Time-reversal Approach Research Articles

Concepts in quantum state tomography and classical implementation with intense light: a tutorial

A tomographic measurement is a ubiquitous tool for estimating the properties of quantum states, and its application is known as quantum state tomography (QST). The process involves manipulating single photons in a sequence of projective measurements, often to construct a density matrix from which other information can be inferred, and is as laborious as it is complex. Here we unravel the steps of a QST and outline how it may be demonstrated in a fast and simple manner with intense (classical) light. We use scalar beams in a time reversal approach to simulate the outcome of a QST and exploit non-separability in classical vector beams as a means to treat the latter as a “classically entangled” state for illustrating QSTs directly. We provide a complete do-it-yourself resource for the practical implementation of this approach, complete with tutorial video, which we hope will facilitate the introduction of this core quantum tool into teaching and research laboratories alike. Our work highlights the value of using intense classical light as a means to study quantum systems and in the process provides a tutorial on the fundamentals of QSTs.

Sparsity-based photoacoustic image reconstruction with a linear array transducer and direct measurement of the forward model.

Photoacoustic (PA) imaging is an emerging imaging technique for many clinical applications. One of the challenges posed by clinical translation is that imaging systems often rely on a finite-aperture transducer rather than a full tomography system. This results in imaging artifacts arising from an underdetermined reconstruction of the initial pressure distribution (IPD). Furthermore, clinical applications often require deep imaging, resulting in a low-signal-to-noise ratio for the acquired signal because of strong light attenuation in tissue. Conventional approaches to reconstruct the IPD, such as back projection and time-reversal, do not adequately suppress the artifacts and noise. We propose a sparsity-based optimization approach that improves the reconstruction of IPD in PA imaging with a linear array ultrasound transducer. In simulation studies, the forward model matrix was measured from k-Wave simulations, and the approach was applied to reconstruct simulated point objects and the Shepp-Logan phantom. The results were compared with the conventional back projection, time-reversal approach, frequency-domain reconstruction, and the iterative least-squares approaches. In experimental studies, the forward model of our imaging system is directly measured by scanning a graphite point source through the imaging field of view. Experimental images of graphite inclusions in tissue-mimicking phantoms are reconstructed and compared with the back projection and iterative least-squares approaches. Overall these results show that our proposed optimization approach can leverage the sparsity of the PA images to improve the reconstruction of the IPD and outperform the existing popular reconstruction approaches.

Notice of Retraction: Quantification of the Fault Impedance and Its Location by a Time Reversal Approach

The electromagnetic time reversal method is not only suitable to accurately identify the location of a phase-to-ground fault in an electrical network but also is able to estimate the value of the fault impedance. In this letter, a closed-form procedure is developed to compute the fault resistance associated to a soft fault between the line and the reference conductor. Some numerical examples are given and discussed.

Precise Localization of Multiple Noncooperative Objects in a Disordered Cavity by Wave Front Shaping.

Complicated multipath trajectories of waves in disordered cavities cause object localization to be very challenging with traditional ray-tracing approaches. Yet it is known that information about the object position is encoded in the Green's function. After a calibration step, traditional time-reversal approaches retrieve a source's location from a broadband impulse response measurement. Here, we show that a nonemitting object's scattering contribution to a reverberant medium suffices to localize the object. We demonstrate our finding in the microwave domain. Then, we further simplify the scheme by replacing the temporal degrees of freedom (d.o.f.) of the broadband measurement with spatial d.o.f. obtained from wave front shaping. A simple electronically reconfigurable reflectarray inside the cavity dynamically modulates parts of the cavity boundaries, thereby providing spatial d.o.f. The demonstrated ability to localize multiple noncooperative objects with a single-frequency scheme may have important applications for sensors in smart homes.

Notice of Retraction: Electromagnetic Time Reversal Approach to Locate Multiple Soft Faults

In this letter, the electromagnetic time reversal (TR) method is applied to the location of multiple faults along a branch of an electric transmission line (TL). Under simplifying assumptions, the formulation of the TR transfer function for the detection of a single fault is extended to the case of two or more faults along the line. This extension does not alter the energy properties of the transfer function used to identify the coordinates of the faults. The derivation of the transfer function is presented and applied to different cases ranging from a long high-voltage transmission line (TL) to a short high-speed interconnect.

The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach

We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the n-marginal SEP using first hitting times of barrier sets by the time–space process. The barriers are characterised by means of a recursive sequence of optimal stopping problems. Moreover, we prove that our solution enjoys a global optimality property extending the one-marginal Root case. Our results hold for general, one-dimensional, martingale diffusions.

Virtual acoustics in inhomogeneous media with single-sided access

A virtual acoustic source inside a medium can be created by emitting a time-reversed point-source response from the enclosing boundary into the medium. However, in many practical situations the medium can be accessed from one side only. In those cases the time-reversal approach is not exact. Here, we demonstrate the experimental design and use of complex focusing functions to create virtual acoustic sources and virtual receivers inside an inhomogeneous medium with single-sided access. The retrieved virtual acoustic responses between those sources and receivers mimic the complex propagation and multiple scattering paths of waves that would be ignited by physical sources and recorded by physical receivers inside the medium. The possibility to predict complex virtual acoustic responses between any two points inside an inhomogeneous medium, without needing a detailed model of the medium, has large potential for holographic imaging and monitoring of objects with single-sided access, ranging from photoacoustic medical imaging to the monitoring of induced-earthquake waves all the way from the source to the earth’s surface.

A multi-dataset time-reversal approach to clinical trial placebo response and the relationship to natural variability in epilepsy

PurposeClinical epilepsy drug trials have been measuring increasingly high placebo response rates, up to 40%. This study was designed to examine the relationship between the natural variability in epilepsy, and the placebo response seen in trials. We tested the hypothesis that ‘reversing' trial direction, with the baseline period as the treatment observation phase, would reveal effects of natural variability. MethodClinical trial simulations were run with time running forward and in reverse. Data sources were: SeizureTracker.com (patient reported diaries), a randomized sham-controlled TMS trial, and chronically implanted intracranial EEG electrodes. Outcomes were 50%-responder rates (RR50) and median percentage change (MPC). ResultsThe RR50 results showed evidence that temporal reversal does not prevent large responder rates across datasets. The MPC results negative in the TMS dataset, and positive in the other two. ConclusionsTypical RR50s of clinical trials can be reproduced using the natural variability of epilepsy as a substrate across multiple datasets. Therefore, the placebo response in epilepsy clinical trials may be attributable almost entirely to this variability, rather than the “placebo effect”.

Time Reversal Imaging Based on the Space-Frequency ESPRIT

A novel time reversal approach for the point target imaging is proposed in this paper. This method requires only single measurement by the time reversal array, and employs the space-frequency decomposition plus the rotation invariance of the signal subspace for the target detecting. Numerical simulations are carried out to validate the performance of the proposed method for single target located at different positions in homogenous and continuous random medium respectively. The results indicate that the proposed method performs better than the conventional signal subspace based space-frequency algorithm both in imaging resolution and efficiency.

Enhanced Energy Localization in Hyperthermia Treatment Based on Hybrid Electromagnetic and Ultrasonic System: Proof of Concept with Numerical Simulations.

This paper proposes a hybrid hyperthermia treatment system, utilizing two noninvasive modalities for treating brain tumors. The proposed system depends on focusing electromagnetic (EM) and ultrasound (US) energies. The EM hyperthermia subsystem enhances energy localization by incorporating a multichannel wideband setting and coherent-phased-array technique. A genetic algorithm based optimization tool is developed to enhance the specific absorption rate (SAR) distribution by reducing hotspots and maximizing energy deposition at tumor regions. The treatment performance is also enhanced by augmenting an ultrasonic subsystem to allow focused energy deposition into deep tumors. The therapeutic faculty of ultrasonic energy is assessed by examining the control of mechanical alignment of transducer array elements. A time reversal (TR) approach is then investigated to address challenges in energy focus in both subsystems. Simulation results of the synergetic effect of both modalities assuming a simplified model of human head phantom demonstrate the feasibility of the proposed hybrid technique as a noninvasive tool for thermal treatment of brain tumors.

Enabling Heterogeneous Connectivity in Internet of Things: A Time-Reversal Approach

With the pervasive presence of massive smart devices, Internet of Things (IoT) is enabled by wireless communication technology. The devices in IoT usually have very diverse bandwidth capabilities and thus in need of many communication standards. To facilitate communications between these heterogeneous bandwidths of devices, middlewares have often been developed. However, they are often not suitable for resource-constrained scenario due to their complexity. It leads us to ask is there a unified approach that can support the communication between the devices with heterogeneous bandwidths? In this paper, we propose the time-reversal (TR) approach to answer such a question. A novel TR-based heterogeneous system is proposed, which can address the bandwidth heterogeneity and maintain the benefit of TR at the same time. Although there is an increase in complexity, it concentrates mostly on the digital processing of the access point (AP), which can be easily handled with more powerful digital signal processor (DSP). Since there is no middleware in the proposed system and the additional physical layer complexity concentrates on the AP side, the proposed TR approach better satisfies the requirement of low complexity and energy efficiency for terminal devices (TDs). We further conduct the theoretical analysis of the interference in the proposed system. Simulations show the bit-error-rate (BER) performance can be significantly improved with appropriate spectrum allocation. Finally, Smart Homes is chosen as an example of IoT applications to evaluate the performance of the proposed system.

Time-reversal of nonlinear waves: Applicability and limitations

Time-reversal (TR) refocusing of waves is one of fundamental principles in wave physics. Using the TR approach, "Time-reversal mirrors" can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backwards. Lately, laboratory experiments proved that this approach can be applied not only in acoustics and electromagnetism but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic TR using a uni-directional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.

Localising Defective Components with a Time-Reversal Approach

Localising Defective Components with a Time-Reversal Approach

A comparison of time-reversal and inverse-source methods for the optimal delivery of wave energy to subsurface targets

Elastic wave stimulation of targets embedded in heterogeneous elastic solids has potential applications in medicine (treatment of tumors, lithotripsy), petroleum engineering, environmental engineering, hydro-geology, etc. Systematic methodologies for designing the wave sources that focus optimally the emitted energy into the target zone are important for ensuring the efficiency of the wave energy delivery process. In this article, we compare two methodologies that could be used for designing wave sources that maximize wave-based stimulation of the target region: a time-reversal (TR) approach and an inverse-source (IS) approach. The former relies on the linearity and reciprocity admitted by the governing physics, and the latter is an optimization-based framework that attempts maximization of a wave motion metric in the target zone. Whereas closed cavity problems are easier to treat, here we concentrate on the challenging problem of wave energy focusing to subsurface geo-formations using motion actuators placed on the ground surface. We formulate the underlying wave propagation problem for two-dimensional, semi-infinite, elastic, heterogeneous domains. We define motion metrics to measure the energy expended by the wave sources, and the kinetic energy delivered to the target formation. We conduct numerical experiments and compare the relative performance of the wave sources designed using the TR and the IS approaches. Both methods have advantages and disadvantages: for remote targets in well-characterized formations IS is preferred; whereas TR is preferable when a source can be embedded in the target. Both methods have similar efficiency.

An Overview of Underwater Time-Reversal Communication

Time reversal (TR) exploits spatial diversity to achieve spatial and temporal focusing in complex environments. Over the last decade, the TR concept has been applied successfully to phase-coherent acoustic communications in time-varying multipath ocean environments, as an alternative to conventional adaptive multichannel equalization. Temporal focusing (pulse compression) mitigates the intersymbol interference (ISI) and subsequent single-channel equalization removes the residual ISI, thus providing nearly optimal performance in theory. The spatial focusing capability facilitates multiuser or multiple-input–multiple-output (MIMO) communications without explicit use of time, frequency, or code division multiplexing, while an adaptive TR approach can reduce further the crosstalk among users or multiple transmitters. TR communications can be extended easily to time-varying channels using a block-based approach with channel updates. This paper provides an overview of TR communications in both shallow and deep water and recent advances including bidirectional equalization, multiuser communications with mobile users, and communication with a glider serving as a mobile gateway.

Full-wave acoustic and thermal modeling of transcranial ultrasound propagation and investigation of skull-induced aberration correction techniques: a feasibility study.

BackgroundTranscranial focused ultrasound (tcFUS) is an attractive noninvasive modality for neurosurgical interventions. The presence of the skull, however, compromises the efficiency of tcFUS therapy, as its heterogeneous nature and acoustic characteristics induce significant distortion of the acoustic energy deposition, focal shifts, and thermal gain decrease. Phased-array transducers allow for partial compensation of skull-induced aberrations by application of precalculated phase and amplitude corrections.MethodsAn integrated numerical framework allowing for 3D full-wave, nonlinear acoustic and thermal simulations has been developed and applied to tcFUS. Simulations were performed to investigate the impact of skull aberrations, the possibility of extending the treatment envelope, and adverse secondary effects. The simulated setup comprised an idealized model of the ExAblate Neuro and a detailed MR-based anatomical head model. Four different approaches were employed to calculate aberration corrections (analytical calculation of the aberration corrections disregarding tissue heterogeneities; a semi-analytical ray-tracing approach compensating for the presence of the skull; two simulation-based time-reversal approaches with and without pressure amplitude corrections which account for the entire anatomy). These impact of these approaches on the pressure and temperature distributions were evaluated for 22 brain-targetsResultsWhile (semi-)analytical approaches failed to induced high pressure or ablative temperatures in any but the targets in the close vicinity of the geometric focus, simulation-based approaches indicate the possibility of considerably extending the treatment envelope (including targets below the transducer level and locations several centimeters off the geometric focus), generation of sharper foci, and increased targeting accuracy. While the prediction of achievable aberration correction appears to be unaffected by the detailed bone-structure, proper consideration of inhomogeneity is required to predict the pressure distribution for given steering parametersConclusionsSimulation-based approaches to calculate aberration corrections may aid in the extension of the tcFUS treatment envelope as well as predict and avoid secondary effects (standing waves, skull heating). Due to their superior performance, simulationbased techniques may prove invaluable in the amelioration of skull-induced aberration effects in tcFUS therapy. The next steps are to investigate shear-wave-induced effects in order to reliably exclude secondary hot-spots, and to develop comprehensive uncertainty assessment and validation procedures.

Branching particle systems in spectrally one-sided Lévy processes

We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps upcrossing the level. By regarding the size of a jump as the birth site of a particle, we construct a branching particle system in which the particles undergo nonlocal branchings and deterministic spatial motions to the left on the positive half line. A particle is removed from the system as soon as it reaches the origin. Then a measure-valued Borel right Markov process can be defined as the counting measures of the particle system. Its total mass evolves according to a Crump-Mode-Jagers (CMJ) branching process and its support represents the residual life times of those existing particles. A similar result for spectrally negative Levy process is established by a time reversal approach. Properties of the measure-valued processes can be studied via the excursions for the corresponding Levy processes.

Enhancing Least Squares Monte Carlo with diffusion bridges: an application to energy facilities

The aim of this study is to present an efficient and easy framework for the application of the Least Squares Monte Carlo methodology to the pricing of gas or power facilities as detailed in Boogert and de Jong [J. Derivatives, 2008, 15, 81–91]. As mentioned in the seminal paper by Longstaff and Schwartz [Rev. Financ. Stud. 2001, 113–147], the convergence of the Least Squares Monte Carlo algorithm depends on the convergence of the optimization combined with the convergence of the pure Monte Carlo method. In the context of the energy facilities, the optimization is more complex and its convergence is of fundamental importance in particular for the computation of sensitivities and optimal dispatched quantities. To our knowledge, an extensive study of the convergence, and hence of the reliability of the algorithm, has not been performed yet, in our opinion this is because the apparent infeasibility and complexity uses a very high number of simulations. We present then an easy way to simulate random trajectories by means of diffusion bridges in contrast to Dutt and Welke [J. Derivatives, 2008, 15 (4), 29–47] that considers time-reversal Itô diffusions and subordinated processes. In particular, we show that in the case of Cox-Ingersoll-Ross and Heston models, the bridge approach has the advantage to produce exact simulations even for non-Gaussian processes, in contrast to the time-reversal approach. Our methodology permits performing a backward dynamic programming strategy based on a huge number of simulations without storing the whole simulated trajectory. Generally, in the valuation of energy facilities, one is also interested in the forward recursion. We then design backward and forward recursion algorithms such that one can produce the same random trajectories by the use of multiple independent random streams without storing data at intermediate time steps. Finally, we show the advantages of our methodology for the valuation of virtual hydro power plants and gas storages.

Time-reversal generation of rogue waves.

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

Time-reversal imaging based on the space-frequency MDM and cancellation operator

This study presents a novel time-reversal approach to locate targets based on the spatial information from the space-frequency multistatic data matrix plus the maximum detection and signal subtraction. The cancellation operator enables us to cancel the echoes coming from preliminarily detected targets, and we can transfer the multitarget imaging program into a series of single-target ones. Therefore, the targets can be accurately focused in the new environment. The advantages of the new algorithm over the conventional multitarget imaging algorithm are demonstrated by several numerical simulations.