Matthew Pepin

SAR-Based Vibration Estimation Using the Discrete Fractional Fourier Transform

A vibration estimation method for synthetic aperture radar (SAR) is presented based on a novel application of the discrete fractional Fourier transform (DFRFT). Small vibrations of ground targets introduce phase modulation in the SAR returned signals. With standard preprocessing of the returned signals, followed by the application of the DFRFT, the time-varying accelerations, frequencies, and displacements associated with vibrating objects can be extracted by successively estimating the quasi-instantaneous chirp rate in the phase-modulated signal in each subaperture. The performance of the proposed method is investigated quantitatively, and the measurable vibration frequencies and displacements are determined. Simulation results show that the proposed method can successfully estimate a two-component vibration at practical signal-to-noise levels. Two airborne experiments were also conducted using the Lynx SAR system in conjunction with vibrating ground test targets. The experiments demonstrated the correct estimation of a 1-Hz vibration with an amplitude of 1.5 cm and a 5-Hz vibration with an amplitude of 1.5 mm.

Reduction of Vibration-Induced Artifacts in Synthetic Aperture Radar Imagery

Target vibrations introduce nonstationary phase modulation, which is termed the micro-Doppler effect, into returned synthetic aperture radar (SAR) signals. This causes artifacts, or ghost targets, which appear near vibrating targets in reconstructed SAR images. Recently, a vibration estimation method based on the discrete fractional Fourier transform (DFrFT) has been developed. This method is capable of estimating the instantaneous vibration accelerations and vibration frequencies. In this paper, a deghosting method for vibrating targets in SAR images is proposed. For single-component vibrations, this method first exploits the estimation results provided by the DFrFT-based vibration estimation method to reconstruct the instantaneous vibration displacements. A reference signal, whose phase is modulated by the estimated vibration displacements, is then synthesized to compensate for the vibration-induced phase modulation in returned SAR signals before forming the SAR image. The performance of the proposed method with respect to the signal-to-noise and signalto-clutter ratios is analyzed using simulations. Experimental results using the Lynx SAR system show a substantial reduction in ghosting caused by a 1.5-cm 0.8-Hz target vibration in a true SAR image.

Demonstration of target vibration estimation in synthetic aperture radar imagery

Synthetic-aperture radar (SAR) can be used to remotely estimate ground target vibrations by exploiting the Doppler in the returned signals. Recent studies suggest that time-frequency signal-processing tools can retrieve the vibration signature from the returned SAR signals. A vibration estimation method based on the fractional Fourier transform (FRFT) was reported earlier and it was tested on simulated SAR data. In this paper, a first-time demonstration of the FRFT-based vibration estimation method is reported using real SAR data collected by the Lynx (Ku-band) SAR system. The vibrating target is an aluminum triangular trihedral with lateral length of 15 inches. The FRFT-based algorithm is shown to successfully retrieve a 3 mm peak-to-peak amplitude, 5 Hz vibration of the target from real SAR data.

SAR-based vibration retrieval using the fractional Fourier transform in slow time

Recent reports on the effects of vibrating targets on synthetic-aperture radar (SAR) imagery and the potential of SAR to extract non-stationary signatures have drawn significant interest from the remote-sensing community. SAR returned signals are the superposition of the transmitted pulses modulated by both static and non-static targets in both amplitude and phase. More precisely, the vibration of a target causes a small sinusoid-like frequency modulation along the synthetic aperture (slow time), whereby the phase deviation is proportional to the displacement of the vibrating object. By looking at successive small segments in slow time, each frequency modulated pulse can be tracked and further approximated as a piecewise-linear frequency-modulated signal. The discrete-time fractional Fourier transform (DFRFT) is an analysis tool geared toward such signals containing linear frequency modulated components. Within each segment, the DFRFT transforms each frequency-modulated component into a peak in the DFRFT plane, and the peak position corresponds to the frequency modulation rate. A series of such measurements provides the instantaneous-acceleration history and its spectrum bears the vibrating signature of the target. Additionally, when the chirp z-transform (CZT) is incorporated into the DFRFT, vibration-induced modulations can be identified with high resolution. In this work, the interplay amongst SAR system parameters, vibration parameters, the DFRFTs window size, and the CZTs zoom-in factor is characterized analytically for the proposed SAR-vibrometry approach. Simulations verify the analysis showing that the detection of vibration using the slow-time approach has significantly higher fidelity than that of the previously reported fast-time approach.

Performance analysis on synthetic aperture radar-based vibration estimation in clutter

Recently, a time-frequency method based on the discrete fractional Fourier transform (DFrFT) was proposed for estimating target vibrations using synthetic aperture radar (SAR). Later on, a subspace method was incorporated into the DFrFT-based method. It is shown that the subspace method provides better performance than the direct DFrFT-based method in noise. However, the performance of these two methods has not been studied in clutter that cause strong interference with signals from vibrating targets in real-world applications. In this paper, the performance of the two vibration estimation methods in clutter is characterized and compared via simulations. Simulation results demonstrate that the DFrFT-based method, that yielded reliable results when signal-to-clutter ratios (SCR) exceeds 18 dB, now yields reliable results when SCR exceeds 8 dB with the incorporation of the subspace method. Experimental results show that the subspace method correctly estimates the vibration frequency of a 7 Hz vibration from actual SAR data at an estimated SCR of 14 dB.

Separation of vibrating and static SAR object signatures via an orthogonal subspace transformation

When vibrating objects are present in a Synthetic Aperture Radar image they induce a modulation in the pulse-to-pulse Doppler collected. At higher frequencies (up to a sampling limit dictated by half the PRF) the modulation is low amplitude due to physical limits of vibrating structures and swamped by the Doppler from static objects (clutter). This paper presents an orthogonal subspace transform that separates the modulation of a vibrating object from the static clutter. After the transformation the major frequencies of the vibration are estimated with asymptotically (as the number of pulses increases) decreasing variance and bias. Although the e¤ects and SAR image artifacts from vibrating objects are widely known their utility has been limited to high signal-to-noise, low frequency vibrating objects. The method presented here lowers the minimum required signal-to-noise ratio of the vibrating object over other methods. Additionally vibrations over the full (azimuth- sampled) frequency range from one over the aperture time to the pulse repetition frequency (PRF) are equally measured with respect to the noise level at each speci…c frequency. After separation of the vibrating and static object signal sub-spaces any of the many spectral estimation methods can be applied to estimate the vibration spectrum.

Reduction of vibration-induced artifacts in synthetic-aperture-radar imagery using the fractional fourier transform

In synthetic aperture radar (SAR) images of objects exhibiting low-level vibrations are accompanied by localized artifacts, or ghost targets, caused by the micro-Doppler present in the returned SAR signals. Conventional Fourier-transform-based SAR processing techniques are not fit to remove ghosting effects prior to image formation due to the non-stationary nature of the returned signals from vibrating objects. Recently, a method based on the discrete fractional Fourier transform (DFrFT) has been developed for estimating the instantaneous vibration accelerations and vibrating frequencies from returned SAR signals. Here, a novel image de-ghosting algorithm for vibrating targets in SAR imagery is proposed by employing the DFrFT-based vibration-estimation algorithm. The proposed de-ghosting method is applied to SAR data collected by the Lynx SAR system. Experimental results show a substantial reduction in ghosting caused by a 1.5-cm amplitude, 0.8-Hz vibration present in a test target.

Information content per photon versus image fidelity in three-dimensional photon-counting integral imaging.

Photon-counting integral imaging has been introduced recently, and its applications in three-dimensional (3D) object sensing, visualization, recognition, and classification under photon-starved conditions have been demonstrated. This paper sheds light on the underlying information-theoretic foundation behind the ability of photon-counting integral imaging in performing complex tasks with far fewer photons than conventional imaging systems. A metric for photon-information content is formulated in the context of 3D photon-counting imaging, and its properties are investigated. It is shown that there is an inherent trade-off between imaging fidelity, measured by the entropy-normalized mutual information associated with a given imaging system, and the amount of information in each photon used in the imaging process, as represented by the photon-number-normalized mutual information. The dependence of this trade-off on photon statistics, correlation in the 3D image, and the signal-to-noise ratio of the photon-detection system is also investigated.

Fast synthetic aperture radar imaging with a streamlined 2D fractional Fourier transform

The 2-D Fractional Fourier Transform (FRFT) has been shown to be applicable to the Synthetic Aperture Radar (SAR) imaging problem. Streamlined versions presented here makes the 2-D FRFT comparable with and slightly faster than the Range Doppler (RD) and Extended Chirp Scaling (ECS) methods. The 2-D FRFT is streamlined by eliminating redundancy due to the fact that the same fractional angle is applied to each pulse in the SAR phase historys range dimension while one other fractional angle is applied across each range-gate in the phase historys azimuth dimension. Eliminating the redundancy and approximating the 2-D Fractional Fourier Transform operation in each dimension produces several streamlined 2-D FRFT methods as well as a very fast approximate 2-D FRFT. The computational order of the fast approximate 2-D FRFT is less than that of other corrective SAR imaging techniques. Examples of SAR imaging with these streamlined and approximate FRFTs are given as well as a comparison of the computational speed and impulse response of the full, streamlined and approximate 2-D FRFT, and the RD and ECS methods of SAR imaging.

A three-dimensional fractional Fourier transformation methodology for volumetric linear, circular, and orbital synthetic aperture radar formation

The 3-D Fractional Fourier Transformation (FrFT) has unique applicability to multi-pass and multiple receiver Synthetic Aperture Radar (SAR) scenarios which can collect radar returns to create volumetric reflectivity data. The 3-D FrFT can independently compress and image radar data in each dimension for a broad set of parameters. The 3-D FrFT can be applied at closer ranges and over more aperture sampling conditions than other imaging algorithms. The FrFT provides optimal processing matched to the quadratic signal content in SAR (i.e. the pulse chirp and the spherical wave-front across the aperture). The different parameters for 3-D linear, circular, and orbital SAR case are derived and specifi…c considerations such as squint and scene extent for each scenario are addressed. Example imaged volumes are presented for linear, circular and orbital cases. The imaged volume is sampled in the radar coordinate system and can be transformed to a target based coordinate system. Advantages of the FrFT which extend to the 3-D FrFT include its applicability to a wide variety of imaging condition (standoff range and aperture sub-sampling) as well as inherent phase preservation in the images formed. The FrFT closely matches the imaging process and thus is able to focus SAR images over a large variation in standoff ranges specifi…cally at close range. The FrFT is based on the relationship between time and frequency and thus can create an image from an under-sampled wave-front. This ability allows the length of the synthetic aperture to be increased for a fixed number of aperture samples.