Synthetic Aperture Radar Image Segmentation with Quantum Annealing

In image processing, image segmentation is the process of partitioning a digital image into multiple image segment. Among state-of-the-art methods, Markov Random Fields (MRF) can be used to model dependencies between pixels, and achieve a segmentation by minimizing an associated cost function. Currently, finding the optimal set of segments for a given image modeled as a MRF appears to be NP-hard. In this paper, we aim to take advantage of the exponential scalability of quantum computing to speed up the segmentation of Synthetic Aperture Radar images. For that purpose, we propose an hybrid quantum annealing classical optimization Expectation Maximization algorithm to obtain optimal sets of segments. After proposing suitable formulations, we discuss the performances and the scalability of our approach on the D-Wave quantum computer. We also propose a short study of optimal computation parameters to enlighten the limits and potential of the adiabatic quantum computation to solve large instances of combinatorial optimization problems.Comment: 13 pages, 6 figures, to be published in IET Radar, Sonar and Navigatio

Phase-coded Radar Waveform Design with Quantum Annealing

The Integrated Side Lobe Ratio (ISLR) problem we consider here consists in finding optimal sequences of phase shifts in order to minimize the mean squared cross-correlation side lobes of a transmitted radar signal and a mismatched replica. Currently, ISLR does not seem to be easier than the general polynomial unconstrained binary problem, which is NP-hard. In our work, we aim to take advantage of the exponential scalability of quantum computing to find new optima, by solving the ISLR problem on a quantum annealer. This quantum device is designed to solve quadratic optimization problems with binary variables (QUBO). After proposing suitable formulation for different instances of the ISLR, we discuss the performances and the scalability of our approach on the D-Wave quantum computer. More broadly, our work enlightens the limits and potential of the adiabatic quantum computation for the solving of large instances of combinatorial optimization problems.Comment: 11 pages, 4 figures, 1 table, to be published in IET Radar, Sonar and Navigatio

Joint EigenValue Decomposition for Quantum Information Theory and Processing

The interest in quantum information processing has given rise to the development of programming languages and tools that facilitate the design and simulation of quantum circuits. However, since the quantum theory is fundamentally based on linear algebra, these high-level languages partially hide the underlying structure of quantum systems. We show that in certain cases of practical interest, keeping a handle on the matrix representation of the quantum systems is a fruitful approach because it allows the use of powerful tools of linear algebra to better understand their behavior and to better implement simulation programs. We especially focus on the Joint EigenValue Decomposition (JEVD). After giving a theoretical description of this method, which aims at finding a common basis of eigenvectors of a set of matrices, we show how it can easily be implemented on a Matrix-oriented programming language, such as Matlab (or, equivalently, Octave). Then, through two examples taken from the quantum information domain (quantum search based on a quantum walk and quantum coding), we show that JEVD is a powerful tool both for elaborating new theoretical developments and for simulation

Deadness and how to disprove liveness in hybrid dynamical systems

© 2016 The Authors. Published by Elsevier. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1016/j.tcs.2016.06.009What if we designed a tool to automatically prove the dynamical properties of systems for which analytic proof is difficult or impossible to obtain? Such a tool would represent a significant advance in the understanding of complex dynamical systems with nonlinearities. This is precisely what this paper offers: a solution to the problem of automatically proving some dynamic stability properties of complex systems with multiple discontinuities and modes of operation modelled as hybrid dynamical systems. For this purpose, we propose a reinterpretation of some stability properties from a computational viewpoint, chiefly by using the computer science concepts of safety and liveness. However, these concepts need to be redefined within the framework of hybrid dynamical systems. In computer science terms, here, we consider the problem of automatically disproving the liveness properties of nonlinear hybrid dynamical systems. For this purpose, we define a new property, which we call deadness. This is a dynamically-aware property of a hybrid system which, if true, disproves the liveness property by means of a finite execution. We formally define this property, and give an algorithm which can derive deadness properties automatically for a type of liveness property called inevitability. We show how this algorithm works for three different examples that represent three classes of hybrid systems with complex behaviours.This work has been supported by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under the framework of the project DYVERSE: A New Kind of Control for Hybrid Systems (EP/I001689/1). The first author also acknowledges the support of the Research Councils UK under the grant EP/E50048/1.Published versio

“LORENZ ATTRACTOR” FROM DIFFERENTIAL EQUATIONS WITH PIECEWISE-LINEAR TERMS

International audienceIn this paper we present a simple piecewise-linear circuit which exhibits a chaotic attractor similar to that observed from the Lorenz equation. Whereas the nonlinearities in the Lorenz equation consists of two product terms between two state variables, the nonlinearities in our circuit consists of two piecewise-linear terms

Etude d'un systeme differentiel a termes discontinus fortement non lineaires, derive du modele de Lorenz et presentant un comportement chaotique

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : T 81302 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

New approach for the treatement of FBRLS algorithm with long impulse response

International audienc

Optimal generalized design of transform-based block digital filters

International audienceTransform-based block implementation of digital filters is useful for high throughput filtering due to inherent parallelism and complexity reduction provided by using the fast transforms. In basic form, for example the overlap-save implementation, the block digital filter (BDF) is represented by a vector. In this paper, the basic form of block filtering and the optimal design of BDF are described. Therefore, we propose a generalization of the block digital filtering where the BDF is represented by a matrix. This generalized form and its corresponding optimal BDF design are developed. The generalized BDF allows reducing the global distortion of the block filtering

Block Robust Algorithm for Network Echo Cancellation

http://www.praiseworthyprize.com/IRECAP.htmInternational audienceThis paper is about an efficient implementation of adaptive filtering for echo cancelers. Recently a fast converging algorithm called Robust Proportionate Normalized Least Mean Squares (RPNLMS++) against double-talk has been proposed. This paper presents a realization of an improved version of the previous RPNLMS++ adaptive filter using block structure in which the filter coefficients are adjusted one per each output block. Then, an efficient implementation of the block filtering process is proposed using Number Theoretic Transforms (NTT) which can significantly reduce the computation complexity of filter implantation on Digital Signal Processor (DSP). Analyses of convergence properties, during single and double-talk, and complexity show that the new block adaptive filter permits fast implementations while maintaining performance equivalent to that of the widely used RPNLMS++ adaptive filter

New approach for the treatement of FBRLS algorithm with long impulse response

International audienceA flexible Block Recursive Least Squares frequency domain (FBRLS) using the multidelay filter (MDF) is presented throughout this paper. The choice of implanting the FBRLS algorithm using MDF adaptive filter, allows one to choose the size of an FFT consecrated to use efficiently the hardware, rather than the requirement of a specific application. In term of performances, the MDF-FBRLS adaptive filter introduces smaller block delay and is usually faster, ideal for a time-varying system, such as modelling an acoustic path in a teleconference room. These good performances are achieved by using smaller block size, updating frequently the weight vectors. Those issues, will reduce the total execution time of the adaptive process. The comparison between MDF-FBRLS and FBRLS algorithms, proved the advantages of the first one, in term of the total execution time, and the efficiency of the computational complexity of the adaptive filter