Backpropagation Imaging Research Articles

Improved Methods for Fourier-Based Microwave Imaging.

Fourier-based imaging has been widely adopted for microwave imaging thanks to its efficiency in terms of computational complexity without compromising image resolution. Together with other backpropagation imaging algorithms like delay-and-sum (DAS), they are based on a far-field approach to the electromagnetic expression relating to fields and sources. To improve the accuracy of these techniques, this contribution presents a modified version of the well-known Fourier-based algorithm by taking into account the field radiated by the Tx/Rx antennas of the microwave imaging system. The impact on the imaged targets is discussed, providing a quantitative and qualitative analysis. The performance of the proposed method for subsampled microwave imaging scenarios is compared against other well-known aliasing mitigation methods.

A Backpropagation Imaging Technique for Subsampled Synthetic Apertures

Synthetic Aperture Radar (SAR)-based microwave imaging systems have been widely used in a great variety of application areas, ranging from Earth monitoring to nondestructive testing. The scanning speed is one of the key performance indicators of SAR-based imaging systems. One possibility to increase it is by widening the distance between measurements. However, this results in the presence of grating lobes which degrade the recovered microwave SAR images. To overcome this issue, this contribution presents a novel methodology that introduces the amplitude and phase of the field radiated by the transmitting and receiving antennas of the SAR system in the backpropagation imaging algorithm. The method takes advantage of the directive pattern of the Tx/Rx antennas to reduce the level of the grating lobes appearing in the SAR image. Results presented in this contribution confirm the effectiveness of the proposed methodology to work with subsampled apertures while minimizing the impact of the grating lobes in the SAR images. Subsampling rates of, at least, one wavelength, have been achieved while keeping the quality of the recovered SAR images similar to the ones retrieved when the Nyquist sampling rate is fulfilled.

Pump-probe localization technique of varying solid contacts.

A baseline-free defect localization method in thin plates is proposed and tested. In this proof-of-concept work, a steel ball pressed against an aluminum plate is used to mimic a surface contact defect. The technique takes benefit of a repetitive nonlinear pump-probe interaction with a backpropagation imaging algorithm. High-frequency probe waves are periodically emitted by a piezoelectric patch transducer glued to the plate. Propagated flexural waves are recorded using a distributed array of transducers. At the same time, a continuous low-frequency pump vibration provided by a shaker fixed to the plate modulates the contact state. By combining multiple probe signals, the contact can be successfully localized. Contrast of the localization images is finally improved by a factor of 3 to 5 by implementing a modified version based on synchronous detection of the imaging algorithm.

O‐MedAL: Online active deep learning for medical image analysis

AbstractActive learning (AL) methods create an optimized labeled training set from unlabeled data. We introduce a novel online active deep learning method for medical image analysis. We extend our MedAL AL framework to present new results in this paper. A novel sampling method queries the unlabeled examples that maximize the average distance to all training set examples. Our online method enhances performance of its underlying baseline deep network. These novelties contribute to significant performance improvements, including improving the model's underlying deep network accuracy by 6.30%, using only 25% of the labeled dataset to achieve baseline accuracy, reducing backpropagated images during training by as much as 67%, and demonstrating robustness to class imbalance in binary and multiclass tasks.This article is categorized under:Technologies > Machine LearningTechnologies > ClassificationApplication Areas > Health Care

Back-propagation imaging by exploiting multipath from point scatterers

An inverse scattering problem under the linearised Born approximation is considered for a non-homogeneous background medium. An ensemble of pointlike scatterers is oppositely deployed in the scattering scene in order to introduce multipath and to gain an advantage in the reconstruction procedure. It is well known that inverse scattering can benefit from multipath, but at the same time it can produce artefacts in the reconstructions. This is confirmed once again in this study. Indeed, we show that some artefacts, which have been discarded in some previous works, are actually the cause of resolution improvement. To this end, standard stationary phase arguments are employed along with an adjoint inversion method (backpropagation). Theoretical results succeeds in predicting the reconstruction’s leading order terms. However, spurious artefacts due to high order terms become relevant, because more than one point scatterer is used. A simple way to mitigate such artefacts without renouncing the gain in resolution is introduced for the case where the unknown scatterers are small compared to the wavelength.

Sparse Emission Source Microscopy for Rapid Emission Source Imaging

Emission source microscopy (ESM) technique can be utilized for the localization of electromagnetic interference sources in complex and large systems. This paper presents a sparse and nonuniform sampling technique for ESM. Compared with the traditional way of acquiring abundant and uniformly distributed scanning points on the scanning plane using a robotic scanning system, the proposed method is much more time-efficient in identifying the major radiation sources, even though the image quality is sacrificed. The feasibility of sparse sampling is mathematically proved, and it is shown that increasing number of scanning points increases the signal-to-noise ratio of reconstructed images. Besides, a nearest neighbor interpolation method is applied in the real-time processing to estimate the radiated power through the scanning plane. Thus, back-propagated images and estimated radiated power can be obtained in the real-time measurement process, which can efficiently and instantaneously provide the locations and the radiation strength of the most significant emission sources.

MUSIC Imaging Using Phase-Space Gaussian-Beams Processing

In a recent paper we presented a beam-based backpropagation and correlation imaging scheme for targets in a homogeneous medium. This beam-based approach is extended here for MUSIC-imaging algorithms. In the beam approach, the fields of the physical arrays of point-sources and point receivers are expanded using special sets of collimated beam-sources and beam-receivers. This converts the physical scattering data into a beam-domain data, describing the scattering amplitudes seen (synthetically) by receiver beams due to excitation by source beams. The image is then formed by applying the MUSIC algorithm directly in the beam domain. We derive a closed form expression for the data transformation to the beam domain and then derive multi-experiments MUSIC-imaging algorithms that accommodate the measurement noise. The beam approach enables local imaging of any given sub-domain of interest by retaining only the subset of beams that pass through that domain, thus reducing the overall computation complexity relative to the conventional Green function approach, and filtering out of data and noise that arrive from non-relevant directions. Numerical investigations reveal that the beam approach also provides a better resolution under low S/N conditions.

Backpropagation Imaging in Nonlinear Harmonic Holography in the Presence of Measurement and Medium Noises

In this paper, the detection of a small reflector in a randomly heterogeneous medium using second- harmonic generation is investigated. The medium is illuminated by a time-harmonic plane wave at frequency ω. It is assumed that the reflector has a nonzero second-order nonlinear susceptibility, and thus emits a wave at frequency 2ω in addition to the fundamental frequency linear scattering. It is shown how the fundamental frequency signal and the second-harmonic signal propagate in the medium. A statistical study of the images obtained by migrating the boundary data is performed. It is proved that the second-harmonic image is more stable with respect to medium noise than the one obtained with the fundamental signal. Moreover, the signal-to-noise ratio for the second-harmonic image does not depend either on the second-order susceptibility tensor or on the volume of the particle.

Back-Propagation and Correlation Imaging Using Phase-Space Gaussian-Beams Processing

We present a beam-based imaging scheme for targets in homogeneous medium whereby the fields of the source and receiver arrays are expanded using special phase-space bases of collimated beam fields, thus converting the physical data into a beam-domain data describing the scattering amplitudes seen (synthetically) by the receiver beams due to excitation by the source beams. The image is then formed by correlating the backpropagated beam data with the incident beams. The formulation utilizes the ultra-wideband phase-space beam-summation method where the beam bases consist of Gaussian beams that emerge from a discrete set of points and directions in the source and the receiver domains. An important feature of this method is that the beam-sets are frequency independent and hence are calculated once and then used for all frequencies. A closed form expression for the data-transformation matrix from the physical domain to the beam domain is derived, leading to sparse beam-domain data. The beam approach enables local imaging of any sub-domain of interest by retaining only the subset of source and receiver beams that pass through that domain, thus reducing the overall computation complexity. The method properties are explored via numerical simulations in a noisy environment.

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.

Resolution issues of time-reversal operator decomposition (DORT) in beam space

DORT has been previously demonstrated to work using beam-space source excitations and beam-space receiver using a vertical line array in shallow water. The backpropagation images of those results are shown to display effects that arise from incomplete ensonifications of the echo repeater, which was at relatively close range of approximately 20 water depths. The small improvement of the backpropagation images from the use of different receiver beam spaces is shown. Greater improvements are shown when more appropriate source beams are also used. These beam spaces include narrower ranges of beams as well as combinations of plane-wave beams. These results are shown to be consistent with the theoretical space of beams related to the detection volume. [Work supported by the ONR.]

Backpropagation image analysis of broadband decomposition of the time reversal operator (DORT) data from TREX-04

Single-frequency DORT is a method of isolating scatterers with a multiple-source/multiple-receiver system [C. Prada et al., J. Acoust. Soc. Am. 99, 2067–2076 (1996)]. Broadband DORT overcomes problems of frequency fading and dispersion by exploiting the response of singular values across the entire signal bandwidth. In spring 2004, the Time Reversal Experiment, TREX-04, collected data for the evaluation of the broadband DORT technique. An 80 m vertical source/receiver array with 64 hydrophones was deployed in 100 m deep water in an area south of Hudson Canyon off the New Jersey coast. Sets of four, five, or six beams were transmitted at small angles from horizontal and the response from an echo repeater was recorded on 64 channels. Data was collected in 500 Hz bands between 500 and 3500 Hz with the echo repeater at ranges from 0.5 to 5.0 km and at mid-water column and near-bottom depths. Applying the broadband DORT algorithm, the isolation of the echo repeater signal in the singular vectors and the robustness of broadband backpropagation images will be presented as a function of frequency band, signal coherence, echo repeater range and depth, noise levels, and receiver aperture. [Work supported by the ONR.]

Experimental testing of broadband decomposition of the time reversal operator (DORT) in shallow water

Results are shown from the application of DORT to at-sea data taken in an area south of Hudson Canyon off the New Jersey coast during Spring 2004. A vertical source/receiver array with 64 hydrophones spanning the water column of 100-m depth was operated in 500-Hz bands between 500 and 3500 Hz. Sets of four, five, or six beams were transmitted at small angles from horizontal and the response from an echo repeater was recorded on 64 channels. The resulting data were analyzed using broadband DORT. Specific transmissions were used to quantify the degradation of coherence due to temporal variability of the source/receiver, environment, and echo repeater. The isolation in the singular vectors of the echo repeater using sets of independent source beams is comparable to that from the coherence tests. The singular spectrum of the noise field is compared with the expected results from that of a random matrix. Backpropagation images based on at-sea data and propagation using in situ XBT measurements are shown. [Work supported by ONR.]

Time-domain ultrasound diffraction tomography

A quantitative ultrasonic imaging method employing time-domain scattering data is presented. This method provides tomographic images of inhomogeneous media using scattering measurements made on a surface surrounding the medium of interest, e.g., on a circle for two-dimensional problems or on a sphere for three-dimensional problems. These scattering data are used to construct a time-domain analog of the far-field scattering operator. Images of compressibility variations are then reconstructed using a coherent combination of the far-field scattered waveforms, delayed and summed in a manner that numerically focuses on the unknown medium. This approach is closely related to synthetic aperture imaging; however, unlike conventional synthetic-aperture methods, the present method provides quantitative reconstructions of compressibility variations, analogous to frequency-compunded filtered backpropagation images weighted by the spectrum of the incident wave. Example reconstructions, obtained using synthetic data for two-dimensional scattering of wideband pulses, show that the time-domain reconstruction method can provide image quality superior to single-frequency reconstructions for objects of size and contrast relevant to medical imaging problems such as ultrasonic mammography. Reconstructions also illustrate the dependence of image quality on the number of incident-wave insonifications and on the range of scattering angles available for measurements.

Imaging of strongly-scattering targets from real data

Measured bistatic scattered fields for five new targets were added to the Ipswich data set. Three of the targets remained a mystery until revealed at a special session on image reconstruction from real data, at the 1996 IEEE AP-S International Symposium and URSI Radio Science Meeting in Baltimore. We provided coherent scattered-field data for more complicated scattering structures, as well as many more transmit-illumination directions, or views, than we had previously. Reconstructions corresponding to the first. We show back-propagated images of all five targets, using aspect diversity in diffraction tomography at a 3 cm wavelength. As expected, those targets that possess multiple-scattering effects, and/or have high contrast, fail to image properly. Targets from the Ipswich data set may serve as a useful standard against which researchers, involved in inverse scattering, can compare the merits of their inversion algorithms.

Nonlinear filtering applied to single-view backpropagated images of strong scatterers

In weak scattering diffraction tomography, there is a well-known Fourier relationship between the field scattered by an unknown object and the scattering potential that characterizes the object. For these weakly scattering objects, those that satisfy the Born or Rytov approximation, the scattered field generated from a sequence of different illumination directions complements Fourier data on the unknown scattering potential. A low-pass reconstruction is found by Fourier inversion. A simulation is presented in which the scattered far field from several strongly scattering penetrable two-dimensional cylinders is backpropagated into the object domain. For these more strongly scattering objects, a single wavelength and a single illumination direction are used to provide limited Fourier data on the product of the scattering potential and the total field. A nonlinear filtering technique, known as differential cepstral filtering, is used to isolate the scattering potential and to suppress artifacts introduced by the perturbing field component. Reconstructed images calculated by this technique from exact scattered-field data from cylindrically symmetric objects are shown.

A homomorphic filtering method for imaging strongly scattering penetrable objects

This paper describes a new method for determining the structure of strongly scattering penetrable objects having permittivity fluctuations with scales comparable to the illuminating wavelength. We are concerned with the case when small wavelength or weakly scattering approximations, such as the Born or distorted wave Born approximations, or slowly varying approximations such as the Rytov approximation, are not valid. The problem is formulated as one of recovering, in principle, a quantitative image of the object's permittivity distribution function from a set of perturbed images. Each perturbed image is obtained by backpropagating the scattered field measured around the object for different illumination directions. These backpropagated images are filtered in the differential cepstral domain to recover the object permittivity distribution, and we show reconstructions from both simulated and real microwave scattered data. >

Synthetic aperture focusing technique signal processing

The synthetic aperture focusing technique (SAFT) is briefly reviewed and addressed as a heuristic digital ultrasonic imaging scheme which exploits the idea of back-propagating a set of measured and digitally stored A-scans. It is shown that for a far-field experimental set-up, ie for small, isolated defects remote to the transducer, SAFT reduces to the filtered back-projection imaging scheme which is well known within the framework of conventional X-ray computer tomography. Therefore, alternative data processing via Fourier transforms only, similar to the Fourier slice theorem of tomography, is possible, which sheds considerable light upon the heuristic SAFT pixel-space envelope-detection scheme. The resulting imaging identity has been termed POFFIS (physical optics far-field inverse scattering). The far-field assumption is then omitted yielding a Fourier-transform-SAFT algorithm (FT-SAFT) whose results are identical to back-propagation imaging with the definite advantage of fast processing capabilities based upon standard hardware and allowing immediate implementation of high resolution procedures as well as inclusion of mode-conversion effects; the theoretical background is pulse-echo diffraction tomography. The above results are supported and illustrated by application of all three algorithms — SAFT, POFFIS, FT-SAFT — to experimental data obtained from scanning a line aperture for several test specimens.