Sparsity Order Estimation from a Single Compressed Observation Vector

We investigate the problem of estimating the unknown degree of sparsity from compressive measurements without the need to carry out a sparse recovery step. While the sparsity order can be directly inferred from the effective rank of the observation matrix in the multiple snapshot case, this appears to be impossible in the more challenging single snapshot case. We show that specially designed measurement matrices allow to rearrange the measurement vector into a matrix such that its effective rank coincides with the effective sparsity order. In fact, we prove that matrices which are composed of a Khatri-Rao product of smaller matrices generate measurements that allow to infer the sparsity order. Moreover, if some samples are used more than once, one of the matrices needs to be Vandermonde. These structural constraints reduce the degrees of freedom in choosing the measurement matrix which may incur in a degradation in the achievable coherence. We thus also address suitable choices of the measurement matrices. In particular, we analyze Khatri-Rao and Vandermonde matrices in terms of their coherence and provide a new design for Vandermonde matrices that achieves a low coherence

Risk, colon cancer & physical activity: a qualitative exploration in older adults

Rationale and Objectives There is convincing evidence that physical activity (PA) reduces risk of colon cancer (CC) and may improve survival after cancer, although few older adults achieve recommended PA guidelines. Numerous barriers to participation exist, though few studies focus on socio-cultural influences. This study explores barriers specific to individuals at elevated risk of CC following screening colonoscopy, as well as how health professionals or a ‘diagnosis’ may provide additional motivation to change. Methods Interviews were conducted with colonic polyp patients and CC survivors over 60 years old, selectively sampled from a feasibility study for a randomised controlled PA intervention. Narrative accounts enabled discussion of influences on health behaviour throughout participants’ lifetimes, the impact of their recent ‘diagnosis’, and attitudes towards PA. Interviews and focus groups were conducted with health professionals to triangulate data collection. All interviews were transcribed verbatim and a constructivist grounded theory approach to data analysis was followed. Findings Despite not meeting current PA guidelines, participants perceived a lifetime of ‘natural’ PA. CC survivors were more inclined to initiate PA engagement to improve their health; conversely, elevated risk individuals were often not aware of their change in health status, leading them to conclude that no lifestyle change was necessary. Professionals confirmed that no PA guidance is currently offered to screening patients, but believed that there may be scope to implement health promotion advice. Barriers towards this however, are complex and numerous. Conclusions The ‘meaning of PA’ is situated and understandings may differ. Despite reporting perceptions of high PA, this study sample did not seem to understand what constitutes sufficient PA to elicit a positive health response. Risk status awareness and the benefits of PA is lacking in elevated risk individuals. For the screening setting to be utilised, questions around ‘why’, ‘when’ ‘who’ and ‘how’ health promotion should be delivered, need to be addressed

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

Circulation along the northern slope of the Greenland-Scotland Ridge

The Greenland-Scotland Ridge separates the subpolar North Atlantic from the Nordic Seas and constrains the flow of the upper and lower branches of the northern extremity of the Atlantic Meridional Overturning Circulation (AMOC). Warm, saline Atlantic Water flowing northward across the Greenland-Scotland Ridge into the Nordic Seas is transformed into cold, dense water, which returns to the south as overflow plumes through gaps in the ridge. The exchange flows across the ridge have been monitored for several decades, but gaps in our knowledge remain about where and how the dense waters are formed and transported toward the overflows. In this thesis, observational data are used to clarify the upstream pathways of the densest overflow waters and to examine the transformation of the Atlantic Water inflow through Denmark Strait. Paper I focuses on the North Icelandic Jet (NIJ), which supplies the densest water to the overflow plume passing through Denmark Strait. The properties, structure, and transport of the NIJ are investigated for the first time along its entire pathway along the slope north of Iceland, using 13 high-resolution hydrographic/velocity surveys conducted between 2004 and 2018. The comprehensive data set reveals that the current originates northeast of Iceland and that its volume transport increases toward Denmark Strait. The bulk of the NIJ transport is confined to a small area in temperature-salinity space, and these hydrographic properties are not significantly modified along the NIJ's pathway. The transport of overflow water 300 km upstream of Denmark Strait exceeds 1.8±0.3 Sv (1 Sv ≡10^6 m^3/s), which implies a more substantial contribution from the NIJ to the overflow plume than previously envisaged. In paper II we present evidence of a previously unrecognised deep current following the slope from Iceland toward the Faroe Bank Channel, using a high-resolution hydrographic/velocity survey from 2011 along with long-term hydrographic and velocity measurements north of the Faroe Islands. We refer to this current as the Iceland-Faroe Slope Jet (IFSJ). The bulk of the IFSJ's volume transport occupies a small area in temperature-salinity space. The similarity of the hydrographic properties of the eastward-flowing IFSJ and the westward-flowing NIJ suggests that the densest components of the two major overflows across the Greenland-Scotland Ridge have a common source. We estimate that the IFSJ transports approximately 1.0±0.1 Sv, which can account for roughly half of the total overflow transport through the Faroe Bank Channel. As such, the IFSJ is a significant component of the overturning circulation in the Nordic Seas. In paper III we quantify the along-stream evolution of the North Icelandic Irminger Current (NIIC) as it progresses along the shelf break north of Iceland, using a high-resolution shipboard hydrographic/velocity survey, satellite and surface drifter data, and historical hydrographic measurements. The NIIC cools and freshens along its pathway, predominantly due to mixing with cold, fresh offshore waters. Dense-water formation on the shelf is limited, occurring sporadically in only 7% of all historical winter profiles. The hydrographic properties of this locally formed water match the lighter, shallower portion of the NIJ. Along the northeast Iceland slope, enhanced eddy activity and variability in sea surface temperature indicate that locally formed eddies due to instability of the NIIC divert heat and salt into the interior Iceland Sea. The emergence of the NIJ in the same region suggests that there may be a dynamical link to the formation of the NIJ. As such, our results indicate that while the NIIC rarely supplies the NIJ directly, it may be dynamically important for the overturning circulation in the Nordic Seas. The three papers advance our knowledge about the circulation along the northern slope of the Greenland-Scotland Ridge and highlight its significance for water mass transformation in the Nordic Seas and our understanding of the Nordic Seas–North Atlantic exchange. In particular, my results contribute to an improved understanding of the pathways of dense water feeding the overflows, which is imperative to accurately predict how the AMOC will respond to a changing climate.Doktorgradsavhandlin

Examining A Hypersonic Turbulent Boundary Layer at Low Reynolds Number

The purpose of the current study was to answer several questions related to hypersonic, low Reynolds number, turbulent boundary layers, of which available data related to turbulence quantities is scarce. To that end, a unique research facility was created, instrumentation was developed to acquire data in the challenging low Reynolds number (low density) domain, and meaningful data was collected and analyzed. The low Reynolds number nature of the boundary layer (Re_theta = 3700) allows for tangible DNS computations/validations using the current geometry and conditions. The boundary layer examined in this experiment resembled other, higher Reynolds number boundary layers, but also exhibited its own unique characteristics. The Van Driest equivalent velocity scaling method was found to perform well, and the log layer of the law of the wall plot matched expected theory. Noticeably absent from the data was an overlap region between the two layers, which suggests a different profile for the velocity profiles at these low Reynolds number, hypersonic conditions. The low density effects near the wall may be having an effect on the turbulence that modifies this region in a manner not currently anticipated. The Crocco-Busemann relation was found to provide satisfactory results under its general assumptions. When compared to available data, the Morkovin scaled velocity fluctuations fell almost an order of magnitude short. Currently, it is not known if this deficit is due to inadequacies with the Strong Reynolds Analogy, or the Morkovin scaling parameters. The trips seem to promote uniformity across the span of the model, and the data seems to generally be in agreement across the spanwise stations. However, additional information is needed to determine if two-dimensional simulations are sufficient for these boundary layers. When the turbulent boundary layer power spectra is analyzed, the result is found to follow the traditional power law. This result verifies that even at low Reynolds numbers, the length scales still follow the behavior described by Kolmogorov. Moving downstream of the trips, the peak RMS disturbance value grows in amplitude until it reaches a critical value. After this point, the peak begins to decrease in amplitude, but the affected region spreads throughout the boundary layer. Once the influenced region covers a significant portion of the boundary layer, transition occurs

Offenders’ perceptions of the UK prison smoking ban

Purpose Despite overall reductions in levels of smoking in the UK, rates of offender smoking remain high. In 2016, it was announced that prisons in England and Wales would gradually introduce a smoking ban. The purpose of this paper is to explore offenders’ perceptions around the upcoming smoking ban. Design/methodology/approach A total of eight focus groups were conducted in four prisons across the North of England. Both smoking and non-smoking offenders participated in the focus groups, and thematic analysis was used to explore the findings. Findings Themes generated from the data were “freedom and rights”, “the prison environment” and “guiding support”. Participants discussed how the smoking ban was viewed as a punishment and restricted their freedom, with perceptions as to why the ban was being implemented centring around others trying to control them. Participants expressed concerns around the financial implications of the smoking ban on already stretched prison resources. Participants also recommended improving the nicotine replacement therapy on offer, and increasing the range of leisure activities within the prison to prepare for the smoking ban. Originality/value Overall, it was apparent that participants’ awareness of the smoking ban was generally poor. It is recommended that offenders need to be made more aware of the smoking cessation support they will receive and given the opportunity to ask questions about the smoking ban. Increasing offenders’ awareness of the ban may reduce stress associated with a perceived lack of choice around their smoking behaviours