A coding approach to the multicast stream authentication problem

We study the multicast stream authentication problem when an opponent can drop, reorder and introduce data packets into the communication channel. In such a model, packet overhead and computing efficiency are two parameters to be taken into account when designing a multicast stream protocol. In this paper, we propose to use two families of erasure codes to deal with this problem, namely, rateless codes and maximum distance separable codes. Our constructions will have the following advantages. First, our packet overhead will be small. Second, the number of signature verifications to be performed at the receiver is O(1). Third, every receiver will be able to recover all the original data packets emitted by the sender despite losses and injection occurred during the transmission of information.

An hybrid approach for efficient multicast stream authentication over unsecured channels

We study the multicast stream authentication problem when an opponent can drop, reorder and inject data packets into the communication channel. In this context, bandwidth limitation and fast authentication are the core concerns. Therefore any authentication scheme is to reduce as much as possible the packet overhead and the time spent at the receiver to check the authenticity of collected elements. Recently, Tartary and Wang developed a provably secure protocol with small packet overhead and a reduced number of signature verifications to be performed at the receiver. In this paper, we propose an hybrid scheme based on Tartary and Wang’s approach and Merkle hash trees. Our construction will exhibit a smaller overhead and a much faster processing at the receiver making it even more suitable for multicast than the earlier approach. As Tartary and Wang’s protocol, our construction is provably secure and allows the total recovery of the data stream despite erasures and injections occurred during transmission.

Robust network reconstruction in polynomial time

This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work [1] on robust reconstruction to provide a practical implementation with polynomial computational complexity. Following the same experimental protocol, the algorithm obtains a set of structurally-related candidate solutions spanning every level of sparsity. We prove the existence of a magnitude bound on the noise, which if satisfied, guarantees that one of these structures is the correct solution. A problem-specific model-selection procedure then selects a single solution from this set and provides a measure of confidence in that solution. Extensive simulations quantify the expected performance for different levels of noise and show that significantly more noise can be tolerated in comparison to the original method. © 2012 IEEE.

A comparison of techniques for the reconstruction of leaf surfaces from scanned data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

B-Spline potential function for maximum a-posteriori image reconstruction in fluorescence microscopy

An iterative image reconstruction technique employing B-Spline potential function in a Bayesian framework is proposed for fluorescence microscopy images. B-splines are piecewise polynomials with smooth transition, compact support and are the shortest polynomial splines. Incorporation of the B-spline potential function in the maximum-a-posteriori reconstruction technique resulted in improved contrast, enhanced resolution and substantial background reduction. The proposed technique is validated on simulated data as well as on the images acquired from fluorescence microscopes (widefield, confocal laser scanning fluorescence and super-resolution 4Pi microscopy). A comparative study of the proposed technique with the state-of-art maximum likelihood (ML) and maximum-a-posteriori (MAP) with quadratic potential function shows its superiority over the others. B-Spline MAP technique can find applications in several imaging modalities of fluorescence microscopy like selective plane illumination microscopy, localization microscopy and STED. (C) 2015 Author(s).

Reconstruction of arbitrary biochemical reaction networks: A compressive sensing approach

Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model biochemical reaction networks. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data quite difficult. In this paper, we present a network reconstruction algorithm that can deal with ODE model descriptions containing polynomial and rational functions. Rather than identifying the parameters of linear or nonlinear ODEs characterised by pre-defined equation structures, our methodology allows us to determine the nonlinear ODEs structure together with their associated parameters. To solve the network reconstruction problem, we cast it as a compressive sensing (CS) problem and use sparse Bayesian learning (SBL) algorithms as a computationally efficient and robust way to obtain its solution. © 2012 IEEE.

Reconstruction of geomagnetic activity and near-Earth interplanetary conditions over the past 167 yr – Part 2: A new reconstruction of the interplanetary magnetic field

We present a new reconstruction of the interplanetary magnetic field (IMF, B) for 1846–2012 with a full analysis of errors, based on the homogeneously constructed IDV(1d)composite of geomagnetic activity presented in Part 1 (Lockwood et al., 2013a). Analysis of the dependence of the commonly used geomagnetic indices on solar wind parameters is presented which helps explain why annual means of interdiurnal range data, such as the new composite, depend only on the IMF with only a very weak influence of the solar wind flow speed. The best results are obtained using a polynomial (rather than a linear) fit of the form B = χ · (IDV(1d) − β)α with best-fit coefficients χ = 3.469, β = 1.393 nT, and α = 0.420. The results are contrasted with the reconstruction of the IMF since 1835 by Svalgaard and Cliver (2010).

Application of MFBD Algorithms to Image Reconstruction Under Anisoplanatic Conditions

All optical systems that operate in or through the atmosphere suffer from turbulence induced image blur. Both military and civilian surveillance, gun-sighting, and target identification systems are interested in terrestrial imaging over very long horizontal paths, but atmospheric turbulence can blur the resulting images beyond usefulness. My dissertation explores the performance of a multi-frame-blind-deconvolution technique applied under anisoplanatic conditions for both Gaussian and Poisson noise model assumptions. The technique is evaluated for use in reconstructing images of scenes corrupted by turbulence in long horizontal-path imaging scenarios and compared to other speckle imaging techniques. Performance is evaluated via the reconstruction of a common object from three sets of simulated turbulence degraded imagery representing low, moderate and severe turbulence conditions. Each set consisted of 1000 simulated, turbulence degraded images. The MSE performance of the estimator is evaluated as a function of the number of images, and the number of Zernike polynomial terms used to characterize the point spread function. I will compare the mean-square-error (MSE) performance of speckle imaging methods and a maximum-likelihood, multi-frame blind deconvolution (MFBD) method applied to long-path horizontal imaging scenarios. Both methods are used to reconstruct a scene from simulated imagery featuring anisoplanatic turbulence induced aberrations. This comparison is performed over three sets of 1000 simulated images each for low, moderate and severe turbulence-induced image degradation. The comparison shows that speckle-imaging techniques reduce the MSE 46 percent, 42 percent and 47 percent on average for low, moderate, and severe cases, respectively using 15 input frames under daytime conditions and moderate frame rates. Similarly, the MFBD method provides, 40 percent, 29 percent, and 36 percent improvements in MSE on average under the same conditions. The comparison is repeated under low light conditions (less than 100 photons per pixel) where improvements of 39 percent, 29 percent and 27 percent are available using speckle imaging methods and 25 input frames and 38 percent, 34 percent and 33 percent respectively for the MFBD method and 150 input frames. The MFBD estimator is applied to three sets of field data and the results presented. Finally, a combined Bispectrum-MFBD Hybrid estimator is proposed and investigated. This technique consistently provides a lower MSE and smaller variance in the estimate under all three simulated turbulence conditions.

A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established.

Towards automatic tree crown detection and delineation in spectral feature space using PCNN and morphological reconstruction

The application of object-based approaches to the problem of extracting vegetation information from images requires accurate delineation of individual tree crowns. This paper presents an automated method for individual tree crown detection and delineation by applying a simplified PCNN model in spectral feature space followed by post-processing using morphological reconstruction. The algorithm was tested on high resolution multi-spectral aerial images and the results are compared with two existing image segmentation algorithms. The results demonstrate that our algorithm outperforms the other two solutions with the average accuracy of 81.8%.

Fast reconstruction of aerodynamic shapes using evolutionary algorithms and virtual Nash strategies in a CFD design environment

This paper compares the performances of two different optimisation techniques for solving inverse problems; the first one deals with the Hierarchical Asynchronous Parallel Evolutionary Algorithms software (HAPEA) and the second is implemented with a game strategy named Nash-EA. The HAPEA software is based on a hierarchical topology and asynchronous parallel computation. The Nash-EA methodology is introduced as a distributed virtual game and consists of splitting the wing design variables - aerofoil sections - supervised by players optimising their own strategy. The HAPEA and Nash-EA software methodologies are applied to a single objective aerodynamic ONERA M6 wing reconstruction. Numerical results from the two approaches are compared in terms of the quality of model and computational expense and demonstrate the superiority of the distributed Nash-EA methodology in a parallel environment for a similar design quality.

3-D reconstruction of an ancient Egyptian mummy using X-ray computer tomography

Computer tomography has been used to image and reconstruct in 3-D an Egyptian mummy from the collection of the British Museum. This study of Tjentmutengebtiu, a priestess from the 22nd dynasty (945-715 BC) revealed invaluable information of a scientific, Egyptological and palaeopathological nature without mutilation and destruction of the painted cartonnage case or linen wrappings. Precise details on the removal of the brain through the nasal cavity and the viscera from the abdominal cavity were obtained. The nature and composition of the false eyes were investigated. The detailed analysis of the teeth provided a much closer approximation of age at death. The identification of materials used for the various amulets including that of the figures placed in the viscera was graphically demonstrated using this technique.