Cooperative greedy pursuit strategies for sparse signal representation by partitioning

Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly coherent redundant dictionaries. The cooperation takes place by ranking the partition units for their sequential stepwise approximation, and is realized by means of i)forward steps for the upgrading of an approximation and/or ii) backward steps for the corresponding downgrading. The advantage of the strategy is illustrated by approximation of music signals using redundant trigonometric dictionaries. In addition to rendering stunning improvements in sparsity with respect to the concomitant trigonometric basis, these dictionaries enable a fast implementation of the approach via the Fast Fourier Transfor

Sparsity & [and] dictionaries - algorithms & [and] design

With the flood of information available today the question how to deal with high dimensional data/signals, which are cumbersome to handle, to calculate with and to store, is highly important. One approach to reducing this flood is to find sparse signal representations, as a signal that is the linear combination of a few elements from a pool of building blocks, can be reduced to the few coefficients of this representation. If these building blocks form a basis, finding the sparse representation poses no problem but unfortunately not many signal classes are sparse in a basis. Taking more building blocks, i.e. a redundant dictionary, increases the chances of having sparse representations, but actually finding them becomes very hard. This led to the development of numerous strategies and algorithms for finding sparse representations, with varying complexity and success rate. The first part of the thesis deals with two of those algorithms, Thresholding and Matching Pursuit, from a more theoretical point of view. It is shown that both those greedy algorithms can be improved with a little trick, that does not increase their complexity, and that when considering their average instead of their worst case performance they perform quite well in comparison to more complex methods. The second part of thesis treats questions concerning the whole dictionary and its properties. First it gives more evidence that sparsity is useful by extending the concept of compressed sensing to signals that are sparse not in a basis but in a redundant dictionary. Thus to record a sparse signal it is not necessary to make as many measurements as the dimension of the signal but only a multiple of the number of dictionary elements used to represent it. Next we show that dictionaries cannot only provide sparse representations but that their geometric properties can also be exploited to model data structures. Here we explain how to model different subclasses of a class of signals by incoherent subspaces, present an algorithm to learn a dictionary made out of these subspaces and then use it for classification of faces. Finally we turn back to the sparse representation problem and study the fundamental question how to find a dictionary providing sparse representations. We pick up the idea to learn a dictionary via minimisation of a continuous cost function and provide conditions, guaranteeing that the decomposition of a collection of training signals into a dictionary and a coefficient matrix constitutes a local minimum. We also analyse statistically when these conditions are fulfilled with high probability

Compressed sensing of monostatic and multistatic SAR

In this paper we study the impact of sparse aperture data collection of a SAR sensor on reconstruction quality of a scene of interest. Different mono and multi-static SAR measurement configurations produce different Fourier sampling patterns. These patterns reflect different spectral and spatial diversity trade-offs that must be made during task planning. Compressed sensing theory argues that the mutual coherence of the measurement probes is related to the reconstruction performance of sparse domains. With this motivation we compare the mutual coherence and corresponding reconstruction behavior of various mono-static and ultra-narrow band multi-static configurations, which trade-off frequency for geometric diversity. We investigate if such simple metrics are related to SAR reconstruction quality in an obvious way

SAR image reconstruction and autofocus by compressed sensing

Cataloged from PDF version of article.A new SAR signal processing technique based on compressed sensing is proposed for autofocused image reconstruction on subsampled raw SAR data. It is shown that, if the residual phase error after INS/GPS corrected platform motion is captured in the signal model, then the optimal autofocused image formation can be formulated as a sparse reconstruction problem. To further improve image quality, the total variation of the reconstruction is used as a penalty term. In order to demonstrate the performance of the proposed technique in wide-band SAR systems, the measurements used in the reconstruction are formed by a new under-sampling pattern that can be easily implemented in practice by using slower rate A/D converters. Under a variety of metrics for the reconstruction quality, it is demonstrated that, even at high under-sampling ratios, the proposed technique provides reconstruction quality comparable to that obtained by the classical techniques which require full-band data without any under-sampling. (C) 2012 Elsevier Inc. All rights reserved

A unified approach to sparse signal processing

A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i

Numerical Simulation and Design Assessment of Limited Feedback Channel Estimation in Massive MIMO Communication System

The Internet of Things (IoT) has attracted a great deal of interest in various fields including governments, business, academia as an evolving technology that aims to make anything connected, communicate, and exchange of data. The massive connectivity, stringent energy restrictions, and ultra-reliable transmission requirements are also defined as the most distinctive features of IoT. This feature is a natural IoT supporting technology, as massive multiple input (MIMO) inputs will result in enormous spectral/energy efficiency gains and boost IoT transmission reliability dramatically through a coherent processing of the large-scale antenna array signals. However, the processing is coherent and relies on accurate estimation of channel state information (CSI) between BS and users. Massive multiple input (MIMO) is a powerous support technology that fulfils the Internet of Things' (IoT) energy/spectral performance and reliability needs. However, the benefit of MIMOs is dependent on the availability of CSIs. This research proposes an adaptive sparse channel calculation with limited feedback to estimate accurate and prompt CSIs for large multi-intimate-output systems based on Duplex Frequency Division (DFD) systems. The minimal retro-feedback scheme must retrofit the burden of the base station antennas in a linear proportion. This work offers a narrow feedback algorithm to elevate the burden by means of a MIMO double-way representation (DD) channel using uniform dictionaries linked to the arrival angle and start angle (AoA) (AoD). Although the number of transmission antennas in the BS is high, the algorithms offer an acceptable channel estimation accuracy using a limited number of feedback bits, making it suitable for 5G massively MIMO. The results of the simulation indicate the output limit can be achieved with the proposed algorithm

ON SOME COMMON COMPRESSIVE SENSING RECOVERY ALGORITHMS AND APPLICATIONS

Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its’ common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy with significantly reduced number of samples needed for accurate signal reconstruction. The basic ideas and motivation behind this approach are provided in the theoretical part of the paper. The commonly used algorithms for missing data reconstruction are presented. The Compressive Sensing applications have gained significant attention leading to an intensive growth of signal processing possibilities. Hence, some of the existing practical applications assuming different types of signals in real-world scenarios are described and analyzed as well