Polynomial Functions and the Riesz Interpolation Property

Building on a proof by D. Handelman of a generalisation of an example due to L. Fuchs, we show that the space of real-valued polynomials on a non-empty set X of reals has the Riesz Interpolation Property if and only if X is bounded.

Multi-standard sub-pixel interpolation architecture for video motion estimation

A new domain-specific reconfigurable sub-pixel interpolation architecture for multi-standard video Motion Estimation (ME) is presented. The mixed use of parallel and serial-input FIR filters achieves high throughput rate and efficient silicon utilisation. Flexibility has been achieved by using a multiplexed reconfigurable data-path controlled by a selection signal. Silicon design studies show that this can be implemented using 34.8K gates with area and performance that compares very favourably with existing fixed solutions based solely on the H.264 standard. ©2008 IEEE.

Design methodology for low power and arametric robustness through output-quality modulation:Application to color-interpolation filtering

Power dissipation and robustness to process variation have conflicting design requirements. Scaling of voltage is associated with larger variations, while Vdd upscaling or transistor upsizing for parametric-delay variation tolerance can be detrimental for power dissipation. However, for a class of signal-processing systems, effective tradeoff can be achieved between Vdd scaling, variation tolerance, and output quality. In this paper, we develop a novel low-power variation-tolerant algorithm/architecture for color interpolation that allows a graceful degradation in the peak-signal-to-noise ratio (PSNR) under aggressive voltage scaling as well as extreme process variations. This feature is achieved by exploiting the fact that all computations used in interpolating the pixel values do not equally contribute to PSNR improvement. In the presence of Vdd scaling and process variations, the architecture ensures that only the less important computations are affected by delay failures. We also propose a different sliding-window size than the conventional one to improve interpolation performance by a factor of two with negligible overhead. Simulation results show that, even at a scaled voltage of 77% of nominal value, our design provides reasonable image PSNR with 40% power savings. © 2006 IEEE.

Design methodology to trade off power, output quality and error resiliency: Application to color interpolation filtering

Power dissipation and tolerance to process variations pose conflicting design requirements. Scaling of voltage is associated with larger variations, while Vdd upscaling or transistor up-sizing for process tolerance can be detrimental for power dissipation. However, for certain signal processing systems such as those used in color image processing, we noted that effective trade-offs can be achieved between Vdd scaling, process tolerance and "output quality". In this paper we demonstrate how these tradeoffs can be effectively utilized in the development of novel low-power variation tolerant architectures for color interpolation. The proposed architecture supports a graceful degradation in the PSNR (Peak Signal to Noise Ratio) under aggressive voltage scaling as well as extreme process variations in. sub-70nm technologies. This is achieved by exploiting the fact that some computations are more important and contribute more to the PSNR improvement compared to the others. The computations are mapped to the hardware in such a way that only the less important computations are affected by Vdd-scaling and process variations. Simulation results show that even at a scaled voltage of 60% of nominal Vdd value, our design provides reasonable image PSNR with 69% power savings.

Deriving meteorological variables across Africa for the study and control of vector-borne disease:a comparison of remote sensing and spatial interpolation of climate

This paper presents the results of an investigation into the utility of remote sensing (RS) using meteorological satellites sensors and spatial interpolation (SI) of data from meteorological stations, for the prediction of spatial variation in monthly climate across continental Africa in 1990. Information from the Advanced Very High Resolution Radiometer (AVHRR) of the National Oceanic and Atmospheric Administration's (NOAA) polar-orbiting meteorological satellites was used to estimate land surface temperature (LST) and atmospheric moisture. Cold cloud duration (CCD) data derived from the High Resolution Radiometer (HRR) onboard the European Meteorological Satellite programme's (EUMETSAT) Meteosat satellite series were also used as a RS proxy measurement of rainfall. Temperature, atmospheric moisture and rainfall surfaces were independently derived from SI of measurements from the World Meteorological Organization (WMO) member stations of Africa. These meteorological station data were then used to test the accuracy of each methodology, so that the appropriateness of the two techniques for epidemiological research could be compared. SI was a more accurate predictor of temperature, whereas RS provided a better surrogate for rainfall; both were equally accurate at predicting atmospheric moisture. The implications of these results for mapping short and long-term climate change and hence their potential for the study anti control of disease vectors are considered. Taking into account logistic and analytical problems, there were no clear conclusions regarding the optimality of either technique, but there was considerable potential for synergy.

Wind resource mapping using landscape roughness and spatial interpolation methods

Energy saving, reduction of greenhouse gasses and increased use of renewables are key policies to achieve the European 2020 targets. In particular, distributed renewable energy sources, integrated with spatial planning, require novel methods to optimise supply and demand. In contrast with large scale wind turbines, small and medium wind turbines (SMWTs) have a less extensive impact on the use of space and the power system, nevertheless, a significant spatial footprint is still present and the need for good spatial planning is a necessity. To optimise the location of SMWTs, detailed knowledge of the spatial distribution of the average wind speed is essential, hence, in this article, wind measurements and roughness maps were used to create a reliable annual mean wind speed map of Flanders at 10 m above the Earth’s surface. Via roughness transformation, the surface wind speed measurements were converted into meso- and macroscale wind data. The data were further processed by using seven different spatial interpolation methods in order to develop regional wind resource maps. Based on statistical analysis, it was found that the transformation into mesoscale wind, in combination with Simple Kriging, was the most adequate method to create reliable maps for decision-making on optimal production sites for SMWTs in Flanders.

Compression Efficiency Analysis of Wyner-Ziv Video Coding with Motion Compensated Side Information Interpolation

The Wyner-Ziv video coding (WZVC) rate distortion performance is highly dependent on the quality of the side information, an estimation of the original frame, created at the decoder. This paper, characterizes the WZVC efficiency when motion compensated frame interpolation (MCFI) techniques are used to generate the side information, a difficult problem in WZVC especially because the decoder only has available some reference decoded frames. The proposed WZVC compression efficiency rate model relates the power spectral of the estimation error to the accuracy of the MCFI motion field. Then, some interesting conclusions may be derived related to the impact of the motion field smoothness and the correlation to the true motion trajectories on the compression performance.

Evaluation of the reconstruction limits of a frequency-independent crosshole georadar waveform inversion scheme in the presence of dispersion

Waveform tomographic imaging of crosshole georadar data is a powerful method to investigate the shallow subsurface because of its ability to provide images of pertinent petrophysical parameters with extremely high spatial resolution. All current crosshole georadar waveform inversion strategies are based on the assumption of frequency-independent electromagnetic constitutive parameters. However, in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behavior. In this paper, we evaluate synthetically the reconstruction limits of a recently published crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. Our results indicate that, when combined with a source wavelet estimation procedure that provides a means of partially accounting for the frequency-dependent effects through an "effective" wavelet, the inversion algorithm performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

Area and Volume Calculation of Necrotic Tissue regions of heart using Interpolation

This paper attempts to develop an improved tool, which would read two dimensional(2D) cardiac MRI images and compute areas and volume of the scar tissue. Here the computation would be done on the cardiac MR images to quantify the extent of damage inflicted by myocardial infarction on the cardiac muscle (myocardium) using Interpolation

Quasi-Interpolation von Funktionen und Anwendungen auf Potentialprobleme

Ausgangspunkt der Dissertation ist ein von V. Maz'ya entwickeltes Verfahren, eine gegebene Funktion f : Rn ! R durch eine Linearkombination fh radialer glatter exponentiell fallender Basisfunktionen zu approximieren, die im Gegensatz zu den Splines lediglich eine näherungsweise Zerlegung der Eins bilden und somit ein für h ! 0 nicht konvergentes Verfahren definieren. Dieses Verfahren wurde unter dem Namen Approximate Approximations bekannt. Es zeigt sich jedoch, dass diese fehlende Konvergenz für die Praxis nicht relevant ist, da der Fehler zwischen f und der Approximation fh über gewisse Parameter unterhalb der Maschinengenauigkeit heutiger Rechner eingestellt werden kann. Darüber hinaus besitzt das Verfahren große Vorteile bei der numerischen Lösung von Cauchy-Problemen der Form Lu = f mit einem geeigneten linearen partiellen Differentialoperator L im Rn. Approximiert man die rechte Seite f durch fh, so lassen sich in vielen Fällen explizite Formeln für die entsprechenden approximativen Volumenpotentiale uh angeben, die nur noch eine eindimensionale Integration (z.B. die Errorfunktion) enthalten. Zur numerischen Lösung von Randwertproblemen ist das von Maz'ya entwickelte Verfahren bisher noch nicht genutzt worden, mit Ausnahme heuristischer bzw. experimenteller Betrachtungen zur sogenannten Randpunktmethode. Hier setzt die Dissertation ein. Auf der Grundlage radialer Basisfunktionen wird ein neues Approximationsverfahren entwickelt, welches die Vorzüge der von Maz'ya für Cauchy-Probleme entwickelten Methode auf die numerische Lösung von Randwertproblemen überträgt. Dabei werden stellvertretend das innere Dirichlet-Problem für die Laplace-Gleichung und für die Stokes-Gleichungen im R2 behandelt, wobei für jeden der einzelnen Approximationsschritte Konvergenzuntersuchungen durchgeführt und Fehlerabschätzungen angegeben werden.

Construction of fractal interpolation surfaces on rectangular grids

We present a general method of generating continuous fractal interpolation surfaces by iterated function systems on an arbitrary data set over rectangular grids and estimate their Box-counting dimension.