Colour image coding with wavelets and matching pursuit

This thesis considers sparse approximation of still images as the basis of a lossy compression system. The Matching Pursuit (MP) algorithm is presented as a method particularly suited for application in lossy scalable image coding. Its multichannel extension, capable of exploiting inter-channel correlations, is found to be an efficient way to represent colour data in RGB colour space. Known problems with MP, high computational complexity of encoding and dictionary design, are tackled by finding an appropriate partitioning of an image. The idea of performing MP in the spatio-frequency domain after transform such as Discrete Wavelet Transform (DWT) is explored. The main challenge, though, is to encode the image representation obtained after MP into a bit-stream. Novel approaches for encoding the atomic decomposition of a signal and colour amplitudes quantisation are proposed and evaluated. The image codec that has been built is capable of competing with scalable coders such as JPEG 2000 and SPIHT in terms of compression ratio

Quantifying pervasive authentication: the case of the Hancke-Kuhn protocol

As mobile devices pervade physical space, the familiar authentication patterns are becoming insufficient: besides entity authentication, many applications require, e.g., location authentication. Many interesting protocols have been proposed and implemented to provide such strengthened forms of authentication, but there are very few proofs that such protocols satisfy the required security properties. The logical formalisms, devised for reasoning about security protocols on standard computer networks, turn out to be difficult to adapt for reasoning about hybrid protocols, used in pervasive and heterogenous networks. We refine the Dolev-Yao-style algebraic method for protocol analysis by a probabilistic model of guessing, needed to analyze protocols that mix weak cryptography with physical properties of nonstandard communication channels. Applying this model, we provide a precise security proof for a proximity authentication protocol, due to Hancke and Kuhn, that uses a subtle form of probabilistic reasoning to achieve its goals.Comment: 31 pages, 2 figures; short version of this paper appeared in the Proceedings of MFPS 201

The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes

We review the bootstrap method for constructing six- and seven-particle amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory, by exploiting their analytic structure. We focus on two recently discovered properties which greatly simplify this construction at symbol and function level, respectively: the extended Steinmann relations, or equivalently cluster adjacency, and the coaction principle. We then demonstrate their power in determining the six-particle amplitude through six and seven loops in the NMHV and MHV sectors respectively, as well as the symbol of the NMHV seven-particle amplitude to four loops.Comment: 36 pages, 4 figures, 5 tables, 1 ancillary file. Contribution to the proceedings of the Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019), 31 August - 25 September 2019, Corfu, Greec

A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4,7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the $7 \parallel 6$ collinear limit. This unique symbol is both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the three-loop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n>6.Comment: 30 pages, 3 ancillary files, v3: minor corrections, including a typo in (33

Future spatial audio : Subjective evaluation of 3D surround systems

Current surround systems are being developed to include height channels to provide the listener with a 3D listening experience. It is not well understood the impact the height channels will have on the listening experience and aspects associated with multichannel reproduction like localisation and envelopment or if there are any new subjective attributes concerned with 3D surround systems. Therefore in this research subjective factors like localisation and envelopment were investigated and then descriptive analysis was used. In terms of localisation it was found that for sources panned in the median plane localisation accuracy was not improved with higher order ambisonics. However for sources in the frontal plane higher order ambisonics improves localisation accuracy for elevated sound sources. It was also found that for a simulation of a number of 2D and 3D surround systems, using a decorrelated noise signal to simulate a diffuse soundfield, there was no improvement in envelopment with the addition of height. On the other hand height was found to improve the perception of envelopment with the use of 3D recorded sound scenes, although for an applause sample which had similar properties to that of the decorrelated noise sample there was no significant difference between 2D and 3D systems. Five attribute scales emerged from the descriptive analysis of which it was found that there were significant differences between 2D and 3D systems using the attribute scale size for both ambisonics and VBAP rendered systems. Also 3D higher order ambisonics significantly enhances the perception of presence. A final principal component analysis found that there were 2 factors which characterised the ambisonic rendered systems and 3 factors which characterised the VBAP rendered sound scenes. This suggests that the derived scales need to be used with a wider number of sound scenes in order to fully validate them