Wavelets for the Analysis and Compression of Power System Disturbances

Wavelets introduce new classes of basis functions for time-frequency signal analysis and have properties particularly suited to the transient components and discontinuities evident in power system disturbances. Wavelet analysis involves representing signals in terms of simpler, fixed building blocks at different scales and positions. This paper examines the analysis and subsequent compression properties of the discrete wavelet and wavelet packet transforms and evaluates both transforms using an actual power system disturbance from a digital fault recorder. The paper presents comparative compression results using the wavelet and discrete cosine transforms and examines the application of wavelet compression in power monitoring to mitigate against data communications overheads.

Watermarking for Multimedia Security using Complex Wavelets

This paper investigates the application of complex wavelet transforms to the field of digital data hiding. Complex wavelets offer improved directional selectivity and shift invariance over their discretely sampled counterparts allowing for better adaptation of watermark distortions to the host media. Two methods of deriving visual models for the watermarking system are adapted to the complex wavelet transforms and their performances are compared. To produce improved capacity a spread transform embedding algorithm is devised, this combines the robustness of spread spectrum methods with the high capacity of quantization based methods. Using established information theoretic methods, limits of watermark capacity are derived that demonstrate the superiority of complex wavelets over discretely sampled wavelets. Finally results for the algorithm against commonly used attacks demonstrate its robustness and the improved performance offered by complex wavelet transforms.

Fast Retinal Vessel Detection and Measurement Using Wavelets and Edge Location Refinement

The relationship between changes in retinal vessel morphology and the onset and progression of diseases such as diabetes, hypertension and retinopathy of prematurity (ROP) has been the subject of several large scale clinical studies. However, the difficulty of quantifying changes in retinal vessels in a sufficiently fast, accurate and repeatable manner has restricted the application of the insights gleaned from these studies to clinical practice. This paper presents a novel algorithm for the efficient detection and measurement of retinal vessels, which is general enough that it can be applied to both low and high resolution fundus photographs and fluorescein angiograms upon the adjustment of only a few intuitive parameters. Firstly, we describe the simple vessel segmentation strategy, formulated in the language of wavelets, that is used for fast vessel detection. When validated using a publicly available database of retinal images, this segmentation achieves a true positive rate of 70.27%, false positive rate of 2.83%, and accuracy score of 0.9371. Vessel edges are then more precisely localised using image profiles computed perpendicularly across a spline fit of each detected vessel centreline, so that both local and global changes in vessel diameter can be readily quantified. Using a second image database, we show that the diameters output by our algorithm display good agreement with the manual measurements made by three independent observers. We conclude that the improved speed and generality offered by our algorithm are achieved without sacrificing accuracy. The algorithm is implemented in MATLAB along with a graphical user interface, and we have made the source code freely available.