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

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

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