Compressed Sensing Applied to Weather Radar

We propose an innovative meteorological radar, which uses reduced number of spatiotemporal samples without compromising the accuracy of target information. Our approach extends recent research on compressed sensing (CS) for radar remote sensing of hard point scatterers to volumetric targets. The previously published CS-based radar techniques are not applicable for sampling weather since the precipitation echoes lack sparsity in both range-time and Doppler domains. We propose an alternative approach by adopting the latest advances in matrix completion algorithms to demonstrate the sparse sensing of weather echoes. We use Iowa X-band Polarimetric (XPOL) radar data to test and illustrate our algorithms.Comment: 4 pages, 5 figrue

Theory and Design of a Highly Compressed Dropped-Channel Polarimetric Synthetic Aperture Radar

Compressed sensing (CS) is a recent mathematical technique that leverages the sparsity in certain sets of data to solve an underdetermined system and recover a full set of data from a sub-Nyquist set of measurements of the data. Given the size and sparsity of the data, radar has been a natural choice to apply compressed sensing to, typically in the fast-time and slow-time domains. Polarimetric synthetic aperture radar (PolSAR) generates a particularly large amount of data for a given scene; however, the data tends to be sparse. Recently a technique was developed to recover a dropped PolSAR channel by leveraging antenna crosstalk information and using compressed sensing. In this dissertation, we build upon the initial concept of the dropped-channel PolSAR CS in three ways. First, we determine a metric which relates the measurement matrix to the l2 recovery error. The new metric is necessary given the deterministic nature of the measurement matrix. We then determine a range of antenna crosstalk required to recover a dropped PolSAR channel. Second, we propose a new antenna design that incorporates the relatively high levels of crosstalk required by a dropped-channel PolSAR system. Finally, we integrate fast- and slow-time compression schemes into the dropped-channel model in order to leverage sparsity in additional PolSAR domains and overall increase the compression ratio. The completion of these research tasks has allowed a more accurate description of a PolSAR system that compresses in fast-time, slow-time, and polarization; termed herein as highly compressed PolSAR. The description of a highly compressed PolSAR system is a big step towards the development of prototype hardware in the future

Convex Model-Based Synthetic Aperture Radar Processing

The use of radar often conjures up images of small blobs on a screen. But current synthetic aperture radar (SAR) systems are able to generate near-optical quality images with amazing benefits compared to optical sensors. These SAR sensors work in all weather conditions, day or night, and provide many advanced capabilities to detect and identify targets of interest. These amazing abilities have made SAR sensors a work-horse in remote sensing, and military applications. SAR sensors are ranging instruments that operate in a 3D environment, but unfortunately the results and interpretation of SAR images have traditionally been done in 2D. Three-dimensional SAR images could provide improved target detection and identification along with improved scene interpretability. As technology has increased, particularly regarding our ability to solve difficult optimization problems, the 3D SAR reconstruction problem has gathered more interest. This dissertation provides the SAR and mathematical background required to pose a SAR 3D reconstruction problem. The problem is posed in a way that allows prior knowledge about the target of interest to be integrated into the optimization problem when known. The developed model is demonstrated on simulated data initially in order to illustrate critical concepts in the development. Then once comprehension is achieved the processing is applied to actual SAR data. The 3D results are contrasted against the current gold- standard. The results are shown as 3D images demonstrating the improvement regarding scene interpretability that this approach provides

A PARTIAL ACQUISITION TECHNIQUE OF SAR SYSTEM USING COMPRESSIVE SAMPLING METHOD

In line with the development of Synthetic Aperture Radar (SAR) technology, there is a serious problem when the SAR signal is acquired using high rate analog digital converter (ADC), that require large volumes data storage. The other problem on compressive sensing method,which frequently occurs, is a large measurement matrix that may cause intensive calculation. In this paper, a new approach was proposed, particularly on the partial acquisition technique of SAR system using compressive sampling method in both the azimuth and range direction. The main objectives of the study are to reduce the radar raw data by decreasing the sampling rate of ADC and to reduce the computational load by decreasing the dimension of the measurement matrix. The simulation results found that the reconstruction of SAR image using partial acquisition model has better resolution compared to the conventional method (Range Doppler Algorithm/RDA). On a target of a ship, that represents a low-level sparsity, a good reconstruction image could be achieved from a fewer number measurement. The study concludes that the method may speed up the computation time by a factor 4.49 times faster than with a full acquisition matrix

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

Efficient algorithms and data structures for compressive sensing

Wegen der kontinuierlich anwachsenden Anzahl von Sensoren, und den stetig wachsenden Datenmengen, die jene produzieren, stößt die konventielle Art Signale zu verarbeiten, beruhend auf dem Nyquist-Kriterium, auf immer mehr Hindernisse und Probleme. Die kürzlich entwickelte Theorie des Compressive Sensing (CS) formuliert das Versprechen einige dieser Hindernisse zu beseitigen, indem hier allgemeinere Signalaufnahme und -rekonstruktionsverfahren zum Einsatz kommen können. Dies erlaubt, dass hierbei einzelne Abtastwerte komplexer strukturierte Informationen über das Signal enthalten können als dies bei konventiellem Nyquistsampling der Fall ist. Gleichzeitig verändert sich die Signalrekonstruktion notwendigerweise zu einem nicht-linearen Vorgang und ebenso müssen viele Hardwarekonzepte für praktische Anwendungen neu überdacht werden. Das heißt, dass man zwischen der Menge an Information, die man über Signale gewinnen kann, und dem Aufwand für das Design und Betreiben eines Signalverarbeitungssystems abwägen kann und muss. Die hier vorgestellte Arbeit trägt dazu bei, dass bei diesem Abwägen CS mehr begünstigt werden kann, indem neue Resultate vorgestellt werden, die es erlauben, dass CS einfacher in der Praxis Anwendung finden kann, wobei die zu erwartende Leistungsfähigkeit des Systems theoretisch fundiert ist. Beispielsweise spielt das Konzept der Sparsity eine zentrale Rolle, weshalb diese Arbeit eine Methode präsentiert, womit der Grad der Sparsity eines Vektors mittels einer einzelnen Beobachtung geschätzt werden kann. Wir zeigen auf, dass dieser Ansatz für Sparsity Order Estimation zu einem niedrigeren Rekonstruktionsfehler führt, wenn man diesen mit einer Rekonstruktion vergleicht, welcher die Sparsity des Vektors unbekannt ist. Um die Modellierung von Signalen und deren Rekonstruktion effizienter zu gestalten, stellen wir das Konzept von der matrixfreien Darstellung linearer Operatoren vor. Für die einfachere Anwendung dieser Darstellung präsentieren wir eine freie Softwarearchitektur und demonstrieren deren Vorzüge, wenn sie für die Rekonstruktion in einem CS-System genutzt wird. Konkret wird der Nutzen dieser Bibliothek, einerseits für das Ermitteln von Defektpositionen in Prüfkörpern mittels Ultraschall, und andererseits für das Schätzen von Streuern in einem Funkkanal aus Ultrabreitbanddaten, demonstriert. Darüber hinaus stellen wir für die Verarbeitung der Ultraschalldaten eine Rekonstruktionspipeline vor, welche Daten verarbeitet, die im Frequenzbereich Unterabtastung erfahren haben. Wir beschreiben effiziente Algorithmen, die bei der Modellierung und der Rekonstruktion zum Einsatz kommen und wir leiten asymptotische Resultate für die benötigte Anzahl von Messwerten, sowie die zu erwartenden Lokalisierungsgenauigkeiten der Defekte her. Wir zeigen auf, dass das vorgestellte System starke Kompression zulässt, ohne die Bildgebung und Defektlokalisierung maßgeblich zu beeinträchtigen. Für die Lokalisierung von Streuern mittels Ultrabreitbandradaren stellen wir ein CS-System vor, welches auf einem Random Demodulators basiert. Im Vergleich zu existierenden Messverfahren ist die hieraus resultierende Schätzung der Kanalimpulsantwort robuster gegen die Effekte von zeitvarianten Funkkanälen. Um den inhärenten Modellfehler, den gitterbasiertes CS begehen muss, zu beseitigen, zeigen wir auf wie Atomic Norm Minimierung es erlaubt ohne die Einschränkung auf ein endliches und diskretes Gitter R-dimensionale spektrale Komponenten aus komprimierten Beobachtungen zu schätzen. Hierzu leiten wir eine R-dimensionale Variante des ADMM her, welcher dazu in der Lage ist die Signalkovarianz in diesem allgemeinen Szenario zu schätzen. Weiterhin zeigen wir, wie dieser Ansatz zur Richtungsschätzung mit realistischen Antennenarraygeometrien genutzt werden kann. In diesem Zusammenhang präsentieren wir auch eine Methode, welche mittels Stochastic gradient descent Messmatrizen ermitteln kann, die sich gut für Parameterschätzung eignen. Die hieraus resultierenden Kompressionsverfahren haben die Eigenschaft, dass die Schätzgenauigkeit über den gesamten Parameterraum ein möglichst uniformes Verhalten zeigt. Zuletzt zeigen wir auf, dass die Kombination des ADMM und des Stochastic Gradient descent das Design eines CS-Systems ermöglicht, welches in diesem gitterfreien Szenario wünschenswerte Eigenschaften hat.Along with the ever increasing number of sensors, which are also generating rapidly growing amounts of data, the traditional paradigm of sampling adhering the Nyquist criterion is facing an equally increasing number of obstacles. The rather recent theory of Compressive Sensing (CS) promises to alleviate some of these drawbacks by proposing to generalize the sampling and reconstruction schemes such that the acquired samples can contain more complex information about the signal than Nyquist samples. The proposed measurement process is more complex and the reconstruction algorithms necessarily need to be nonlinear. Additionally, the hardware design process needs to be revisited as well in order to account for this new acquisition scheme. Hence, one can identify a trade-off between information that is contained in individual samples of a signal and effort during development and operation of the sensing system. This thesis addresses the necessary steps to shift the mentioned trade-off more to the favor of CS. We do so by providing new results that make CS easier to deploy in practice while also maintaining the performance indicated by theoretical results. The sparsity order of a signal plays a central role in any CS system. Hence, we present a method to estimate this crucial quantity prior to recovery from a single snapshot. As we show, this proposed Sparsity Order Estimation method allows to improve the reconstruction error compared to an unguided reconstruction. During the development of the theory we notice that the matrix-free view on the involved linear mappings offers a lot of possibilities to render the reconstruction and modeling stage much more efficient. Hence, we present an open source software architecture to construct these matrix-free representations and showcase its ease of use and performance when used for sparse recovery to detect defects from ultrasound data as well as estimating scatterers in a radio channel using ultra-wideband impulse responses. For the former of these two applications, we present a complete reconstruction pipeline when the ultrasound data is compressed by means of sub-sampling in the frequency domain. Here, we present the algorithms for the forward model, the reconstruction stage and we give asymptotic bounds for the number of measurements and the expected reconstruction error. We show that our proposed system allows significant compression levels without substantially deteriorating the imaging quality. For the second application, we develop a sampling scheme to acquire the channel Impulse Response (IR) based on a Random Demodulator that allows to capture enough information in the recorded samples to reliably estimate the IR when exploiting sparsity. Compared to the state of the art, this in turn allows to improve the robustness to the effects of time-variant radar channels while also outperforming state of the art methods based on Nyquist sampling in terms of reconstruction error. In order to circumvent the inherent model mismatch of early grid-based compressive sensing theory, we make use of the Atomic Norm Minimization framework and show how it can be used for the estimation of the signal covariance with R-dimensional parameters from multiple compressive snapshots. To this end, we derive a variant of the ADMM that can estimate this covariance in a very general setting and we show how to use this for direction finding with realistic antenna geometries. In this context we also present a method based on a Stochastic gradient descent iteration scheme to find compression schemes that are well suited for parameter estimation, since the resulting sub-sampling has a uniform effect on the whole parameter space. Finally, we show numerically that the combination of these two approaches yields a well performing grid-free CS pipeline