T. L. Grobler

Calibration artefacts in radio interferometry - I. Ghost sources in Westerbork Synthesis Radio Telescope data

This work investigates a particular class of artefacts, or ghost sources, in radio interferometric images. Earlier observations with (and simulations of) the Westerbork Synthesis Radio Telescope (WSRT) suggested that these were due to calibration with incomplete sky models. A theoretical framework is derived that validates this suggestion, and provides predictions of ghost formation in a two-source scenario. The predictions are found to accurately match the result of simulations, and qualitatively reproduce the ghosts previously seen in observational data. The theory also provides explanations for many previously puzzling features of these artefacts (regular geometry, PSF-like sidelobes, seeming independence on model flux), and shows that the observed phenomenon of flux suppression affecting unmodelled sources is due to the same mechanism. We demonstrate that this ghost formation mechanism is a fundamental feature of calibration, and exhibits a particularly strong and localized signature due to array redundancy. To some extent this mechanism will affect all observations (including those with non-redundant arrays), though in most cases the ghosts remain hidden below the noise or masked by other instrumental artefacts. The implications of such errors on future deep observations are discussed.

Using Page's Cumulative Sum Test on MODIS Time Series to Detect Land-Cover Changes

Human settlement expansion is one of the most pervasive forms of land-cover change in South Africa. The use of Pages cumulative sum (CUSUM) test is proposed as a method to detect new settlement developments in areas that were previously covered by natural vegetation using 500-m Moderate Resolution Imaging Spectroradiometer time-series satellite data. The method is a sequential per-pixel change alarm algorithm that can take into account positive detection delay, probability of detection, and false-alarm probability to construct a threshold. Simulated change data were generated to determine a threshold during a preliminary offline optimization phase. After optimization, the method was evaluated on examples of known land-cover change in the Gauteng and Limpopo provinces of South Africa. The experimental results indicated that CUSUM performs better than band differencing in the before-mentioned study areas.

Land Cover Change Detection Using Autocorrelation Analysis on MODIS Time-Series Data: Detection of New Human Settlements in the Gauteng Province of South Africa

Human settlement expansion is one of the most pervasive forms of land cover change in the Gauteng province of South Africa. A method for detecting new settlement developments in areas that are typically covered by natural vegetation using 500 m MODIS time-series satellite data is proposed. The method is a per pixel change alarm that uses the temporal autocorrelation to infer a change index which yields a change or no-change decision after thresholding. Simulated change data was generated and used to determine a threshold during an off-line optimization phase. After optimization the method was evaluated on examples of known land cover change in the study area and experimental results indicate a 92% change detection accuracy with a 15% false alarm rate. The method shows good performance when compared to a traditional NDVI differencing method that achieved a 75% change detection accuracy with a 24% false alarm rate for the same study area.

Land-Cover Separability Analysis of MODIS Time-Series Data Using a Combined Simple Harmonic Oscillator and a Mean Reverting Stochastic Process

It is proposed that the time series extracted from moderate resolution imaging spectroradiometer satellite data be modeled as a simple harmonic oscillator with additive colored noise. The colored noise is modeled with an Ornstein-Uhlenbeck process. The Fourier transform and maximum-likelihood parameter estimation are used to estimate the harmonic and noise parameters of the colored simple harmonic oscillator. Two case studies in South Africa show that reliable class differentiation can be obtained between natural vegetation and settlement land cover types, when using the parameters of the colored simple harmonic oscillator as input features to a classifier. The two case studies were conducted in the Gauteng and Limpopo provinces of South Africa. In the case of the Gauteng case study, we obtained an average for single-band classification, while standard harmonic features only achieved an average . In conclusion, the results obtained from the colored simple harmonic oscillator approach outperformed standard harmonic features and the minimum distance classifier.

Land Cover Change Detection Using the Internal Covariance Matrix of the Extended Kalman Filter Over Multiple Spectral Bands

In this paper, the internal operations of an Extended Kalman Filter is investigated to observe if information can be derived to detect land cover change in a MODerate-resolution Imaging Spectroradiometer (MODIS) time series. The concept is based on the internal covariance matrix used by the Extended Kalman Filter, which adjusts the internal state of the filter for any changes occurring in the time series. The Extended Kalman Filter expands the internal covariance matrix if a significant change in reflectance value is observed, followed by adapting the state parameters to compensate for this change. The analysis shows that a change detection accuracy above 90% can be attained when evaluating the elements within the internal covariance matrix to detect new human settlements, with a corresponding false alarm rate below 6%.

Systematic Luby Transform codes as incremental redundancy scheme

Systematic Luby Transform (fountain) codes are investigated as a possible incremental redundancy scheme for EDGE. The convolutional incremental redundancy scheme currently used by EDGE is replaced by the fountain approach. The results of the simulations performed for each incremental redundancy scheme show that the fountain approach outperforms the convolutional approach on the second retransmission when implemented on the EDGE platform. The results also indicate that if the packet sizes used by a specific platform is large enough the fountain approach will always outperform the convolutional approach.

Meta-Optimization of the Extended Kalman Filter’s Parameters Through the Use of the Bias Variance Equilibrium Point Criterion

The extraction of information on land cover classes using unsupervised methods has always been of relevance to the remote sensing community. In this paper, a novel criterion is proposed, which extracts the inherent information in an unsupervised fashion from a time series. The criterion is used to fit a parametric model to a time series, derive the corresponding covariance matrices of the parameters for the model, and estimate the additive noise on the time series. The proposed criterion uses both spatial and temporal information when estimating the covariance matrices and can be extended to incorporate spectral information. The algorithm used to estimate the parameters for the model is the extended Kalman filter (EKF). An unsupervised search algorithm, specifically designed for this criterion, is proposed in conjunction with the criterion that is used to rapidly and efficiently estimate the variables. The search algorithm attempts to satisfy the criterion by employing density adaptation to the current candidate system. The application in this paper is the use of an EKF to model Moderate Resolution Imaging Spectroradiometer time series with a triply modulated cosine function as the underlying model. The results show that the criterion improved the fit of the triply modulated cosine function by an order of magnitude on the time series over all seven spectral bands when compared with the other methods. The state space variables derived from the EKF are then used for both land cover classification and land cover change detection. The method was evaluated in the Gauteng province of South Africa where it was found to significantly improve on land cover classification and change detection accuracies when compared with other methods.

A search algorithm to meta-optimize the parameters for an extended KALMAN FILTER TO IMPROVE CLASSIFICATION ON HYPER-TEMPORAL IMAGES

In this paper the Bias Variance Search Algorithm is proposed as an algorithm to optimize a candidate set of initial parameters for an Extended Kalman filter (EKF). The search algorithm operates on a Bias Variance Equilibrium Point criterion to determine how to set the initial parameters. The candidate set is then used by the EKF to estimate state parameters to fit a triply modulated cosine function to time series of the first two spectral bands of the MODerate-resolution Imaging Spectroradiometer (MODIS) land product. The state parameters are then used for land cover classification. The results of the search algorithm was tested on classifying land cover in the Limpopo province, South Africa. An improvement in land cover classification was observed when the method was compared to a robust regression method.

Minimum error land cover separability analysis and classification of MODIS time series data

Three minimum-error land cover classifiers are compared on coarse resolution MODerate-resolution Imaging Spectroradiometer (MODIS) surface reflectance data for discerning between vegetation and settlement classes. It is shown that good class separability can be achieved using only the seasonal component of Normalized Difference Vegetation Index (NDVI) data, or the mean component of several other MODIS land bands. It is also shown why particular classifiers fail in certain spectral bands. Finally it is shown that after NDVI, band 2 has the highest separability of all the MODIS land bands, and band 5 has the lowest separability.

An Inductive Approach to Simulating Multispectral MODIS Surface Reflectance Time Series

In this letter, a first-order Moderate Resolution Imaging Spectroradiometer time-series simulator, which uses a colored simple harmonic oscillator, is proposed. The simulated data can be used to augment data sets so that data intensive classification and change detection algorithms can be applied without enlarging the available ground truth data sets. The simulators validity is tested by simulating data sets of natural vegetation and human settlement areas and comparing it with the ground truth data in Gauteng province located in South Africa. The difference found between the real and simulated data sets, which is reported in the experiments, is negligent. The simulated and real-world data sets are compared by using a wide selection of class and pixel metrics. In particular, the average temporal Hellinger distance between the real and simulated data sets is 0.2364 and 0.2269 for the vegetation and settlement classes, respectively, whereas the average parameter Hellinger distance is 0.1835 and 0.2554, respectively.