Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast

Ultrasound Tomography has seen a revival of interest in the past decade, especially for breast imaging, due to improvements in both ultrasound and computing hardware. In particular, three-dimensional ultrasound tomography, a fully tomographic method in which the medium to be imaged is surrounded by ultrasound transducers, has become feasible. In this paper, a comprehensive derivation and study of a robust framework for large-scale bent-ray ultrasound tomography in 3D for a hemispherical detector array is presented. Two ray-tracing approaches are derived and compared. More significantly, the problem of linking the rays between emitters and receivers, which is challenging in 3D due to the high number of degrees of freedom for the trajectory of rays, is analysed both as a minimisation and as a root-finding problem. The ray-linking problem is parameterised for a convex detection surface and three robust, accurate, and efficient ray-linking algorithms are formulated and demonstrated. To stabilise these methods, novel adaptive-smoothing approaches are proposed that control the conditioning of the update matrices to ensure accurate linking. The nonlinear UST problem of estimating the sound speed was recast as a series of linearised subproblems, each solved using the above algorithms and within a steepest descent scheme. The whole imaging algorithm was demonstrated to be robust and accurate on realistic data simulated using a full-wave acoustic model and an anatomical breast phantom, and incorporating the errors due to time-of-flight picking that would be present with measured data. This method can used to provide a low-artefact, quantitatively accurate, 3D sound speed maps. In addition to being useful in their own right, such 3D sound speed maps can be used to initialise full-wave inversion methods, or as an input to photoacoustic tomography reconstructions

Projected Nesterov’s Proximal-Gradient Signal Recovery from Compressive Poisson Measurements

We develop a projected Nesterov’s proximalgradient (PNPG) scheme for reconstructing sparse signals from compressive Poisson-distributed measurements with the mean signal intensity that follows an affine model with known intercept. The objective function to be minimized is a sum of convex data fidelity (negative log-likelihood (NLL)) and regularization terms. We apply sparse signal regularization where the signal belongs to a nonempty closed convex set within the domain of the NLL and signal sparsity is imposed using total-variation (TV) penalty. We present analytical upper bounds on the regularization tuning constant. The proposed PNPG method employs projected Nesterov’s acceleration step, function restart, and an adaptive stepsize selection scheme that accounts for varying local Lipschitz constant of the NLL.We establish O k2 convergence of the PNPG method with step-size backtracking only and no restart. Numerical examples compare PNPG with the state-of-the-art sparse Poisson-intensity reconstruction algorithm (SPIRAL)

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Design and development of CSP techniques for finding robust solutions in job-shop scheduling problems with Operators

[ES] Se desarrolla una técnica CSP para buscar soluciones robustas en el problema job-shop scheduling. La técnica esta desarrollada en tres pasos. El primer paso resuelve el problema sin tener en cuenta operadores. El segundo paso introduce las restricciones de los operadores y obtiene soluciones teniendo en cuenta el makespan y la robustez. En el tercer paso se mejora la robustez redistribuyendo los buffers. Para probar las robustez de las soluciones obtenidas se aplican incidencias virtuales en las soluciones.[EN] A CSP technique have been developed for finding robust solutions in job-shop scheduling problems with operators. The technique is developed in three steps. The first step solve the problem without operators minimizing the makespan. The second step introduce the operator constraints and give solutions take into account makespan and robustness. The third step improve the robustness redistributing the buffer. Some virtual incidences are created and to check the robustness of the solutions.Escamilla Fuster, J. (2012). Design and development of CSP techniques for finding robust solutions in job-shop scheduling problems with Operators. http://hdl.handle.net/10251/18029Archivo delegad

Analysis of a Group of Automorphisms of a Free Group as a Platform for Conjugacy-Based Group Cryptography

Let F be a finitely generated free group and Aut(F) its group of automorphisms. In this monograph we discuss potential uses of Aut(F) in group-based cryptography. Our main focus is on using Aut(F) as a platform group for the Anshel-Anshel-Goldfeld protocol, Ko-Lee protocol, and other protocols based on different versions of the conjugacy search problem or decomposition problem, such as Shpilrain-Ushakov protocol. We attack the Anshel-Anshel-Goldfeld and Ko-Lee protocols by adapting the existing types of the length-based attack to the specifics of Aut(F). We also present our own version of the length-based attack that significantly increases the attack\u27 success rate. After discussing attacks, we discuss the ways to make keys from Aut(F) resistant to the different versions of length-based attacks including our own

Fast Interactive Search with a Scale-Free Comparison Oracle

A comparison-based search algorithm lets a user find a target item $t$ in a database by answering queries of the form, ``Which of items $i$ and $j$ is closer to $t$?'' Instead of formulating an explicit query (such as one or several keywords), the user navigates towards the target via a sequence of such (typically noisy) queries. We propose a scale-free probabilistic oracle model called $\gamma$-CKL for such similarity triplets $(i,j;t)$, which generalizes the CKL triplet model proposed in the literature. The generalization affords independent control over the discriminating power of the oracle and the dimension of the feature space containing the items. We develop a search algorithm with provably exponential rate of convergence under the $\gamma$-CKL oracle, thanks to a backtracking strategy that deals with the unavoidable errors in updating the belief region around the target. We evaluate the performance of the algorithm both over the posited oracle and over several real-world triplet datasets. We also report on a comprehensive user study, where human subjects navigate a database of face portraits

Disruption management

The main objective of this project is to model the ARP (Aircraft Recovery Problem) from a constraint programming (CP) point of view. The information required for this project is extracted from previous papers that cope with the problem using heuristics, metaheuristics or using network-models. Also, two scenarios will be tested to verify that the implementation is correct