Decomposition Of Time Reversal Operator Research Articles

Sound Source Localization Method Based on Time Reversal Operator Decomposition in Reverberant Environments

Predicting sound sources in reverberant environments is a challenging task because reverberation causes reflection and scattering of sound waves, making it difficult to accurately determine the position of the sound source. Due to the characteristics of overcoming multipath effects and adaptive focusing of the time reversal technology, this paper focuses on the application of the time reversal operator decomposition method for sound source localization in reverberant environments and proposes the image-source time reversal multiple signals classification (ISTR-MUSIC) method. Firstly, the time reversal operator is derived, followed by the proposal of a subspace method to achieve sound source localization. Meanwhile, the use of the image-source method is proposed to calculate and construct the transfer matrix. To validate the effectiveness of the proposed method, simulations and real-data experiments were performed. In the simulation experiments, the performance of the proposed method under different array element numbers, signal-to-noise ratios, reverberation times, frequencies, and numbers of sound sources were studied and analyzed. A comparison was also made with the traditional time reversal method and the MUSIC algorithm. The experiment was conducted in a reverberation chamber. Simulation and experimental results show that the proposed method has good localization performance and robustness in reverberant environments.

Cable Fault Location in Distribution Network Based on Decomposition of Time Reversal Operator

Cable Fault Location in Distribution Network Based on Decomposition of Time Reversal Operator

Resolution-Enhanced and Accurate Cascade Time-Reversal Operator Decomposition (C-DORT) Approach for Positioning Radiated Passive Intermodulation Sources

Attaining a high-resolution and accurate location for a radiated passive intermodulation source (R-PIMS) has been an increasingly interesting problem in modern multi-carrier wireless communication systems. For precisely positioning multiple closely spaced R-PIMSs, a novel imaging method called cascade decomposition of time-reversal operator (C-DORT) was developed. C-DORT constructs a new spectrum calculation by normalizing and multiplying the pseudo-spectrum at each sampled frequency together. The cascade process focuses the pseudo-spectrum at R-PIMS positions to form a highly brightened spectrum peak and to suppress the remained pseudo-spectrum to approximately zero, contributing to distinguishing the closely spaced R-PIMSs. The positioning performance of the positioning resolution, pseudo-spectrum width, positioning accuracy, and imaging robustness are analyzed by numerical simulations. Compared with the conventional central frequency decomposition of time-reversal operator (CF-DORT) and the time domain decomposition of time-reversal operator (TD-DORT) methods, the multiple R-PIMSs, spaced at a distance of diffraction limit, which is the spacing of 1/2 of a wavelength, are distinguished effectively in C-DORT. Additionally, the cross-range pseudo-spectrum full width at half maxima (CRPS-FWHM) is suppressed to the width of 1/4 of a wavelength by multiplication to improve the cross-range resolution in C-DORT. In addition, accurate positioning is obtained by providing the approximately zero positioning root mean square estimation (RMSE) at an SNR ranging from 0 dB to 10 dB. The results show that the proposed C-DORT improves the positioning accuracy and enhances the positioning resolution for locating an R-PIMS.

Improving three-dimensional target reconstruction in the multiple scattering regime using the decomposition of the time-reversal operator

The singular vectors of the time reversal operator (décomposition de l'opérateur de retournement temporel, time reversal operator decomposition (DORT) processing) are often used for localizing small echogeneous targets in a cluttered environment. In this work, we show that they can also improve the imaging of relatively large and contrasted targets in a homogeneous environment. It is observed that non-linear inversion schemes, minimizing iteratively the discrepancy between experimental data and simulated field scattered by target estimates, are more efficient when the illuminations correspond to the DORT singular vectors. In addition, DORT preprocessing permits a drastic diminution of the data load and computer burden. This study is conducted with experimental microwave data of targets with size comparable or greater than the wavelength.

Wideband imaging with the decomposition of time reversal operator

It has been shown that the decomposition of the time reversal operator (DORT) is effective to achieve detection and selectively focusing on pointlike scatterers. Moreover, the multiplicity of the invariant of the time reversal operator for a single extended (non-pointlike) scatterer has been also revealed. In this paper, we investigate the characterization and imaging of the scatterers when an extended scatterer and a pointlike scatterer are simultaneously present. The relationship between the quality of focusing and frequency is investigated by backpropagation of singular vectors using a model of the waveguide in each frequency bin. When the extended scatterer is present, it is shown that the second singular vector can also focus on the target. However, the task of focusing can only be achieved in frequency bins with relatively large singular values. When both scatterers are simultaneously present, the singular vectors are a linear combination of the transfer vector from each scatterer. The first singular vector can achieve focusing on the extended scatterer in frequency bins with relatively large singular values. The second singular vector can approximately focus on the pointlike scatterer in frequency bins that its scattering coefficients are relatively high and the first scattering coefficient of the extended scatterer are relatively low.

Targets Detection Based on Time Reversal Operator with Uniform Circular Array

In order to detect targets accurately in electromagnetic environment, a decomposition of time reversal operator method for detecting targets with uniform circular array (UCA) is proposed in this paper. In this method, the time reversal operator in UCA is obtained by the transmission functions of targets and antenna array. And then, the eigenvector decomposition of time reversal operator is performed. According to the eigenvectors and the transmission functions of targets and scanning points in the given targets area, the focusing values of all scanning points are calculated, and the direction of scanning points whose focusing values are far greater than others are the direction of targets. Finally, the simulations verify the effectiveness of the proposed method.

Analysis of the time reversal operator for a scatterer undergoing small displacements

The method of the time reversal operator decomposition is usually employed to detect and characterize static targets using the invariants of the time reversal operator. This paper presents a theoretical and experimental investigation into the impact of small displacements of the target on these invariants. To find these invariants, the time reversal operator is built from the multistatic response matrix and then diagonalized. Two methods of recording the multistatic response matrix while the target is moving are studied: Acquisition either element by element or column by column. It is demonstrated that the target displacement generates new significant eigenvalues. Using a perturbation theory, the analytical expressions of the eigenvalues of the time-reversal operator for both acquisition methods are derived. We show that the distribution of the new eigenvalues strongly depends on these two methods. It is also found that for the column by column acquisition, the second eigenvector is simply linked to the scatterer displacements. At last, the implications on the Maximum Likelihood and Multiple Signal Classification detection are also discussed. The theoretical results are in good agreement with numerical and 3.4 MHz ultrasonic experiments.

On the Sensitivity of Time-Reversal Imaging Techniques to Model Perturbations

Time-reversal (TR) techniques involve physical or synthetic retransmission of signals acquired by a set of transceivers in a time-reversed fashion, and can be used for a host of applications, including ultrawideband imaging of obscured targets. This work investigates the performance of some TR-based techniques under non-ideal conditions, and is divided into three main parts. In the first part, we investigate the robustness of TR-based imaging techniques via the decomposition of TR operator (DORT) algorithm and the multiple signal classification (MUSIC) algorithm under clutter and (additive) noise. In the second part, we examine the effect of TR-invariance breaking (due to losses in the intervening media) on the performance of both DORT and (TR-based) MUSIC. In the third part, effects of translational perturbations of the TR array are examined, as a class of model perturbations. These ensuing effects are then exploited, in a controlled manner, as a means to extract second-order spatial statistics of the probed media.

Novel DORT Method in Non-Well-Resolved Scatterer Case

The decomposition of time reversal operator (DORT) method is an efficient technique to select focusing signal on the target in well-resolved scatterer case. The DORT method requires the measurement of the inter-element impulse responses and diagonalizes these responses to find eigenstructure of the medium. However, the DORT method is not able to produce satisfactory result for non-well-resolved scatterer case (i.e., two scatterers that are placed closely about 0.2lambda). Therefore, in this letter, a weighted least squares (WLS) algorithm is introduced in the DORT method to perform selective focusing in non-well-resolved scatterer case. This technique called the WLS-DORT method performs better spatial focusing resolution than the conventional DORT method and results in simpler computational complexity than the minimum variance beamforming method under practical implementation.

Time reversal operator decomposition with focused transmission and robustness to speckle noise: Application to microcalcification detection

The decomposition of the time reversal operator (DORT) is a detection and focusing technique using an array of transmit-receive transducers. In the absence of noise and under certain conditions, the eigenvectors of the time reversal operator contain the focal laws to focus ideally on well-resolved scatterers even in the presence of strong aberration. This paper describes a new algorithm, FDORT, which uses focused transmission schemes to acquire the operator. It can be performed from medical scanner data. A mathematical derivation of this algorithm is given and it is compared with the conventional algorithm, both theoretically and with numerical experiments. In the presence of strong speckle signals, the DORT method usually fails. The influence of the speckle noise is explained and a solution based on FDORT is presented, that enables detection of targets in complex media. Finally, an algorithm for microcalcification detection is proposed. In-vivo results show the potential of these techniques.

Demonstration at sea of the decomposition-of-the-time-reversal-operator technique

This paper presents a derivation of the time reversal operator decomposition (DORT) using the sonar equation. DORT is inherently a frequency-domain technique, but the derivation is shown in the time-frequency domain to preserve range resolution. The magnitude of the singular values is related to sonar equation parameters. The time spreading of the time-domain back-propagation image is also related to the sonar equation. Noise-free, noise-only, and signal-plus-noise data are considered theoretically. Contamination of the echo singular component by noise is shown quantitatively to be very small at a signal-to-noise ratio of 0dB. Results are shown from the TREX-04 experiment during April 22 to May 4, 2004 in 94m deep, shallow water southwest of the Hudson Canyon. Rapid transmission of short, 500Hz wide linear frequency modulated beams with center frequencies of 750, 1250, 1750, 2250, 2750, and 3250Hz are used. Degradation caused by a lack of time invariance is found to be small at 750Hz and nearly complete at 3250Hz. A back-propagation image at 750Hz shows focusing on the echo repeater. These results are discussed with comments about further research.

Adaptive instant record signals applied to detection with time reversal operator decomposition

Time reversal arrays are becoming common tools whether for detection or tomography. These applications require the measurement of the response from the array to one or several receivers. The most natural way to record the impulse responses for several sources is to generate pulses successively from each emitting point and record simultaneously the signals from the receivers. However, this method is very time consuming or inefficient in terms of signal-to-noise ratio. To overcome this limitation quasi-orthogonal pseudonoise signals like Kasami sequences can be used. For guided wave propagation, a very high degree of orthogonality between the signal is necessary to allow an accurate measure of the whole multipath structure of the transfer function. Hence, in this work, we propose a new family of pseudo-orthogonal signals that is adapted to the environment and more specifically, to highly dispersive media. These adaptive instant records signals are used experimentally to detect targets using the time reversal operator decomposition method. The accuracy of the 15 x 15 transfer functions acquired simultaneously, and therefore the detection capability, are demonstrated in an experimental ultrasonic waveguide as a small-scale model of shallow water propagation including bottom absorption and reverberation.

Adaptive instant record signals applied to shallow water detection

Time reversal arrays are becoming common tools whether for detection, tomography or communication. These applications require the measurement of the response from the array to one or several receivers. The most natural way to record different impulse responses between several points is to generate pulses successively from each emitting point and directly record all the impulse responses on the recording points. However, this method is very time consuming and inefficient in terms of signal-to-noise ratio. Hence, in this work, we propose an original way of sending continuous signals simultaneously from all the sources, recording all the pressure fields on the receivers and processing them in order to extract the exact impulse responses by matched filter. To this end, the signals are adapted to the environment and, more specifically, to highly dispersive media. These adaptive instant records signals (AIRS) are used experimentally to detect targets using the time reversal operator decomposition method. The quality of the 15×15 transfer functions acquired simultaneously, and therefore, the detection capability is demonstrated in shallow water in the presence of bottom absorption and reverberation. Finally, the connection of AIRS with CDMA and FDMA that are two coding techniques used in telecommunication is shown.

Resolution enhancement and separation of reverberation from target echo with the time reversal operator decomposition.

Time reversal operator (TRO) decompositions are performed in a model of an ocean wave guide containing a target and having different kinds of bottom. The objective is to study the effects of bottom reverberation and absorption by means of ultrasonic experiments. It is shown experimentally that the echo from a target can be separated from the bottom reverberation. Reverberation eigenvectors are back propagated in the wave guide leading to focus on the bottom. An amplitude correction is applied to both reverberation and signal eigenvectors to compensate for bottom absorption and thus to improve target resolution.