Inverse-scattering Technique Research Articles

Microwave Tomographic Imaging of Anatomically Realistic Numerical Phantoms with Debye Dispersion for Breast Cancer Detection Using a Regularized Inverse Scattering Technique in the Time Domain

Microwave Tomographic Imaging of Anatomically Realistic Numerical Phantoms with Debye Dispersion for Breast Cancer Detection Using a Regularized Inverse Scattering Technique in the Time Domain

Influence of NNN interaction and existence of breathers in a quasi-discrete Heisenberg helimagnetic spin system

In this work, we investigate the existence and properties of discrete bright and dark breathers in a one-dimensional Heisenberg helimagnet incorporating bilinear, helical, NNN and anisotropic interactions. The Hamiltonian is bosonized using the Dyson–Maleev transformation and the coherent state representation is selected as the fundamental representation of the system. With the help of multiple scales combined with quasi-discreteness approximation, the dynamical equation is reduced to a nonlinear Schrödinger equation (NLSE). By employing the solution of NLSE derived using inverse scattering technique (IST), the bright and dark type breather solutions are constructed. The effect of helicity and NNN interactions on these breather modes is also analysed.

Higher-order rogue-wave fission in the presence of self-steepening and Raman self-frequency shift

Using the generalized nonlinear Schr\"odinger equation, we investigate how the effect of self-steepening and Raman-induced self-frequency shift impact higher-order rogue-wave solutions. We observe that each effect breaks apart the higher-order rogue wave, reducing it to its constituent fundamental parts, in a similar manner to how a higher-order soliton undergoes fission. Applying a local inverse-scattering technique, we show that under the effect of self-frequency shift, the emergence of a rogue wave significantly influences the surrounding wave background, triggering solitons, breathers, and new rogue waves. We demonstrate that under the combined effect of third-order dispersion, self-steepening, and Raman-induced self-frequency shift, the disintegrated elements of higher-order rogue waves become fundamental solitons, creating an asymmetrical spectral profile that generates both red- and blue-shifted frequency components. We also show the intermediary processes of the fission steps prior to soliton transformation which can only be observed in the presence of weak perturbations. These observations reveal the mechanisms that create a large number of solitons in the process of modulation instability-induced supercontinuum generation from a continuous-wave background in optical fibers.

A Two-Step Inverse-Scattering Technique in Variable-Exponent Lebesgue Spaces for Through-the-Wall Microwave Imaging: Experimental Results

A novel two-step inverse-scattering technique is proposed for through-the-wall microwave imaging. The approach is based on a regularization scheme developed in the framework of variable-exponent Lebesgue spaces, which enhances the quality of the reconstruction by properly tuning the exponent function that defines the adopted norm. Such a function is built directly from the available data by using a beamforming technique based on a delay-and-sum scheme. After an initial numerical assessment, the approach is validated against experimental measurements in a laboratory environment, with targets placed behind a brick wall. Measured data are collected in time domain by scanning the transmitting and receiving antennas in a multi-illumination and multi-view arrangement. The processing of experimental data is performed in the frequency domain, where data at multiple frequencies are extracted by a Fast Fourier Transform (FFT) and simultaneously processed by the imaging algorithm. The obtained imaging results confirm the good reconstruction capabilities of the developed inverse-scattering scheme in the case of both metallic and low-contrast targets.

The IST spectral portraits of the first order doubly periodic solutions of the nonlinear Schrödinger equation

The spectra of the inverse scattering technique (IST) play a crucial role in the physics of nonlinear phenomena. They define the long term evolution of dynamical systems. We present the IST spectral portraits for the extensive three-parameter families of the first order doubly periodic solutions of the nonlinear Schrödinger equation that cover a wide range of physical phenomena such as modulation instability, rogue waves and many other problems with periodic boundary conditions. We relate these spectral portraits with the parameters of the family. We show that there are two qualitatively different types of spectral portraits. A-type spectra consist of two continuous bands: a band of purely imaginary eigenvalues within the interval and a finite band of complex eigenvalues. On the contrary, B-type spectra possess only continuous bands of imaginary eigenvalues all located within the interval and separated by a finite band gap. A physical interpretation of these results is given.

Synthesis of One Dimensional Electromagnetic Bandgap Structures with Fully Controlled Parameters

In this paper, we propose a novel synthesis strategy for the design of one dimensional electromagnetic bandgap (1-D-EBG) structures where all the performance parameters of these devices can fully be controlled, i.e., the central frequency of the forbidden band, its attenuation level and bandwidth, and the ripple level at the passbands. The novel synthesis strategy employs a new inverse-scattering technique to accurately synthesize the 1-D-EBG structure, targeting a properly interpolated version of a classical periodic filter fulfilling the required frequency specifications. The new inverse-scattering technique follows a continuous layer peeling approach and relies on the coupled-mode theory to precisely model the microwave structures. Telecommunication and radar systems, as well as material characterization devices, will be profited by this proposal with which enhanced filters, sensors, power dividers, couplers, mixers, oscillators, and amplifiers can be designed in many different technologies. As a proof of concept, a 1-D-EBG structure in microstrip technology with a single forbidden band (free of spurious stopband replicas), with attenuation level of 30 dB, fractional bandwidth larger than 100%, and return loss level at the passbands of 20 dB, has been designed and fabricated. The measurements obtained are in very good agreement with the simulations and target specifications, being free of spurious replicas up to the 15th harmonic, showing the robustness and very good performance of the novel design strategy proposed.

Image Reconstruction Based on Combination of Inverse Scattering Technique and Total Variation Regularization Method

<p>The Forward-Backward Time-Stepping (FBTS) had proven its potential to reconstruct images of buried objects in inhomogeneous medium with useful quantitative information about its size, shape, and locality. The Total Variation regularization method was incorporated with the FBTS algorithm to deal with the ill-posedness or ill-conditionedness of the inverse problem. The effectiveness of the proposed technique is confirmed by numerical simulations. The numerical method was carried out on a simple object detection through FBTS with and without TV regularization method. The detection and reconstruction of relative permittivity and conductivity of the simple object have shown an improvement as TV regularization method applied whereas it smoothed the vibrations of the images and gave a better estimation of the image’s boundaries.</p>

Investigating the transverse optical structure of spider silk micro-fibers using quantitative optical microscopy

Abstract The transverse optical structure of two orb-weaver (family Araneidae) spider dragline silks was investigated using a variant of the inverse-scattering technique. Immersing the silks in a closely refractive index-matched liquid, the minimum achievable image contrast was greater than expected for an optically homogeneous silk, given what is currently known about the optical absorption of these silks. This “excess contrast” indicated the presence of transverse optical structure within the spider silk. Applying electromagnetic scattering theory to a transparent double cylinder, the minimum achievable irradiance contrast for the Plebs eburnus and Argiope keyserlingi dragline silks was determined to be consistent with step index refractive index contrasts of 1−4×10−4 and 6–7×10−4, respectively, supposing outer-layer thicknesses consistent with previous TEM studies (50 nm and 100 nm, respectively). The possibility of graded index refractive index contrasts within the spider silks is also discussed. This is the strongest evidence, to date, that there is a refractive index contrast associated with the layered morphology of spider silks and/or variation of proportion of nanocrystalline components within the spider silk structure. The method is more generally applicable to optical micro-fibers, including those with refractive index variations on a sub-wavelength scale.

Advances in the 3-D Forward–Backward Time-Stepping (FBTS) Inverse Scattering Technique for Breast Cancer Detection

This paper presents recent advances in a 3-D inverse scattering technique, called forward-backward time-stepping (FBTS), applied to the reconstruction of the microwave properties of the breast. The FBTS algorithm is utilized for a numerical-based study of a 3-D breast model based on an MRI. Several illumination schemes, based on different microwave transmitter/receiver configurations, are compared based on the quality of the reconstructed images of the breast model. A combination of cylindrical and planar arrays is shown to provide accurate estimates of the model electrical parameters that delineate the various regions of the breast. Although further analysis with this combination array demonstrates that tumors of reduced size and reduced contrast with the surrounding fibroglandular region are much more difficult (and in some cases not possible) to reconstruct, the study presents some promising initial results of a reconstruction technique for breast imaging and cancer detection.

On the interaction between two Kerr black holes

The double-Kerr solution is generated using both a Backlund transformation and the Belinskii-Zakharov inverse-scattering technique. We build a dictionary between the parametrisations naturally obtained in the two methods and show their equivalence. We then focus on the asymptotically flat double-Kerr system obeying the axis condition which is Z_2^\phi invariant; for this system there is an exact formula for the force between the two black holes, in terms of their physical quantities and the coordinate distance. We then show that 1) the angular velocity of the two black holes decreases from the usual Kerr value at infinite distance to zero in the touching limit; 2) the extremal limit of the two black holes is given by |J|=cM^2, where c depends on the distance and varies from one to infinity as the distance decreases; 3) for sufficiently large angular momentum the temperature of the black holes attains a maximum at a certain finite coordinate distance. All of these results are interpreted in terms of the dragging effects of the system.

Fiber Bragg gratings for pure dispersion-slope compensation.

Single-fiber Bragg gratings designed to compensate for pure third-order dispersion are demonstrated. The devices are designed by use of a layer-peeling inverse-scattering technique and exhibit dispersion profiles across their reflection bandwidths of -20, +/- 40, and -225 ps/nm2 over bandwidths of 4.5, 6, and 3 nm, respectively. Furthermore, they have almost constant peak reflectivities of approximately 75% and are, respectively, only 8, 23, and 40 mm long.

Thin disc around a rotating black hole, but with support in-between

In the previous paper, we presented the metric obtained from a general Weyl seed using the Belinskii–Zakharov inverse-scattering technique with two real solitons. It describes the field of a stationary black hole surrounded by a source inherited from the seed. In the present paper, we study the solution in further detail with the inverted first Morgan–Morgan counter-rotating disc employed as a seed. In particular, the properties of the horizon, the static limit, the equatorial plane, the extreme limit of the solution and the resulting external disc are analysed and illustrated. It turns out that there is a jump in derivatives of the metric in the equatorial plane even below the seed disc, indicating the presence of a ‘suspension layer’ that confines the system against gravitational collapse or decay. Hence, the solution cannot represent a realistic axisymmetric accretion disc around a rotating black hole.

Neural-network-based inverse-scattering technique for online microwave medical imaging

In this paper, the application of radial basis function neural networks (RBFNNs) in inverse-scattering problems related to microwave medical imaging is proposed. The objective of the networks is to estimate the geometric and/or electromagnetic properties of tissues by processing the scattered-field measurements obtained during the illumination of the body by electromagnetic waves. The training of the RBFNNs is based on the orthogonal least-squares algorithm. This approach results in straightforward construction of the network, where both the size and the values of the free parameters of the network are obtained. The proposed methodology is applied to the estimation of the position and the size of proliferated marrow inside the bone of a limb. This application is closely related to the detection and monitoring of leukemia. Different measurement configurations are examined. The performance of the constructed networks in cases of noisy field measurements is also investigated.

Soliton solutions with real poles in the Alekseev formulation of the inverse-scattering method

A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its inverse. For the case in which the electromagnetic field vanishes, some explicit solutions are given using a Minkowski seed metric. The relation with the corresponding soliton solutions that can be constructed using the Belinskii-Zakharov inverse-scattering technique is determined.

Modern microwave: inverse-scattering techniques for image reconstruction

The development of efficient reconstruction procedures is of fundamental importance in microwave imaging applications. A great deal of research has been devoted to the study of optimization techniques based on space-domain formulations for which deterministic or stochastic methodologies are applied. In parallel, strong efforts are also underway to develop effective and accurate illuminating and measurement systems. It should be noted that microwave imaging techniques may be used in a complementary fashion or integrated with other more standard imaging techniques. The data fusion performed should provide a much more comprehensive inspection than any one technique could provide on its own.

Soliton on a disordered lattice.

A stochastic version of the lattice nonlinear Schr\"odinger equation, allowing treatment by means of the inverse-scattering technique and having an exact one-soliton solution, is introduced. It is shown that such a model is a useful tool for investigation of a wide class of nonlinear lattices affected by spatiotemporally random forces. A number of the most important statistical characteristics of soliton dynamics governed by such models can be evaluated without any assumption about the smallness of random perturbations. The problem is studied in detail in two limiting cases: small and large intensities of fluctuations of a stochastic term in the integrable equation.

Spectral averaging of small-amplitude sine-Gordon wave trains.

It is well known that the nonlinear Schroedinger equation is the generic envelope description of nonlinear wave trains in the small-amplitude limit. V. E. Zakharov and E. A. Kuznetsov (Physica 18D, 455 (1986)) have shown that for many systems integrable via inverse-scattering techniques it is possible, through the use of multiscale techniques, to derive the nonlinear Schroedinger Lax pair from the Lax pair of the system that is being modulated. It will be shown that this technique of ''multiscale averaging'' can be applied to the sine-Gordon theory to obtain not only the nonlinear Schroedinger Lax pair from the sine-Gordon Lax pair, but also the nonlinear Schroedinger spectral data, conservation laws, THETA-function solutions, and reality constraint from their sine-Gordon counterparts. This allows a physical interpretation of the mathematical elements of the nonlinear Schroedinger envelope in terms of the physical characteristics of the sine-Gordon system that is being modulated.

Nonlinear self-modulation: An exactly solvable model.

The cubic Schr\"odinger equation (CSE) (${\mathrm{iu}}_{t}$+${u}_{\mathrm{xx}}$\ifmmode\pm\else\textpm\fi{}2\ensuremath{\Vert}u${\ensuremath{\Vert}}^{2}$u=0) is a generic model equation used in the study of modulational problems in one spatial dimension. The CSE is exactly solvable using inverse-scattering techniques. Periodic solutions of the focusing CSE (``+'' sign in the above equation) are also well known to be subject to modulational instabilities. This unique mixture of solvability and instability allows the development of a complete and explicit analytical theory for the long-time behavior of the instabilities. Among the results to be discussed are (i) a method for calculating the growth rates of instabilities around (spatially nonuniform) initial states, (ii) a discussion of recurrence phenomena for systems with finite spatial period, and (iii) a method for calculating the recurrence time.

Application of an inverse-scattering method to determine the effective interaction between composite particles

An inverse-scattering method developed recently by Münchow and Scheid is used to determine the effective potential between two α-particles. The α-α scattering phase shifts from a microscopic calculation using the generator coordinate method are employed with the inversescattering technique to obtain a unique, energy-dependent optical potential. A comparison of this potential with the direct (or folded) potential clearly reveals the Pauli exchange effects arising from the inclusion of nuclear exchange between the two a-particles. It is shown that the inverse-scattering approach is accurate for the α-α system even at low energies and should be applicable to heavy-ion systems.

Nonlinear Interactions of Three Wave Packets in a Homogeneous Medium

The nonlinear coupling of three wave packets is solved for interactions either evolving in time and one-dimensional space or occurring in steady state in two dimensions. Solutions are given using the inverse-scattering technique and numerical integration of the differential equations.