{NN}}=63$TeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=39$TeV in the framework of perturbative QCD by utilizing three parametrization sets of nPDFs: EPS09, DSSZ and nCTEQ. It is found that in heavy-ion collisions at such high colliding energies, both the rapidity distribution and the transverse momentum spectrum of vector bosons are considerably suppressed in wide kinematic regions with respect to p+p reactions due to large nuclear shadowing effect. We demonstrate that in the massive vector boson productions processes with sea quarks in the initial-state may give more contributions than those with valence quarks in the initial-state, therefore in future heavy-ion collisions the isospin effect is less pronounced and the charge asymmetry of W boson will be reduced significantly as compared to that at the LHC. Large difference between results with nCTEQ and results with EPS09 and DSSZ is observed in nuclear modifications of both rapidity and $p_T$ distributions of $Z^0$ and $W$ in the future HIC.Comment: 13 pages, 21 figures, version accepted for publication in Eur. Phys. J.

A Learning Based Approach to Separate Mixed X-Ray Images Associated with Artwork with Concealed Designs

X-ray images are widely used in the study of paintings. When a painting has hidden sub-surface features (e.g., reuse of the canvas or revision of a composition by the artist), the resulting X-ray images can be hard to interpret as they include contributions from both the surface painting and the hidden design. In this paper we propose a self-supervised deep learning-based image separation approach that can be applied to the X-ray images from such paintings (‘mixed X-ray images’) to separate them into two hypothetical X-ray images, one containing information related to the visible painting only and the other containing the hidden features. The proposed approach involves two steps: (1) separation of the mixed X-ray image into two images, guided by the combined use of a reconstruction and an exclusion loss; (2) even allocation of the error map into the two individual, separated X-ray images, yielding separation results that have an appearance that is more familiar in relation to Xray images. The proposed method was demonstrated on a real painting with hidden content, Doña Isabel de Porcel by Francisco de Goya, to show its effectiveness

What do γ\gamma-ray bursts look like?

There have been great and rapid progresses in the field of $\gamma$-ray bursts (denoted as GRBs) since BeppoSAX and other telescopes discovered their afterglows in 1997. Here, we will first give a brief review on the observational facts of GRBs and direct understanding from these facts, which lead to the standard fireball model. The dynamical evolution of the fireball is discussed, especially a generic model is proposed to describe the whole dynamical evolution of GRB remnant from highly radiative to adiabatic, and from ultra-relativistic to non-relativistic phase. Then, Various deviations from the standard model are discussed to give new information about GRBs and their environment. In order to relax the energy crisis, the beaming effects and their possible observational evidences are also discussed in GRB's radiations.Comment: 10 pages, Latex. Invited talk at the Pacific Rim Conference on Stellar Astrophysics, Hong Kong, China, Aug. 199

Heavy metal induced ecological risk in the city of Urumqi, NW China

A total of 169 samples of road dust collected in the city of Urumqi, capital of the Xinjiang Uygur Autonomous Region in northwest China, were analyzed by method of inductively coupled plasma-mass spectrometry for 10 elements (i.e., Cd, Cr, Cu, Ni, Pb, Mn, Be, Co, Zn, and U). The possible sources of metals are identified with multivariate analysis such as correlation analysis, principal component analysis, and cluster analysis. Besides, enrichment factors are used to quantitatively evaluate the influences of human activities on heavy metal concentrations. Moreover, the potential ecological risk index is applied to evaluating the ecological risk of heavy metal pollutants. The results indicate that: (1) the concentrations of the heavy metals involved were much higher in urban areas than the background values, except those of Co and U. Mn, U, and Co are mainly of natural origin; Cu, Pb, Zn, and Cr are mainly of traffic sources and are partly of industrial sources; Ni and Be are mainly the results of industrial activities, such as machine shops, firepower plants, tire and rubber factories, cement factories, and textile mills and are partly of the traffic sources; (2) with high "toxic-response" factor and high concentration, Cd has more serious influences on the environment than other heavy metals. Therefore, commercial and industrial areas are usually characterized by higher potential ecological risk when compared with residential areas and new developing urban areas. The results of this study could be helpful for the management of environment in industrial areas

Contamination levels assessment of potential toxic metals in road dust deposited in different types of urban environment

A total of 42 samples of road dust were collected along ring road, city centre, city side, and freeway in Urumqi, China. Total concentrations of Cd, Cr, Cu, Ni, Pb, Mn, Be, Co, Zn, and U were determined by using the inductively coupled plasma-mass spectrometry in order to assess and to compare road dust contamination levels of metals among the four roads. The results show that, among the four categories of roads, mean concentrations of Co and U vary little. City centre locations show strong enrichments of Cd, Cu, Pb, and Be. Along the ring road, the highest mean concentrations were found for Cr, Ni, Mn, and Co. However, the highest concentrations of Zn and U were found along the freeway. The cluster analysis shows that three main groups can be distinguished. Every group may be associated with different main sources and concentrations of the metals. The results of contamination assessment reveal that, among all of the potential toxic metals, Cd, Cu, and Zn pollution were obviously heavier with moderate or high contamination indices for most road dust samples, while Cr, Ni, and Pb contamination were lower along the four categories of roads. Compared with the city side, Cd, Cu, Pb, Ni, and Zn contamination were heavier along the ring road, the city centre, and the freeway with high traffic density. Low Pb contamination or no contamination in all the road dust samples may be related to the increasing usage of lead-free petrol

Spatial distribution and contamination assessment of heavy metals in urban road dusts from Urumqi, NW China

This study reports the spatial distribution pattern and degree of heavy metal pollution (Cd, Cr, Cu, Ni, Pb, Mn, Be, Co, Zn and U) in 169 urban road dust samples from urban area of Urumqi city. The spatial distribution pattern shows that Cu, Pb, Cr and Zn have similar patterns of spatial distribution. Their hot-spot areas were mainly associated with main roads where high traffic density was identified. Ni and Mn show similar spatial distributions coinciding with the industrial areas, while the spatial distribution patterns of Co and U show hot-spot areas were mainly located in the sides of the urban area where the road dust was significantly influenced by natural soils. The spatial distributions of Be and Cd were very different from other metals. The geo-accumulation index suggests that road dust in Urumqi city was uncontaminated to moderately contaminated with Cd, Cu, Ni, Pb, Mn, Be, Zn and U. The integrated pollution index shows IPIs of all road dust samples were higher than 1, suggesting that the road dust quality of Urumqi city has clearly been polluted by anthropogenic emission of heavy metals. Moreover, the spatial distribution pattern of IPIs also shows several distribution trends in the studied region. (C) 2009 Elsevier B.V. All rights reserved

Chronic kidney disease increases the susceptibility to negative effects of low and high potassium intake

BackgroundDietary potassium (K+) has emerged as a modifiable factor for cardiovascular and kidney health in the general population, but its role in people with chronic kidney disease (CKD) is unclear. Here, we hypothesize that CKD increases the susceptibility to the negative effects of low and high K+ diets.MethodsWe compared the effects of low, normal and high KChloride (KCl) diets and a high KCitrate diet for 4 weeks in male rats with normal kidney function and in male rats with CKD using the 5/6th nephrectomy model (5/6Nx).ResultsCompared with rats with normal kidney function, 5/6Nx rats on the low KCl diet developed more severe extracellular and intracellular K+ depletion and more severe kidney injury, characterized by nephromegaly, infiltration of T cells and macrophages, decreased estimated glomerular filtration rate and increased albuminuria. The high KCl diet caused hyperkalemia, hyperaldosteronism, hyperchloremic metabolic acidosis and severe hypertension in 5/6Nx but not in sham rats. The high KCitrate diet caused hypochloremic metabolic alkalosis but attenuated hypertension despite higher abundance of the phosphorylated sodium chloride cotransporter (pNCC) and similar levels of plasma aldosterone and epithelial sodium channel abundance. All 5/6Nx groups had more collagen deposition than the sham groups and this effect was most pronounced in the high KCitrate group. Plasma aldosterone correlated strongly with kidney collagen deposition.ConclusionsCKD increases the susceptibility to negative effects of low and high K+ diets in male rats, although the injury patterns are different. The low K+ diet caused inflammation, nephromegaly and kidney function decline, whereas the high K+ diet caused hypertension, hyperaldosteronism and kidney fibrosis. High KCitrate attenuated the hypertensive but not the pro-fibrotic effect of high KCl, which may be attributable to K+-induced aldosterone secretion. Our data suggest that especially in people with CKD it is important to identify the optimal threshold of dietary K+ intake