Second generation sparse models

Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a learned dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many applications. The success of these models is largely attributed to two critical features: the use of sparsity as a robust mechanism for regularizing the linear coefficients that represent the data, and the flexibility provided by overcomplete dictionaries that are learned from the data. These features are controlled by two critical hyper-parameters: the desired sparsity of the coefficients, and the size of the dictionaries to be learned. However, lacking theoretical guidelines for selecting these critical parameters, applications based on sparse models often require hand-tuning and cross-validation to select them, for each application, and each data set. This can be both inefficient and ineffective. On the other hand, there are multiple scenarios in which imposing additional constraints to the produced representations, including the sparse codes and the dictionary itself, can result in further improvements. This thesis is about improving and/or extending current sparse models by addressing the two issues discussed above, providing the elements for a new generation of more powerful and flexible sparse models. First, we seek to gain a better understanding of sparse models as data modeling tools, so that critical parameters can be selected automatically, efficiently, and in a principled way. Secondly, we explore new sparse modeling formulations for effectively exploiting the prior information present in different scenarios. In order to achieve these goals, we combine ideas and tools from information theory, statistics, machine learning, and optimization theory. The theoretical contributions are complemented with applications in audio, image and video processing

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Applied Harmonic Analysis and Sparse Approximation

Efficiently analyzing functions, in particular multivariate functions, is a key problem in applied mathematics. The area of applied harmonic analysis has a significant impact on this problem by providing methodologies both for theoretical questions and for a wide range of applications in technology and science, such as image processing. Approximation theory, in particular the branch of the theory of sparse approximations, is closely intertwined with this area with a lot of recent exciting developments in the intersection of both. Research topics typically also involve related areas such as convex optimization, probability theory, and Banach space geometry. The workshop was the continuation of a first event in 2012 and intended to bring together world leading experts in these areas, to report on recent developments, and to foster new developments and collaborations

Convex and Network Flow Optimization for Structured Sparsity

We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of l_infinity-norms can be computed exactly in polynomial time by solving a quadratic min-cost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with non-overlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such as CUR matrix factorization, multi-task learning of tree-structured dictionaries, background subtraction in video sequences, image denoising with wavelets, and topographic dictionary learning of natural image patches.Comment: to appear in the Journal of Machine Learning Research (JMLR

Ensemble approach on enhanced compressed noise EEG data signal in wireless body area sensor network

The Wireless Body Area Sensor Network (WBASN) is used for communication among sensor nodes operating on or inside the human body in order to monitor vital body parameters and movements. One of the important applications of WBASN is patients’ healthcare monitoring of chronic diseases such as epileptic seizure. Normally, epileptic seizure data of the electroencephalograph (EEG) is captured and compressed in order to reduce its transmission time. However, at the same time, this contaminates the overall data and lowers classification accuracy. The current work also did not take into consideration that large size of collected EEG data. Consequently, EEG data is a bandwidth intensive. Hence, the main goal of this work is to design a unified compression and classification framework for delivery of EEG data in order to address its large size issue. EEG data is compressed in order to reduce its transmission time. However, at the same time, noise at the receiver side contaminates the overall data and lowers classification accuracy. Another goal is to reconstruct the compressed data and then recognize it. Therefore, a Noise Signal Combination (NSC) technique is proposed for the compression of the transmitted EEG data and enhancement of its classification accuracy at the receiving side in the presence of noise and incomplete data. The proposed framework combines compressive sensing and discrete cosine transform (DCT) in order to reduce the size of transmission data. Moreover, Gaussian noise model of the transmission channel is practically implemented to the framework. At the receiving side, the proposed NSC is designed based on weighted voting using four classification techniques. The accuracy of these techniques namely Artificial Neural Network, Naïve Bayes, k-Nearest Neighbour, and Support Victor Machine classifiers is fed to the proposed NSC. The experimental results showed that the proposed technique exceeds the conventional techniques by achieving the highest accuracy for noiseless and noisy data. Furthermore, the framework performs a significant role in reducing the size of data and classifying both noisy and noiseless data. The key contributions are the unified framework and proposed NSC, which improved accuracy of the noiseless and noisy EGG large data. The results have demonstrated the effectiveness of the proposed framework and provided several credible benefits including simplicity, and accuracy enhancement. Finally, the research improves clinical information about patients who not only suffer from epilepsy, but also neurological disorders, mental or physiological problems

Situational awareness in low-observable distribution grid - exploiting sparsity and multi-timescale data

Doctor of PhilosophyDepartment of Electrical and Computer EngineeringBalasubramaniam NatarajanThe power distribution grid is typically unobservable due to a lack of real-time measurements. While deploying more sensors can alleviate this issue, it also presents new challenges related to data aggregation and the underlying communication infrastructure. Limited real-time measurements hinders the distribution system state estimation (DSSE). DSSE involves estimation of the system states (i.e., voltage magnitude and voltage angle) based on available measurements and system model information. To cope with the unobservability issue, sparsity-based DSSE approaches allow us to recover system state information from a small number of measurements, provided the states of the distribution system exhibit sparsity. However, these approaches perform poorly in the presence of outliers in measurements and errors in system model information. In this dissertation, we first develop robust formulations of sparsity-based DSSE to deal with uncertainties in the system model and measurement data in a low-observable distribution grid. We also combine the advantages of two sparsity-based DSSE approaches to estimate grid states with high fidelity in low observability regions. In practical distribution systems, information from field sensors and meters are unevenly sampled at different time scales and could be lost during the transmission process. It is critical to effectively aggregate these information sources for DSSE as well as other tasks related to situational awareness. To address this challenge, the second part of this dissertation proposes a Bayesian framework for multi-timescale data aggregation and matrix completion-based state estimation. Specifically, the multi-scale time-series data aggregated from heterogeneous sources are reconciled using a multitask Gaussian process. The resulting consistent time-series alongwith the confidence bound on the imputations are fed into a Bayesian matrix completion method augmented with linearized power-flow constraints for accurate state estimation low-observable distribution system. We also develop a computationally efficient recursive Gaussian process approach that is capable of handling batch-wise or real-time measurements while leveraging the network connectivity information of the grid. To further enhance the scalability and accuracy, we develop neural network-based approaches (latent neural ordinary differential equation approach and stochastic neural differential equation with recurrent neural network approach) to aggregate irregular time-series data in the distribution grid. The stochastic neural differential equation and recurrent neural network also allows us to quantify the uncertainty in a holistic manner. Simulation results on the different IEEE unbalanced test systems illustrate the high fidelity of the Bayesian and neural network-based methods in aggregating multi-timescale measurements. Lastly, we develop phase, and outage awareness approaches for power distribution grid. In this regard, we first design a graph signal processing approach that identifies the phase labels in the presence of limited measurements and incorrect phase labeling. The second approach proposes a novel outage detector for identifying all outages in a reconfigurable distribution network. Simulation results on standard IEEE test systems reveal the potential of these methods to improve situational awareness

Anomaly detection & object classification using multi-spectral LiDAR and sonar

In this thesis, we present the theory of high-dimensional signal approximation of multifrequency signals. We also present both linear and non-linear compressive sensing (CS) algorithms that generate encoded representations of time-correlated single photon counting (TCSPC) light detection and ranging (LiDAR) data, side-scan sonar (SSS) and synthetic aperture sonar (SAS). The main contributions of this thesis are summarised as follows: 1. Research is carried out studying full-waveform (FW) LiDARs, in particular, the TCSPC data, capture, storage and processing. 2. FW-LiDARs are capable of capturing large quantities of photon-counting data in real-time. However, the real-time processing of the raw LiDAR waveforms hasn’t been widely exploited. This thesis answers some of the fundamental questions: • can semantic information be extracted and encoded from raw multi-spectral FW-LiDAR signals? • can these encoded representations then be used for object segmentation and classification? 3. Research is carried out into signal approximation and compressive sensing techniques, its limitations and the application domains. 4. Research is also carried out in 3D point cloud processing, combining geometric features with material spectra (spectral-depth representation), for object segmentation and classification. 5. Extensive experiments have been carried out with publicly available datasets, e.g. the Washington RGB Image and Depth (RGB-D) dataset [108], YaleB face dataset1 [110], real-world multi-frequency aerial laser scans (ALS)2 and an underwater multifrequency (16 wavelengths) TCSPC dataset collected using custom-build targets especially for this thesis. 6. The multi-spectral measurements were made underwater on targets with different shapes and materials. A novel spectral-depth representation is presented with strong discrimination characteristics on target signatures. Several custom-made and realistically scaled exemplars with known and unknown targets have been investigated using a multi-spectral single photon counting LiDAR system. 7. In this work, we also present a new approach to peak modelling and classification for waveform enabled LiDAR systems. Not all existing approaches perform peak modelling and classification simultaneously in real-time. This was tested on both simulated waveform enabled LiDAR data and real ALS data2 . This PhD also led to an industrial secondment at Carbomap, Edinburgh, where some of the waveform modelling algorithms were implemented in C++ and CUDA for Nvidia TX1 boards for real-time performance. 1http://vision.ucsd.edu/~leekc/ExtYaleDatabase/ 2This dataset was captured in collaboration with Carbomap Ltd. Edinburgh, UK. The data was collected during one of the trials in Austria using commercial-off-the-shelf (COTS) sensors

Remote Sensing Data Compression

A huge amount of data is acquired nowadays by different remote sensing systems installed on satellites, aircrafts, and UAV. The acquired data then have to be transferred to image processing centres, stored and/or delivered to customers. In restricted scenarios, data compression is strongly desired or necessary. A wide diversity of coding methods can be used, depending on the requirements and their priority. In addition, the types and properties of images differ a lot, thus, practical implementation aspects have to be taken into account. The Special Issue paper collection taken as basis of this book touches on all of the aforementioned items to some degree, giving the reader an opportunity to learn about recent developments and research directions in the field of image compression. In particular, lossless and near-lossless compression of multi- and hyperspectral images still remains current, since such images constitute data arrays that are of extremely large size with rich information that can be retrieved from them for various applications. Another important aspect is the impact of lossless compression on image classification and segmentation, where a reasonable compromise between the characteristics of compression and the final tasks of data processing has to be achieved. The problems of data transition from UAV-based acquisition platforms, as well as the use of FPGA and neural networks, have become very important. Finally, attempts to apply compressive sensing approaches in remote sensing image processing with positive outcomes are observed. We hope that readers will find our book useful and interestin

Proceedings of the 35th WIC Symposium on Information Theory in the Benelux and the 4th joint WIC/IEEE Symposium on Information Theory and Signal Processing in the Benelux, Eindhoven, the Netherlands May 12-13, 2014

Compressive sensing (CS) as an approach for data acquisition has recently received much attention. In CS, the signal recovery problem from the observed data requires the solution of a sparse vector from an underdetermined system of equations. The underlying sparse signal recovery problem is quite general with many applications and is the focus of this talk. The main emphasis will be on Bayesian approaches for sparse signal recovery. We will examine sparse priors such as the super-Gaussian and student-t priors and appropriate MAP estimation methods. In particular, re-weighted l2 and re-weighted l1 methods developed to solve the optimization problem will be discussed. The talk will also examine a hierarchical Bayesian framework and then study in detail an empirical Bayesian method, the Sparse Bayesian Learning (SBL) method. If time permits, we will also discuss Bayesian methods for sparse recovery problems with structure; Intra-vector correlation in the context of the block sparse model and inter-vector correlation in the context of the multiple measurement vector problem