The Maximum-Weight Stable Matching Problem: Duality and Efficiency

Given a preference system (G,≺) and an integral weight function defined on the edge set of G (not necessarily bipartite), the maximum-weight stable matching problem is to find a stable matching of (G,≺) with maximum total weight. In this paper we study this NP-hard problem using linear programming and polyhedral approaches. We show that the Rothblum system for defining the fractional stable matching polytope of (G,≺) is totally dual integral if and only if this polytope is integral if and only if (G,≺) has a bipartite representation. We also present a combinatorial polynomial-time algorithm for the maximum-weight stable matching problem and its dual on any preference system with a bipartite representation. Our results generalize Király and Pap's theorem on the maximum-weight stable-marriage problem and rely heavily on their work. © 2012 Society for Industrial and Applied Mathematics.published_or_final_versio

Compressive Sensing Reconstruction for Video: An Adaptive Approach Based on Motion Estimation

This paper focuses on the problem of causally reconstructing Compressive Sensing (CS) captured video. The state-of-art causal approaches usually assume the signal support is static or changing sufficiently slowly over time, where Magnetic Resonance Imaging (MRI) is widely used as a motivating example. However, such an assumption is too restrictive for many other video applications, where the signal support changes rapidly. In this paper, we propose a framework that combines Motion Estimation (ME), the Kalman Filter (KF) and CS to adapt the reconstruction process to motions in the video so that the slowly-changing assumption on the signal support is relaxed and consequently is more suitable for video reconstruction. Explicit and implicit ME are designed to provide motion aware predictions, upon which a modified KF procedure is applied. Furthermore, three CS algorithms with embedded ME and KF are developed, and theoretical analyses are conducted via reconstruction error upper bounds, to characterize the various factors that affect reconstruction accuracy. Extensive simulations utilizing actual videos are carried out and the superiority of our methods is demonstrated.This work is supported by EPSRC Research Grant EP/K033700/1; the Natural Science Foundation of China (61401018, U1334202).This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TCSVT.2016.254007

Block-based feature adaptive compressive sensing for video

This paper focuses on the problem of feature adaptive reconstruction of Compressive Sensing (CS) captured video. In CS, sparse signals can be recovered with high probability of success from very few random samples. Utilizing the temporal correlations between video frames, it is possible to exploit improved CS reconstruction algorithms. Features that relate to the changes between frames are one of the options to benefit reconstruction. However, to choose the optimal feature for every particular region in each frame is difficult, as the true images are unknown in a CS framework. In this paper, we propose two systems for block-based feature adaptive CS video reconstruction, i.e., a Cross Validation (CV) based system and a classification based system. The CV based system achieves the selection of the optimal feature by applying the techniques of CV to the results of extra reconstructions and the classification based system reduces complexity by classifying the CS samples directly, where the optimal feature for the particular class is employed for the reconstruction. Simulations demonstrate that both of our systems work appropriately and their performance is better than uniformly using any single feature for the whole video reconstruction.This work is supported by EPSRC Research Grant (EP/K033700/1); the Natural Science Foundation of China (61401018); Beijing Jiaotong University; the Fundamental Research Funds for the Central Universities (2014JBM149).This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/CIT/IUCC/DASC/PICOM.2015.25

Sparsity-fused Kalman filtering for reconstruction of dynamic sparse signals

This article focuses on the problem of reconstructing dynamic sparse signals from a series of noisy compressive sensing measurements using a Kalman Filter (KF). This problem arises in many applications, e.g., Magnetic Resonance Imaging (MRI), Wireless Sensor Networks (WSN) and video reconstruction. The conventional KF does not consider the sparsity structure presented in most practical signals and it is therefore inaccurate when being applied to sparse signal recovery. To deal with this issue, we derive a novel KF procedure which takes the sparsity model into consideration. Furthermore, an algorithm, namely Sparsity-fused KF, is proposed based upon it. The method of iterative soft thresholding is utilized to refine our sparsity model. The superiority of our method is demonstrated by synthetic data and the practical data gathered by a WSN.This work is supported by EPSRC Research Grant (EP/K033700/1); the Natural Science Foundation of China (61401018, U1334202); the State Key Laboratory of Rail Traffic Control and Safety (RCS2014ZT08), Beijing Jiaotong University; the Fundamental Research Funds for the Central Universities (2014JBM149); the Key Grant Project of Chinese Ministry of Education (313006); the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ICC.2015.724938

Study on the application of a new multiepoxy reinforcement agent for sheep leather

Content: Leather is a kind of natural biomass composite material which is made of animal skin as material by a series of chemical and physical processing. Its main structure is Collagen fibers of three-dimensional network structure. As we all know sheep leather always exist a common problem with low strength, while the strength of leather depended on the woven degree of collagen fibers. Through the past decades, many methods have been tried to improve the properties of sheep leather. The most commonly used methods are retanning. However, the strength enhancement of sheep leather is extremely limited by retanning, although the fullness and softness may be improved. In this study, a new type of multi-epoxy reinforcement agent (IGE) and IGE with the synergistic effect of polyamine (IGE-PA) were used to enhance the strength of sheep leather in tanning and fatliquoring process. Comparing with chromium tanned leather, it was found that under the optimized conditions (dosage: 10%, pH: 8, Temperature: 35℃ for penetration and 45℃ for fixation, tanning time: 10 h) with IGE as the main tanning agent, the tearing strength was increased 56.8%. While when the polyamine as the synergetic agent for IGE, the tearing strength was significantly increased 87.9%. While IGE and IGE-PA were used in fatliquoring process, it has significant reinforcement effect for tetrakis hydroxymethyl phosphonium (THP) salt tanned leather. It was found that under the optimized conditions (Dosage: 2.5%, pH: 7-8, Temperature: 50℃, Time: 2h) with IGE in fatliquoring process, the tear strength was increased 50.24%, while the IGE-PA was used, the tear strength was increased 64.3%. Furthermore, TGA results showed that decomposition temperatures of IGE and IGE-PA enhanced leather were all higher than traditional chromium tanned leather. In addition, SEM results showed that IGE and IGE-PA enhanced leather obtained better opened-up fiber structure. Take-Away: 1. A new type of multi-epoxy tanning agent (IGE) has reinforcement effect for sheep leather especially in tear strength. 2. IGE with the synergistic effect of polyamine (IGE-PA) were used in tanning process, which has a significant enhancement for the sheep leather. 3. IGE and IGE-PA can be also used in fatliquoring process to enhance the strength of sheep leather