Sparse and Redundant Representations for Inverse Problems and Recognition

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements. The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented

The University Defence Research Collaboration In Signal Processing

This chapter describes the development of algorithms for automatic detection of anomalies from multi-dimensional, undersampled and incomplete datasets. The challenge in this work is to identify and classify behaviours as normal or abnormal, safe or threatening, from an irregular and often heterogeneous sensor network. Many defence and civilian applications can be modelled as complex networks of interconnected nodes with unknown or uncertain spatio-temporal relations. The behavior of such heterogeneous networks can exhibit dynamic properties, reflecting evolution in both network structure (new nodes appearing and existing nodes disappearing), as well as inter-node relations. The UDRC work has addressed not only the detection of anomalies, but also the identification of their nature and their statistical characteristics. Normal patterns and changes in behavior have been incorporated to provide an acceptable balance between true positive rate, false positive rate, performance and computational cost. Data quality measures have been used to ensure the models of normality are not corrupted by unreliable and ambiguous data. The context for the activity of each node in complex networks offers an even more efficient anomaly detection mechanism. This has allowed the development of efficient approaches which not only detect anomalies but which also go on to classify their behaviour

Sparse Signal Models for Data Augmentation in Deep Learning ATR

Automatic Target Recognition (ATR) algorithms classify a given Synthetic Aperture Radar (SAR) image into one of the known target classes using a set of training images available for each class. Recently, learning methods have shown to achieve state-of-the-art classification accuracy if abundant training data is available, sampled uniformly over the classes, and their poses. In this paper, we consider the task of ATR with a limited set of training images. We propose a data augmentation approach to incorporate domain knowledge and improve the generalization power of a data-intensive learning algorithm, such as a Convolutional neural network (CNN). The proposed data augmentation method employs a limited persistence sparse modeling approach, capitalizing on commonly observed characteristics of wide-angle synthetic aperture radar (SAR) imagery. Specifically, we exploit the sparsity of the scattering centers in the spatial domain and the smoothly-varying structure of the scattering coefficients in the azimuthal domain to solve the ill-posed problem of over-parametrized model fitting. Using this estimated model, we synthesize new images at poses and sub-pixel translations not available in the given data to augment CNN's training data. The experimental results show that for the training data starved region, the proposed method provides a significant gain in the resulting ATR algorithm's generalization performance.Comment: 12 pages, 5 figures, to be submitted to IEEE Transactions on Geoscience and Remote Sensin

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

The University Defence Research Collaboration In Signal Processing: 2013-2018

Signal processing is an enabling technology crucial to all areas of defence and security. It is called for whenever humans and autonomous systems are required to interpret data (i.e. the signal) output from sensors. This leads to the production of the intelligence on which military outcomes depend. Signal processing should be timely, accurate and suited to the decisions to be made. When performed well it is critical, battle-winning and probably the most important weapon which you’ve never heard of. With the plethora of sensors and data sources that are emerging in the future network-enabled battlespace, sensing is becoming ubiquitous. This makes signal processing more complicated but also brings great opportunities. The second phase of the University Defence Research Collaboration in Signal Processing was set up to meet these complex problems head-on while taking advantage of the opportunities. Its unique structure combines two multi-disciplinary academic consortia, in which many researchers can approach different aspects of a problem, with baked-in industrial collaboration enabling early commercial exploitation. This phase of the UDRC will have been running for 5 years by the time it completes in March 2018, with remarkable results. This book aims to present those accomplishments and advances in a style accessible to stakeholders, collaborators and exploiters