Nicholas Kolokotronis

Wavelet-based medical image compression

Abstract In view of the increasingly important role played by digital medical imaging in modern health care and the consequent blow up in the amount of image data that have to be economically stored and/or transmitted, the need for the development of image compression systems that combine high compression performance and preservation of critical information is ever growing. A powerful compression scheme that is based on the state-of-the-art in wavelet-based compression is presented in this paper. Compression is achieved via efficient encoding of wavelet zerotrees (with the embedded zerotree wavelet (EZW) algorithm) and subsequent entropy coding. The performance of the basic version of EZW is improved upon by a simple, yet effective, way of a more accurate estimation of the centroids of the quantization intervals, at a negligible cost in side information. Regarding the entropy coding stage, a novel RLE-based coder is proposed that proves to be much simpler and faster yet only slightly worse than context-dependent adaptive arithmetic coding. A useful and flexible compromise between the need for high compression and the requirement for preservation of selected regions of interest is provided through two intelligent, yet simple, ways of achieving the so-called selective compression. The use of the lifting scheme in achieving compression that is guaranteed to be lossless in the presence of numerical inaccuracies is being investigated with interesting preliminary results. Experimental results are presented that verify the superiority of our scheme over conventional block transform coding techniques (JPEG) with respect to both objective and subjective criteria. The high potential of our scheme for progressive transmission, where the regions of interest are given the highest priority, is also demonstrated.

On the linear complexity of nonlinearly filtered PN-sequences

Binary sequences of period 2/sup n/-1 generated by a linear feedback shift register (LFSR) whose stages are filtered by a nonlinear function, f, are studied. New iterative formulas are derived for the calculation of the linear complexity of the output sequences. It is shown that these tools provide an efficient mechanism for controlling the linear complexity of the nonlinearly filtered maximal-length sequences.

Properties of the Error Linear Complexity Spectrum

This paper studies the error linear complexity spectrum of binary sequences with period 2n. A precise categorization of those sequences having two distinct critical points in their spectra, as well as an enumeration of these sequences, is given. An upper bound on the maximum number of distinct critical points that the spectrum of a sequence can have is proved, and a construction which yields a lower bound on this number is given. In the process simpler proofs of some known results on the linear complexity and k-error linear complexity of sequences with period 2n are provided.

On the Nonlinear Complexity and Lempel–Ziv Complexity of Finite Length Sequences

The nonlinear complexity of binary sequences and its connections with Lempel-Ziv complexity is studied in this paper. A new recursive algorithm is presented, which produces the minimal nonlinear feedback shift register of a given binary sequence. Moreover, it is shown that the eigenvalue profile of a sequence uniquely determines its nonlinear complexity profile, thus establishing a connection between Lempel-Ziv complexity and nonlinear complexity. Furthermore, a lower bound for the Lempel-Ziv compression ratio of a given sequence is proved that depends on its nonlinear complexity.

On the quadratic span of binary sequences

The problem of finding the shortest feedback shift register, with quadratic feedback function that generates a given finite-length sequence is considered. An algorithm for the determination of the quadratic span and the feedback function, which takes advantage of the special block structure of the associated system of linear equations, is proposed.

Minimum linear span approximation of binary sequences

The determination of the minimum linear span sequence that differs from a given binary sequence, of period N=2/sup n/-1, by at most one digit is discussed and three methods are presented: the sequential divisions method, the congruential equations method, and the phase synchronization method. High-level algorithm organizations are provided. Finally, guidelines on sequence characterization and design via the notion of robustness are given.

An integrated approach for securing electronic transactions over the Web

The decentralised nature of Web‐based information systems demands a careful evaluation of the pantheon of security issues in order to avoid the potential occurrence of business risks that could not be easily mitigated. Understanding that information security is not merely a technical solution implemented at each endpoint of the inter‐organizational application, this paper describes an integrated approach based on a rigorous, multi‐level and multi‐dimensional model. Having as a starting point the overall business goals and objectives, the model drives the development of a strategy from the lower levels of securing data in storage and transition to the higher levels of business processes. Its use and applicability is demonstrated over “Billing Mall” – a system for electronic bill presentation and payment.

Physical layer security via secret trellis pruning

Constructions of secure channel encoders based on trellis pruning are considered in this paper. The key defines how pruning is applied on the trellis of a mother convolutional code; this results into a secret pruned trellis that legitimate users are using to perform decoding, in contrast to the eavesdroppers that employ the full mother trellis diagram. We focus on two special forms of the pruning function, and in each case we compute the expected weight enumerating function of the secret pruned code. The theoretical analysis ensures that the legitimate users achieve superior performance, in terms of word and bit error rate, than the eavesdroppers, which depends on the pruning rate. We also derive design guidelines on properties that mother encoders must have to fully exploit the proposed scheme. Simulation results also show the potential of catastrophic encoders for PHY security and yet the ability of the legitimate users to communicate reliably.

Lower bounds on sequence complexity via generalised vandermonde determinants

Binary sequences generated by nonlinearly filtering maximal length sequences with period 2n–1 are studied in this paper. We focus on the particular class of equidistant filters and provide improved lower bounds on the linear complexity of the filtered sequences. This is achieved by first considering and proving properties of generalised Vandermonde determinants. Furthermore, it is shown that the methodology developed can be used for studying properties of any nonlinear filter.

Best Affine and Quadratic Approximations of Particular Classes of Boolean Functions

In this paper, we consider the problem of computing best low-order approximations of Boolean functions; we focus on the best quadratic approximations of a subclass of cubic functions with arbitrary number of variables and we provide formulas for their efficient calculation. Our methodology is developed upon properties of the best affine approximations of quadratic functions, for which formulas for their direct computation (not by means of the Walsh-Hadamard transform) are given. We determine the cubic functions in the above subclass that achieve the maximum second-order nonlinearity, thus yielding a lower bound for the covering radius of the second order Reed-Muller code \ssr RM(2, n) in \ssr RM(3, n). Simple extensions of these results to some special cases of higher degree functions, are seen to hold. Furthermore, a preliminary analysis of well-known constructions for bent functions, in terms of their second-order nonlinearity, is performed that indicates potential weaknesses if construction parameters are not properly chosen.