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

DVB-S based passive polarimetric ISAR – methods and experimental validation

In this work, we focus on passive polarimetric ISAR for ship target imaging using DVB-S signals of opportunity. A first goal of the research is to investigate if, within the challenging passive environment, different scattering mechanisms, belonging to distinct parts of the imaged target, can be separated in the polarimetric domain. Furthermore, a second goal is at verifying if polarimetric diversity could enable the formation of ISAR products with enhanced quality with respect to the single channel case, particularly in terms of better reconstruction of the target shape. To this purpose, a dedicated trial has been conducted along the river Rhine in Germany by means of an experimental DVB-S based system developed at Fraunhofer FHR and considering a ferry as cooperative target. To avoid inaccuracies due to data-driven motion compensation procedures and to fairly interpret the polarimetric results, we processed the data by means of a known-motion back-projection algorithm obtaining ISAR images at each polarimetric channel. Then, different approaches in the polarimetric domain have been introduced. The first one is based on the well-known Pauli Decomposition. The others can be divided in two main groups: (i) techniques aimed at separating the different backscattering mechanisms, and (ii) image domain techniques to fuse the polarimetric information in a single ISAR image with enhanced quality. The different considered techniques have been applied to several data sets with distinct bistatic geometries. The obtained results clearly demonstrate the potentialities of polarimetric diversity that could be fruitfully exploited for classification purposes

Sparse Bases and Bayesian Inference of Electromagnetic Scattering

Many approaches in CEM rely on the decomposition of complex radiation and scattering behavior with a set of basis vectors. Accurate estimation of the quantities of interest can be synthesized through a weighted sum of these vectors. In addition to basis decompositions, sparse signal processing techniques developed in the CS community can be leveraged when only a small subset of the basis vectors are required to sufficiently represent the quantity of interest. We investigate several concepts in which novel bases are applied to common electromagnetic problems and leverage the sparsity property to improve performance and/or reduce computational burden. The first concept explores the use of multiple types of scattering primitives to reconstruct scattering patterns of electrically large targets. Using a combination of isotropic point scatterers and wedge diffraction primitives as our bases, a 40% reduction in reconstruction error can be achieved. Next, a sparse basis is used to improve DOA estimation. We implement the BSBL technique to determine the angle of arrival of multiple incident signals with only a single snapshot of data from an arbitrary arrangement of non-isotropic antennas. This is an improvement over the current state-of-the-art, where restrictions on the antenna type, configuration, and a priori knowledge of the number of signals are often assumed. Lastly, we investigate the feasibility of a basis set to reconstruct the scattering patterns of electrically small targets. The basis is derived from the TCM and can capture non-localized scattering behavior. Preliminary results indicate that this basis may be used in an interpolation and extrapolation scheme to generate scattering patterns over multiple frequencies

Maritime Moving Target Detection, Tracking and Geocoding Using Range-Compressed Airborne Radar Data

Eine regelmäßige und großflächige überwachung des Schiffsverkehrs gewinnt zunehmend an Bedeutung, vor allem auch um maritime Gefahrenlagen und illegale Aktivitäten rechtzeitig zu erkennen. Heutzutage werden dafür überwiegend das automatische Identifikationssystem (AIS) und stationäre Radarstationen an den Küsten eingesetzt. Luft- und weltraumgestützte Radarsensoren, die unabhängig vom Wetter und Tageslicht Daten liefern, können die vorgenannten Systeme sehr gut ergänzen. So können sie beispielsweise Schiffe detektieren, die nicht mit AIS-Transpondern ausgestattet sind oder die sich außerhalb der Reichweite der stationären AIS- und Radarstationen befinden. Luftgestützte Radarsensoren ermöglichen eine quasi-kontinuierliche Beobachtung von räumlich begrenzten Gebieten. Im Gegensatz dazu bieten weltraumgestützte Radare eine große räumliche Abdeckung, haben aber den Nachteil einer geringeren temporalen Abdeckung. In dieser Dissertation wird ein umfassendes Konzept für die Verarbeitung von Radardaten für die Schiffsverkehr-überwachung mit luftgestützten Radarsensoren vorgestellt. Die Hauptkomponenten dieses Konzepts sind die Detektion, das Tracking, die Geokodierung, die Bildgebung und die Fusion mit AIS-Daten. Im Rahmen der Dissertation wurden neuartige Algorithmen für die ersten drei Komponenten entwickelt. Die Algorithmen sind so aufgebaut, dass sie sich prinzipiell für zukünftige Echtzeitanwendungen eignen, die eine Verarbeitung an Bord der Radarplattform erfordern. Darüber hinaus eignen sich die Algorithmen auch für beliebige, nicht-lineare Flugpfade der Radarplattform. Sie sind auch robust gegenüber Lagewinkeländerungen, die während der Datenerfassung aufgrund von Luftturbulenzen jederzeit auftreten können. Die für die Untersuchungen verwendeten Daten sind ausschließlich entfernungskomprimierte Radardaten. Da das Signal-Rausch-Verhältnis von Flugzeugradar-Daten im Allgemeinen sehr hoch ist, benötigen die neuentwickelten Algorithmen keine vollständig fokussierten Radarbilder. Dies reduziert die Gesamtverarbeitungszeit erheblich und ebnet den Weg für zukünftige Echtzeitanwendungen. Der entwickelte neuartige Schiffsdetektor arbeitet direkt im Entfernungs-Doppler-Bereich mit sehr kurzen kohärenten Verarbeitungsintervallen (CPIs) der entfernungskomprimierten Radardaten. Aufgrund der sehr kurzen CPIs werden die detektierten Ziele im Dopplerbereich fokussiert abgebildet. Wenn sich die Schiffe zusätzlich mit einer bestimmten Radialgeschwindigkeit bewegen, werden ihre Signale aus dem Clutter-Bereich hinausgeschoben. Dies erhöht das Verhältnis von Signal- zu Clutter-Energie und verbessert somit die Detektierbarkeit. Die Genauigkeit der Detektion hängt stark von der Qualität der von der Meeresoberfläche rückgestreuten Radardaten ab, die für die Schätzung der Clutter-Statistik verwendet werden. Diese wird benötigt, um einen Detektions-Schwellenwert für eine konstante Fehlalarmrate (CFAR) abzuleiten und die Anzahl der Fehlalarme niedrig zu halten. Daher umfasst der vorgeschlagene Detektor auch eine neuartige Methode zur automatischen Extraktion von Trainingsdaten für die Statistikschätzung sowie geeignete Ozean-Clutter-Modelle. Da es sich bei Schiffen um ausgedehnte Ziele handelt, die in hochauflösenden Radardaten mehr als eine Auflösungszelle belegen, werden nach der Detektion mehrere von einem Ziel stammende Pixel zu einem physischen Objekten zusammengefasst, das dann in aufeinanderfolgenden CPIs mit Hilfe eines Bewegungsmodells und eines neuen Mehrzielverfolgungs-Algorithmus (Multi-Target Tracking) getrackt wird. Während des Trackings werden falsche Zielspuren und Geisterzielspuren automatisch erkannt und durch ein leistungsfähiges datenbankbasiertes Track-Management-System terminiert. Die Zielspuren im Entfernungs-Doppler-Bereich werden geokodiert bzw. auf den Boden projiziert, nachdem die Einfallswinkel (DOA) aller Track-Punkte geschätzt wurden. Es werden verschiedene Methoden zur Schätzung der DOA-Winkel für ausgedehnte Ziele vorgeschlagen und anhand von echten Radardaten, die Signale von echten Schiffen beinhalten, bewertet

Radar Imaging Based on IEEE 802.11ad Waveform in V2I Communications

Since most of vehicular radar systems are already exploiting millimeter-wave (mmWave) spectra, it would become much more feasible to implement a joint radar and communication system by extending communication frequencies into the mmWave band. In this paper, an IEEE 802.11ad waveform-based radar imaging technique is proposed for vehicular settings. A roadside unit (RSU) transmits the IEEE 802.11ad waveform to a vehicle for communications while the RSU also listens to the echoes of transmitted waveform to perform inverse synthetic aperture radar (ISAR) imaging. To obtain high-resolution images of the vehicle, the RSU needs to accurately estimate round-trip delays, Doppler shifts, and velocity of vehicle. The proposed ISAR imaging first estimates the round-trip delays using a good correlation property of Golay complementary sequences in the IEEE 802.11ad preamble. The Doppler shifts are then obtained using least square estimation from the echo signals and refined to compensate phase wrapping caused by phase rotation. The velocity of vehicle is determined using an equation of motion and the estimated Doppler shifts. Simulation results verify that the proposed technique is able to form high-resolution ISAR images from point scatterer models of realistic vehicular settings with different viewpoints. The proposed ISAR imaging technique can be used for various vehicular applications, e.g., traffic condition analyses or advanced collision warning systems

Enhanced WiFi-based passive ISAR for indoor and outdoor surveillance

In this paper we examine the potentiality of passive coherent location (PCL) exploiting WiFi transmissions for indoor and outdoor area monitoring. Particularly, we investigate the advanced capability to obtain high resolution cross-range profiles of the observed targets via Inverse Synthetic Aperture Radar (ISAR) techniques. To these purposes, appropriate processing techniques are introduced and their effectiveness is tested against real data sets concerning both human and man-made targets. The reported results clearly show that the proposed technique allows to effectively discriminate closely spaced human targets moving in a hall, whereas they could not be resolved by a conventional processing. In addition reliable and stable profiles are obtained for the man-made targets moving in the surveyed scene which might fruitfully feed a classification stage. This contributes to demonstrate the effective applicability of the passive radar concept for improving internal and external security of private/public premises. © 2015 IEEE

On-board Processing Architecture of DLR's DBFSAR / V-SAR System

For real-time Synthetic Aperture Radar applications, data must be processed and sent to the ground station efficiently. This paper describes the processing architecture of DLR's DBFSAR system with the aim of presenting recent developments of on-board radar processing. It explains how the low level optimizations were conducted and under which conditions their integration in the SAR imaging process and maritime moving target indication leads to real-time capability