Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data

The ubiquity of integrating detectors in imaging and other applications implies that a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of interest. In this article, we first show how the so-called Skellam distribution arises from the fact that Haar wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of Poisson counts. We then provide two main theorems on Skellam shrinkage, one showing the near-optimality of shrinkage in the Bayesian setting and the other providing for unbiased risk estimation in a frequentist context. These results serve to yield new estimators in the Haar transform domain, including an unbiased risk estimate for shrinkage of Haar-Fisz variance-stabilized data, along with accompanying low-complexity algorithms for inference. We conclude with a simulation study demonstrating the efficacy of our Skellam shrinkage estimators both for the standard univariate wavelet test functions as well as a variety of test images taken from the image processing literature, confirming that they offer substantial performance improvements over existing alternatives.Comment: 27 pages, 8 figures, slight formatting changes; submitted for publicatio

MERITXELL: the Multifrequency Experimental Radiometer with Interference Tracking for Experiments over Land and Littoral—instrument description, calibration and performance

MERITXELL is a ground-based multisensor instrument that includes a multiband dual-polarization radiometer, a GNSS reflectometer, and several optical sensors. Its main goals are twofold: to test data fusion techniques, and to develop Radio-Frequency Interference (RFI) detection, localization and mitigation techniques. The former is necessary to retrieve complementary data useful to develop geophysical models with improved accuracy, whereas the latter aims at solving one of the most important problems of microwave radiometry. This paper describes the hardware design, the instrument control architecture, the calibration of the radiometer, and several captures of RFI signals taken with MERITXELL in urban environment. The multiband radiometer has a dual linear polarization total-power radiometer topology, and it covers the L-, S-, C-, X-, K-, Ka-, and W-band. Its back-end stage is based on a spectrum analyzer structure which allows to perform real-time signal processing, while the rest of the sensors are controlled by a host computer where the off-line processing takes place. The calibration of the radiometer is performed using the hot-cold load procedure, together with the tipping curves technique in the case of the five upper frequency bands. Finally, some captures of RFI signals are shown for most of the radiometric bands under analysis, which evidence the problem of RFI in microwave radiometry, and the limitations they impose in external calibration.Peer ReviewedPostprint (published version

Reconstruction Error and Principal Component Based Anomaly Detection in Hyperspectral imagery

The rapid expansion of remote sensing and information collection capabilities demands methods to highlight interesting or anomalous patterns within an overabundance of data. This research addresses this issue for hyperspectral imagery (HSI). Two new reconstruction based HSI anomaly detectors are outlined: one using principal component analysis (PCA), and the other a form of non-linear PCA called logistic principal component analysis. Two very effective, yet relatively simple, modifications to the autonomous global anomaly detector are also presented, improving algorithm performance and enabling receiver operating characteristic analysis. A novel technique for HSI anomaly detection dubbed multiple PCA is introduced and found to perform as well or better than existing detectors on HYDICE data while using only linear deterministic methods. Finally, a response surface based optimization is performed on algorithm parameters such as to affect consistent desired algorithm performance

Case study:shipping trend estimation and prediction via multiscale variance stabilisation

<p>Shipping and shipping services are a key industry of great importance to the economy of Cyprus and the wider European Union. Assessment, management and future steering of the industry, and its associated economy, is carried out by a range of organisations and is of direct interest to a number of stakeholders. This article presents an analysis of shipping credit flow data: an important and archetypal series whose analysis is hampered by rapid changes of variance. Our analysis uses the recently developed data-driven Haar–Fisz transformation that enables accurate trend estimation and successful prediction in these kinds of situation. Our trend estimation is augmented by bootstrap confidence bands, new in this context. The good performance of the data-driven Haar–Fisz transform contrasts with the poor performance exhibited by popular and established variance stabilisation alternatives: the Box–Cox, logarithm and square root transformations.</p

Radio frequency interference detection and mitigation techniques for navigation and Earth observation

Radio-Frequency Interference (RFI) signals are undesired signals that degrade or disrupt the performance of a wireless receiver. RFI signals can be troublesome for any receiver, but they are especially threatening for applications that use very low power signals. This is the case of applications that rely on the Global Navigation Satellite Systems (GNSS), or passive microwave remote sensing applications such as Microwave Radiometry (MWR) and GNSS-Reflectometry (GNSS-R). In order to solve the problem of RFI, RFI-countermeasures are under development. This PhD thesis is devoted to the design, implementation and test of innovative RFI-countermeasures in the fields of MWR and GNSS. In the part devoted to RFI-countermeasures for MWR applications, first, this PhD thesis completes the development of the MERITXELL instrument. The MERITXELL is a multi-frequency total-power radiometer conceived to be an outstanding platform to perform detection, characterization, and localization of RFI signals at the most common MWR imaging bands up to 92 GHz. Moreover, a novel RFI mitigation technique is proposed for MWR: the Multiresolution Fourier Transform (MFT). An assessment of the performance of the MFT has been carried out by comparison with other time-frequency mitigation techniques. According to the results, the MFT technique is a good trade-off solution among all other techniques since it can mitigate efficiently all kinds of RFI signals under evaluation. In the part devoted to RFI-countermeasures for GNSS and GNSS-R applications, first, a system for RFI detection and localization at GNSS bands is proposed. This system is able to detect RFI signals at the L1 band with a sensitivity of -108 dBm at full-band, and of -135 dBm for continuous wave and chirp-like signals when using the averaged spectrum technique. Besides, the Generalized Spectral Separation Coefficient (GSSC) is proposed as a figure of merit to evaluate the Signal-to-Noise Ratio (SNR) degradation in the Delay-Doppler Maps (DDMs) due to the external RFI effect. Furthermore, the FENIX system has been conceived as an innovative system for RFI detection and mitigation and anti-jamming for GNSS and GNSS-R applications. FENIX uses the MFT blanking as a pre-correlation excision tool to perform the mitigation. In addition, FENIX has been designed to be cross-GNSS compatible and RFI-independent. The principles of operation of the MFT blanking algorithm are assessed and compared with other techniques for GNSS signals. Its performance as a mitigation tool is proven using GNSS-R data samples from a real airborne campaign. After that, the main building blocks of the patented architecture of FENIX have been described. The FENIX architecture has been implemented in three real-time prototypes. Moreover, a simulator named FENIX-Sim allows for testing its performance under different jamming scenarios. The real-time performance of FENIX prototype has been tested using different setups. First, a customized VNA has been built in order to measure the transfer function of FENIX in the presence of several representative RFI/jamming signals. The results show how the power transfer function adapts itself to mitigate the RFI/jamming signal. Moreover, several real-time tests with GNSS receivers have been performed using GPS L1 C/A, GPS L2C, and Galileo E1OS. The results show that FENIX provides an extra resilience against RFI and jamming signals up to 30 dB. Furthermore, FENIX is tested using a real GNSS timing setup. Under nominal conditions, when no RFI/jamming signal is present, a small additional jitter on the order of 2-4 ns is introduced in the system. Besides, a maximum bias of 45 ns has been measured under strong jamming conditions (-30 dBm), which is acceptable for current timing systems requiring accuracy levels of 100 ns. Finally, the design of a backup system for GNSS in tracking applications that require high reliability against RFI and jamming attacks is proposed.Les interferències de radiofreqüència (RFI) són senyals no desitjades que degraden o interrompen el funcionament dels receptors sense fils. Les RFI poden suposar un problema per qualsevol receptor, però són especialment amenaçadores per les a aplicacions que fan servir senyals de molt baixa potència. Aquest és el cas de les aplicacions que depenen dels sistemes mundials de navegació per satèl·lit (GNSS) o de les aplicacions de teledetecció passiva de microones, com la radiometria de microones (MWR) i la reflectometria GNSS (GNSS-R). Per combatre aquest problema, sistemes anti-RFI s'estan desenvolupament actualment. Aquesta tesi doctoral està dedicada al disseny, la implementació i el test de sistemes anti-RFI innovadors en els camps de MWR i GNSS. A la part dedicada als sistemes anti-RFI en MWR, aquesta tesi doctoral completa el desenvolupament de l'instrument MERITXELL. El MERITXELL és un radiòmetre multifreqüència concebut com una plataforma excepcional per la detecció, caracterització i localització de RFI a les bandes de MWR més utilitzades per sota dels 92 GHz. A més a més, es proposa una nova tècnica de mitigació de RFI per MWR: la Transformada de Fourier amb Multiresolució (MFT). El funcionament de la MFT s'ha comparat amb el d'altres tècniques de mitigació en els dominis del temps i la freqüència. D'acord amb els resultats obtinguts, la MFT és una bona solució de compromís entre les altres tècniques, ja que pot mitigar de manera eficient tots els tipus de senyals RFI considerats. A la part dedicada als sistemes anti-RFI en GNSS i GNSS-R, primer es proposa un sistema per a la detecció i localització de RFI a les bandes GNSS. Aquest sistema és capaç de detectar senyals RFI a la banda L1 amb una sensibilitat de -108 dBm a tota la banda, i de -135 dBm per a senyals d'ona contínua i chirp fen un mitjana de l'espectre. A més a més, el Coeficient de Separació Espectral Generalitzada (GSSC) es proposa com una mesura per avaluar la degradació de la relació senyal a soroll (SNR) en els Mapes de Delay-Doppler (DDM) a causa del impacte de les RFI. La major contribució d'aquesta tesi doctoral és el sistema FENIX. FENIX és un sistema innovador de detecció i mitigació de RFI i inhibidors de freqüència per aplicacions GNSS i GNSS-R. FENIX utilitza la MFT per eliminar la interferència abans del procés de correlació amb el codi GNSS independentment del tipus de RFI. L'algoritme de mitigació de FENIX s'ha avaluat i comparat amb altres tècniques i els principals components de la seva arquitectura patentada es descriuen. Finalment, un simulador anomenat FENIX-Sim permet avaluar el seu rendiment en diferents escenaris d'interferència. El funcionament en temps real del prototip FENIX ha estat provat utilitzant diferents mètodes. En primer lloc, s'ha creat un analitzador de xarxes per a mesurar la funció de transferència del FENIX en presència de diverses RFI representatives. Els resultats mostren com la funció de transferència s'adapta per mitigar el senyal interferent. A més a més, s'han realitzat diferents proves en temps real amb receptors GNSS compatibles amb els senyals GPS L1 C/A, GPS L2C i Galileo E1OS. Els resultats mostren que FENIX proporciona una resistència addicional contra les RFI i els senyals dels inhibidors de freqüència de fins a 30 dB. A més a més, FENIX s'ha provat amb un sistema comercial de temporització basat en GNSS. En condicions nominals, sense RFI, FENIX introdueix un petit error addicional de tan sols 2-4 ns. Per contra, el biaix màxim mesurat en condicions d'alta interferència (-30 dBm) és de 45 ns, el qual és acceptable per als sistemes de temporització actuals que requereixen nivells de precisió d'uns 100 ns. Finalment, es proposa el disseny d'un sistema robust de seguiment, complementari als GNSS, per a aplicacions que requereixen alta fiabilitat contra RFI.Postprint (published version

Grey Level and Noise Evaluation of a Foveon X3 Image Sensor: A Statistical and Experimental Approach

Radiometric values on digital imagery are affected by several sources of uncertainty. A practical, comprehensive and flexible procedure to analyze the radiometric values and the uncertainty effects due to the camera sensor system is described in this paper. The procedure is performed on the grey level output signal using image raw units with digital numbers ranging from 0 to 212-1. The procedure is entirely based on statistical and experimental techniques. Design of Experiments (DoE) for Linear Models (LM) are derived to analyze the radiometric values and estimate the uncertainty. The presented linear model integrates all the individual sensor noise sources in one global component and characterizes the radiometric values and the uncertainty effects according to the influential factors such as the scene reflectance, wavelength range and time. The experiments are carried out under laboratory conditions to minimize the rest of uncertainty sources that might affect the radiometric values. It is confirmed the flexibility of the procedure to model and characterize the radiometric values, as well as to determine the behaviour of two phenomena when dealing with image sensors: the noise of a single image and the stability (trend and noise) of a sequence of images.The authors would like to thank the support provided by the Spanish Ministry of Science and Innovation to the project HAR2010-18620. The authors also acknowledge the chance to take pictures with the lighting equipment in the Soils Laboratory at the Universitat Politecnica de Valencia.Riutort Mayol, G.; Marqués Mateu, Á.; Seguí Gil, AE.; Lerma García, JL. (2012). Grey Level and Noise Evaluation of a Foveon X3 Image Sensor: A Statistical and Experimental Approach. Sensors. 12(8):10339-10368. https://doi.org/10.3390/s120810339S103391036812

Spatiotemporal Estuarine Water Quality Parameterization Using Remote Sensing and in-situ Characteristics

This dissertation develops a new paradigm in a water quality monitoring approach to parameterize spatiotemporal estuarine water quality with sustainable reliability, less cost and less time. A key underpinning of this paradigm of the spatiotemporal estuarine water quality parameterization is various water quality parameters\u27 interrelationship with ambient water temperature as a common factor, their time dependent characteristics, and spatiotemporal characteristics of remote sensing. It has two core models to provide input data of water quality parameterization model in a system; the transfer function models of the physical system and an analytical temperature time series model. The objective of this dissertation is to provide an alternative tool for monitoring water quality and decision-making in estuaries with time and space, to identify system components contributing to physical water quality, and to demonstrate the feasibility, reproducibility and applicability of the proposed model. The spatiotemporal estuarine water quality parameterization model monitors chlorophyll concentration using remote sensing, transfer function models of dissolved oxygen (DO) and orthophosphate (PO4) and ambient water temperature in spring and fall in the James River Estuary Mesohaline segment in Virginia. The proposed model is applicable in the temperature range between 6°C and 23°C in spring and in the temperature range between 21°C and 32°C in fall. The optimal operational temperature range of the proposed model is between 19°C and 25°C based on the relative sensitivity analysis of DO transfer function model. The proposed models in two seasons are compared with the models that use different approaches such as a conventional approach and a previously proposed approach based on various criteria. The results show that the proposed models present the variability of chlorophyll concentration better over time and temperature than other approaches. The results also support that the transfer function models can be successfully applied to estimate chlorophyll instead of using monitored water quality data directly. The proposed models present difficulty to estimate extremely high concentrations of chlorophyll; however, they produce estimations comparable to observed chlorophyll concentrations that are less than the extreme outliers in each season. The mean chlorophyll concentration that is produced by the best proposed model is 7.937μg/L and the +/- 95% confidence intervals of the mean are 7.977μg/L and 7.897μg/L after eliminating the extreme outliers (371μg/L) in spring. The mean, 7.937μg/L, is compatible with the mean of the observed concentrations that are less than the extreme outliers, 7.572μg/L. The mean chlorophyll concentration that is produced by the best proposed model is 5.520μg/L, and the +/- 95% confidence intervals (C.I.) of the mean are 5.538μg/L and 5.502μg/L after eliminating the extreme outliers (22μg/L) in fall. The mean, 5.520μg/L, is compatible with the mean of the observed concentrations that are less than the extreme outliers, 6.117μg/L. This dissertation demonstrates the feasibility, reproducibility and applicability of the paradigm in spatiotemporal estuarine water quality parameterization using remote sensing data and field measured water quality data in estuaries. The spatiotemporal estuarine water quality parameterization model can enhance an existing water quality monitoring and assessment program in estuaries that are managed by municipal agencies and local water quality decision makers. The spatiotemporal estuarine water quality parameterization model can be employed as a tool to guide management, since a systematic process of estimating water quality targets is difficult in a complex estuary. Over time, the model provides appropriate, up-to-date guidance. Careful consideration is necessary when applying transfer function models and seasonal spatiotemporal estuarine water quality parameterization models to the different estuaries directly. Although the models appear feasible with significant potential, direct implementation of the model requires a site-specific quality assurance/quality control (QA/QC) check

A Model-Centric Framework for Advanced Operation of Crystallization Processes

Crystallization is the main physical separation process in many chemical industries. It is an old unit operation which can separate solids of high purity from liquids, and is widely applied in the production of food, pharmaceuticals, and fine chemicals. While industries in crystallization operation quite rely on rule-of-thumb techniques to fulfill their requirement, the move towards a scientific- and technological- based approach is becoming more important as it provides a mechanism for driving crystallization processes optimally and in more depth without increasing costs. Optimal operation of industrial crystallizers is a prerequisite these days for achieving the stringent requirements of the consumer-driven manufacturing. To achieve this, a generic and flexible model centric framework is developed for the advanced operation of crystallization processes. The framework deploys the modern software environment combined with the design of a state-of-the-art 1-L crystallization laboratory facility. The emphasis is on developing an economically and practically feasible implementation which can be applied for the optimal operation of various crystallization systems by pharmaceutical industries. The key developments in the framework have occurred in three broad categories: i. Modeling: Using an advanced modeling tool is intended for accurate representation of the behavior of the physical system. This is the cornerstone of any simulation, optimization or model-based control approach. ii. Monitoring: Applying a novel image-based technique for online characterization of the particulate processes. This is a promising method for direct tracking of particle size and size distribution with high adaptability for real-time application iii. Control: Proposing numerous model-based strategies for advanced control of the crystallization system. These strategies enable us to investigate the role of model complexity on real-time control design. Furthermore, the effect of model imperfections, process uncertainty and decision variables on optimal operation of the process can be evaluated. Overall, results from this work presents a robust platform for further research in the area of crystal engineering. Most of the developments described will pave the way for future set of activities being targeted towards extending and adapting advanced modeling, monitoring and control concepts for different crystallization processes

Modelling biomass of the rehabilitation forest around the Buffelsdraai landfill site using remote sensing data, Durban, South Africa.

Masters Degree. University of KwaZulu-Natal, Durban.Forests have important roles in ecosystem service provisions and maintenance of the global carbon cycle hence they are one of the main subjects of the Intergovernmental Panel on Climate Change which recommends strategies to stabilize greenhouse gas emissions. Remote sensing is an advancing science whose data products keep improving spectrally and spatially with time which makes them worth exploitation for broad scientific uses including forest-related studies such as biomass estimations. These are important for understanding of carbon sequestration potential of trees which informs monitoring and forest cover enhancement strategies across various environments. This study investigated the potential of optical data, Landsat 8 Operational Land Imager (OLI) to achieve biomass estimation in a secondary indigenous forest that buffers the Buffelsdraai landfill site. Image processing types used included extraction of spectral reflectance bands, vegetation indices and texture parameters. A Partial Least Squares analysis was performed to determine a significant set of independent variables that could predict aboveground biomass of the Buffelsdraai rehabilitation forest. The findings indicated that the Partial Least Squares models of bands and vegetation indices were rather weak in biomass prediction as only 11.22% and 30.88% biomass variation was explained, respectively. Models inclusive of texture extractions, however, performed much better and demonstrated an improved 77.33% variation explanation of above-ground biomass. Overall, the results indicate that texture parameters derived from Landsat 8 OLI optical data are effective to achieve improved biomass estimation. The development of allometric equations built directly from the species found in the rehabilitation zone and national instilment of environmental responsibility within society for improved local waste management were the major recommendations provided which would assist in the stabilization of greenhouse gas emissions in Buffelsdraai and South Africa

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity