Modified Basis Pursuit Denoising(modified-BPDN) for noisy compressive sensing with partially known support

In this work, we study the problem of reconstructing a sparse signal from a limited number of linear ‘incoherent ’ noisy measurements, when a part of its support is known. The known part of the sup-port may be available from prior knowledge or from the previous time instant (in applications requiring recursive reconstruction of a time sequence of sparse signals, e.g. dynamic MRI). We study a modi¿cation of Basis Pursuit Denoising (BPDN) and bound its re-construction error. A key feature of our work is that the bounds that we obtain are computable. Hence, we are able to use Monte Carlo to study their average behavior as the size of the unknown support increases. We also demonstrate that when the unknown support size is small, modi¿ed-BPDN bounds are much tighter than those for BPDN, and hold under much weaker suf¿cient conditions (require fewer measurements). Index Terms — Compressive sensing, Sparse reconstruction 1

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

Particle filtered modified compressed sensing and applications in visual tracking

The main idea of the thesis is to design an efficient tracking algorithm that is able to track moving objects in presence of spatial illumination variation. The state vectors constitute of the motion parameters and the illumination vectors. The illumination vector is designed as a sparse vector using the fact that the scene parameters (e.g. illumination) at any given instant, can have a sparse representation with respect to the basis i.e. only a few basis elements will contribute to the scene dynamics at each instant. The observation is the entire image frame.The non-linearity and the multimodality of the state-space necessitates the use of Particle Filter. The illumination vector along with motion makes the state-space large dimensional thus making the implementation of regular particle filter expensive. PF-MT has been designed to tackle this problem but it does not utilize the sparsity constraint and hence fails to detect the sparse illumination vector. So we design an algorithm that would use particle filter and importance sample on the motion or the \u27effective space\u27 and the mode tracking step of PF-MT is replaced by the Modified Compressed Sensing for estimating the \u27residual space\u27. Simulation and also experiments with real video demonstrate the advantage of the proposed algorithm over other existing PF based algorithms

Compressive channel estimation

In dieser Arbeit untersuchen wir die kompressive Kanalschätzung (KKS), also die Anwendung der Theorie und Methodologie des Compressed Sensing (CS) auf das Problem der Kanalschätzung doppelt selektiver Kanäle in Multicarrier-Systemen. Nach einer kurzen Einführung in die kabellose Kommunikation und einem kleinen Überblick über CS und einigen seiner Varianten betrachten wir die in [1] präsentierte elementare kompressive Kanalschätzmethode. Wir analysieren ihre Leistungsfähigkeit sowie ihre Komplexität, und wir untersuchen die ihr zugrundeliegende Annahme, nämlich die "delay-Doppler sparsity" typischer Kanäle, genauer. Aufbauend auf dieser Analyse stellen wir einige Varianten und Erweiterungen der kompressiven Kanalschätzmethode vor. Zuerst nutzen wir die Tatsache dass typische Kanäle auch als "group sparse" angesehen werden können. Dies ist eine Folge des sogenannten Leck Effekts, welcher die Leistung einer jeden kompressiven Kanalschätzmethode beeinträchtigt und daher eine enorme Herausforderungen für die KKS darstellt. Weiters betrachten wir die Erweiterung der kompressiven Schätzmethode auf Mehrantennensysteme (MIMO). Wir zeigen, dass die einzelnen Querkanäle eines solchen MIMO Systems (in etwa) als "jointly sparse", sogar als "jointly group sparse" angesehen, und daher Methoden des Multichannel CS (MCS) verwendet werden können. Letztens nutzen wir - unter Verwendung der Konzepte des Modified CS (MOD-CS) - die approximative "sequential sparsity" des Kanals zum Kanal-Tracking über mehrere aufeinanderfolgende Symbolblöcke hinweg. Diese Vorgehensweise kann die Leistung zusätzlich steigern, viel wichtiger jedoch, sie kann die Komplexität der Methode reduzieren. Darüber hinaus adaptieren wir die Technik der Basis-Optimierung, welche in [2, 3] vorgestellt wurde, für die verschiedenen Szenarien, und wir präsentieren Simulationsergebnisse, welche die verbesserte Leistung all jener Kanalschätzmethoden demonstrieren, die in dieser Arbeit erklärt werden.In this thesis we investigate compressive channel estimation (CCE), i.e. the application of the theory and methodology of Compressed Sensing (CS) to the problem of estimating doubly selective channels in multicarrier systems. After a brief introduction to wireless communications and a short survey of CS and some of its variations, we review the basic compressive channel estimator that was introduced in [1]. We analyze its performance as well as its computational complexity, and we explore the basic assumption underlying the compressive estimator, namely the delay-Doppler sparsity of typical channels, in more detail. Based on this analysis, we propose several variations and extensions of the conventional compressive channel estimator. First, we make use of the fact that typical channels can be considered group sparse as well. This is due to the so-called leakage effect, which actually impairs the performance of any channel estimator utilizing CS techniques and therefore is one of the main challenges in CCE. Then, we investigate the extension of the compressive estimators to the multi-antenna (MIMO) case. We show that the various cross-channels of a MIMO system can (approximately) be considered jointly sparse, even jointly group sparse, and that therefore the methodology of multichannel CS can be utilized. Last, by using the recently introduced concept of modified CS, we exploit the approximate sequential sparsity of the channel in order to track it over a period of several consecutive symbol blocks. This approach can yield an additional performance gain, but more importantly it can substantially reduce the computational complexity of the method. Additionally, we adapt the basis optimization techniques introduced in [2, 3] to the various settings, and we present simulation results that demonstrate the performance gains that can be achieved by using each of the compressive estimators presented in this thesis