This letter describes the extension of signal subspace processing (SSP) to the arena of anomaly detection. In particular, we develop an SSP-based, local anomaly detector that exploits the rich information available in the multiple bands of a hyperspectral (HS) image. This SSP approach is based on signal processing considerations, and its entire formulation reduces to a straightforward (and intuitively pleasing) geometric and algebraic development. We extend the basic SSP concepts to the HS anomaly detection problem, develop an SSP HS anomaly detector, and evaluate this algorithm using multiple HS data files

This paper addresses change detection in averaged multilook synthetic aperture radar (SAR) imagery. Averaged multilook SAR images are preferable to full-aperture SAR reconstructions when the imaging algorithm is approximation-based (e.g., polar format processing) or when motion data are not accurate over a long full aperture. We examine the application of a SAR change-detection method, known as signal subspace processing, which is based on the principles of two-dimensional adaptive filtering, and we use it to recognize the addition of surface landmines to a particular area under surveillance. We describe the change-detection problem as a trinary hypothesis testing problem, and define a change signal and its normalized version to determine whether: 1) there is no change in the imaged scene; 2) a target has entered the imaged scene; or 3) a target has exited the imaged scene. A statistical analysis of the error signal is provided to show its properties and merits. Results are presented for averaged noncoherent multilook and coherent single-look X-band SAR imagery.

The paper addresses the problem of calibrating FLIR images of a scene that are acquired at different time points to construct information for moving target indication (MTI) and change detection. A signal model is developed to identify variations and imperfections of an FLIR sensor in time. This model is utilized to compensate for relatively slow variations of a bias in the FLIR sensor via a Fourier-based processing. Furthermore, a two-dimensional adaptive filtering method is developed to compensate for variations of the image point response (IPR) of a FLIR sensor as well as sub-pixel changes in the relative coordinates of the sensor-target over time. Results with time series FLIR, data of a scene with an airborne helicopter and a ground target are provided.

This paper introduces an adaptive method for rejecting clutter in forward-looking infra-red (FLIR) imagery. In this approach, a spatially-varying two-dimensional adaptive filtering method is developed to identify a metric distance (error energy) between a test scene and a library of reference man-made targets (trucks, tanks, etc.). The function of the 2D spatially-varying adaptive filter is to compensate for: a) variations of image point response (IPR) of a FLIR sensor; b) variations of heat distribution on the test and reference targets; c) subpixel shifts in the relative coordinates of these targets; and d) subtle scaling and rotations. A statistic is constructed that is the least square energy of the error between the test target and its projection into each member of the library of reference target chips based on the above-mentioned spatially-varying 2D adaptive filtering; this database is then used to identify the test chip as a man-made target or clutter. Results with FLIR data of scenes composed of trucks, tanks, and APCs at various angles in different types of clutter environment will be provided.

This paper examines two applications of a multi-channel airborne radar system, or an array-based synthetic aperture radar (SAR). The first mode involves a stripmap SAR array whose electronically-steered beam patterns are exploited to achieved the azimuth resolution of its single element while maintaining a relatively high radar power; this system has applications in foliage penetrating (FOPEN) SAR. The second array-based SAR utlilizes two or more elements in the along-track domain to detect moving targets. Signal processing issues associated with these two array-based SAR systems are discussed.

This paper presents the results of three-dimensional imaging of a T-72 tank using its angular azimuthal (turntable) and linear elevation synthetic aperture data at X band. This is achieved using an accurate and computationally-efficient wavefront (Fourier-based) reconstruction algorithm for elevation and circular (E-CSAR) data. The E-CSAR 3D images are then used to synthesize 2D spotlight and stripmap slant plane SAR images of the target at a desired range and squint angle. For this purpose, a procedure is introduced that incorporates the spatially-varying azimuthal and elevation Doppler signatures of individual reflectors on the target as well as the mean range, azimuth and elevation of the flight path. Results using the E-CSAR images of the T-72 tank are provided.

This correspondence addresses the problem of fusing the information content of two uncalibrated sensors. This problem arises in registering images of a scene when it is viewed via two different sensory systems, or detecting change in a scene when it is viewed at two different time points by a sensory system, or via two different sensory systems or observation channels. We are concerned with sensory systems which have not only a relative shift, scaling and rotational calibration error, but also an unknown point spread function (that is time varying for a single sensor, or different for two sensors). By modeling one image in terms of an unknown linear combination of the other image, its powers and their spatially transformed (shift, rotation and scaling) versions, a signal subspace processing is developed for fusing uncalibrated sensors. The proposed method is shown to be applicable in moving target detection (MTD) using monopulse synthetic aperture radar (SAR) with uncalibrated radars. Results are shown for video, magnetic resonance images of a human brain, moving target detector monopulse SAR, and registration of SAR images of a target obtained via two different radars or at different coordinates by the same radar for automatic target recognition (ATR).

This paper is concerned with an echo imaging system which utilizes focused beams of an aperture along a specific contour, for example, a line or a circular arc, in both the transmit and receive modes for data collection. Such data collection strategies are useful for imaging internal structures of a target which are located at a certain depth relative to the aperture; unfocused echo signature of an interior structure possesses a low signal-to-clutter/noise power ratio, and is not desirable. The conventional methods for depth-focused echo imaging use transmit/receive focusing on a set of prescribed points in the spatial domain (that is, a two-dimensional grid); this is exceedingly time-consuming though it does not require any postprocessing of the measured data. The proposed scheme of depth-focusing along a contour requires a significantly smaller time period for data acquisition, and relies on a relatively fast Fourier-based method for image formation. This Fourier-based method is shown to be applicable in near-field as well as far-field imaging scenarios, and does not put any restrictions on the size of the aperture, the size of the target area, and the frequency of radiation. The approach is applicable in depth-focused imaging with a mechanically rotating focused aperture, or a phased array. Results are provided.

This work addresses the problem of representing a dynamic image via its temporal spiral scan data. Two types of spiral scan data are considered: uniform density and foveal. Spatial sampling strategies for these two spiral scans are examined. A signal model is developed to interpret the temporal readouts of repeated spiral scans via two separate time variables, the slow time and fast time. This mathematical model is used to construct a method for forming the time progression of the target image. A method for increasing the repetition rate of the spiral data collection via utilizing both forward and backward spiral scans is presented. Results are provided.

This paper presents a method for volumetric reconstruction from helical computerized tomography (H-CT) data which are collected with a fan beam source. An interpretation of the H-CT data in terms of the axial computerized tomography (A-CT) data is provided. This analysis indicates that the H-CT data for positive and negative detector angles can be combined to form periodically nonuniform hexagonal samples of the A-CT data. A Fourier-based method to reconstruct the A-CT data from this form of data coverage is presented. The target function is then reconstructed using the conventional fan beam computed tomography algorithms for A-CT.

This paper addresses the problem of fusing the information content of two uncalibrated sensors. This problem arises in registering images of a scene when it is viewed via two different sensory systems, or detecting change in a scene when it is viewed at two different time points by a sensory system, or via two different sensory systems or observation channels. We are concerned with sensory systems which have not only a relative shift, scaling and rotational calibration error, but also an unknown point spread function (that is time-varying for a single sensor, or different for two sensors). By modeling one image in terms of an unknown linear combination of the other image, its powers and their spatially-transformed (shift, rotation and scaling) versions, a signal subspace processing is developed for fusing uncalibrated sensors. The proposed method is shown to be applicable in moving target detection (MTD) using monopulse synthetic aperture radar (SAR) with uncalibrated radars. Results are shown for video, magnetic resonance images of a human brain, moving target detector monopulse SAR, and registration of SAR images of a target obtained via two different radars or at different coordinates by the same radar for automatic target recognition (ATR).

This paper presents a system model and inversion for imaging moving targets using phased arrays. The system model provides a mathematical framework to represent the motion of a moving target in the beam-steering domain which is identified as the slow-time domain. The inversion provides a reconstruction of the moving targets in the spatial and velocity domains. It is shown that a randomized beam steering strategy in the slow-time domain can improve the resolution in the velocity domain. The imaging problem is also formulated for a phased array system that spotlights a target area with its transmitted beam to improve the target to clutter power ratio, and obtains beam-steered data in the receive mode for high-resolution imaging. We cite a diagnostic medical ultrasound problem due to the practical difficulties and challenges that are associated with it.

This paper presents a method for detecting moving targets embedded in foliage from the monostatic and bistatic synthetic aperture radar (SAR) data obtained via two airborne radars. The two radars, which are mounted on the same aircraft, have different coordinates in the along track (cross-range) domain. However, unlike the interferometric SAR systems used for topographic mapping, the two radars possess a common range and altitude (i.e., slant range). The resultant monopulse SAR images are used to construct difference and interferometric images for moving target detection. It is shown that the signatures of the stationary targets are weakened in these images. Methods for estimating a moving target's motion parameters are discussed. Results for an ultrawideband UHF SAR system are presented.

This paper presents a system model and inversion for airborne synthetic aperture acoustic (SAA) imaging. The system model accurately represents the intercation of the acoustic source and the target region at near range values. Moreover, the model incorporates the fact that the relative speed of the vehicle's (transmitter/receiver) with respect to the target region is comparable to the acoustic wave propagation speed. The inversion utilizes the principle of spectral decomposition of spherical phase functions to develop a wavefront reconstruction method from SAA data. Processing issues and selection of appropriate acoustic FM-CW sources are discussed. Results are provided that exhibit the superior accuracy of the proposed SAA system model and inversion over their synthetic aperture radar (SAR) counterpart in which the vehicle's speed is assumed to be much smaller than the wave propagation speed.

This paper presents a system model and inversion for imaging moving targets using phased arrays. The system model provides a mathematical framework to represent the motion of a moving target in the beam-steering domain which is identified as the slow-time domain. The inversion provides a reconstruction of the moving targets in the spatial and velocity domains. It is shown that a randomized beam steering strategy in the slow-time domain can improve the resolution in the velocity domain. The imaging problem is also formulated for a phased array system which spotlights a target area with its transmitted beam to improve the target to clutter power ratio, and obtains beam-steered data in the receive mode for high-resolution imaging.

This paper presents a method for imaging from the slant plane data collected by a synthetic aperture radar (SAR) over the full rotation or a partial segment of a circular flight path. A Fourier analysis for the Green's function of the imaging system is provided. This analysis is the basis of an inversion for slant plane circular SAR data. The reconstruction algorithm and resolution for this SAR system are outlined. It is shown that the slant plane circular SAR, unlike the slant plane linear SAR, has the capability to extract three-dimensional imaging information of a target scene. The merits of the algorithm are demonstrated via a simulated target whose ultra wideband foliage penetrating (FOPEN) or ground penetrating (GPEN) ultrahigh frequency (UHF) radar signature varies with the radar's aspect angle.

This paper presents an interferometric processing of an aircraft's monostatic and bistatic inverse synthetic aperture radar (ISAR) signatures for automatic landing. The aircraft's squint angle in this ISAR imaging problem is near 90 degrees . We show that this extreme squint angle does not pose any problem for the ISAR Fourier-based (wavefront) reconstruction algorithm. In fact, the aircraft can be imaged accurately, and without any erroneous shifts in the cross-range domain, within the imposed theoretical resolution. Moreover, the algorithm is accurate enough such that one can utilize the phase of the ISAR monostatic and bistatic measurements for interferometric processing. The resultant interferometric ISAR image is used to detect undesirable rotations in the aircraft's orientation.

This paper presents methods for detecting and identifying moving targets in a synthetic aperture radar (SAR) scene. An analytical expression is derived for the coherent SAR signature of a target. SAR system model of a moving target is developed. These principles are then used to construct a SAR signal statistic (energy function) in a parameter space which is defined by the target's coordinates, speed, and coherent SAR signature. Stochastic gradient techniques are used to search for the maximum point of this energy function which is located at the desired target's parameters.

This paper presents an interferometric processing of an aircraft's monostatic and bistatic inverse synthetic aperture radar signatures for automatic landing. The aircraft's squint angle in this ISAR imaging problem is near 90 degrees. We show that this extreme squint angle does not pose any problem for the ISAR Fourier-based (wavefront) reconstruction algorithm. In fact, the aircraft can be imaged accurately, and without any erroneous shifts in the cross-range domain, within the imposed theoretical resolution. Moreover, the algorithm is accurate enough such that one can utilize the phase of ISAR. Monostatic and bistatic measurements for interferometric processing. The resultant interferometric ISAR image is used to detect undesirable rotations in the aircraft's orientation.

This paper presents a method for automatic detection of targets with nonlinear motion embedded in dynamic clutter. This is achieved via processing the targets' incoherent ISAR data that are less vulnerable to multiplicative noise (phase errors). It is shown that the incoherent ISAR signature of a target scene may be viewed as its baseband ISAR signature. Thus, the magnitude of an ISAR database that is severely contaminated with phase errors, i.e., incoherent ISAR data, may be used for ISAR detection of moving targets. Incoherent ISAR data in the fast-time and slow-time domain are transformed into another two-dimensional domain. The signature of a target in the transformed domain is shown to be localized based on its mid-point range and speed. This localized statistic is suitable for automatic, i.e., machine-based, detection of stationary as well as moving targets in the scene.>

The paper presents two applications of continuous-wave large-band width signaling, also known as FM-CW signaling, in imaging problems that involve moving targets or moving transmitting/receiving data acquisition systems. The first imaging system that is discussed is FM-CW synthetic aperture radar (SAR) imaging. In this imaging system, the echoed signal, that is recorded via a quasi-monostatic radar, is partitioned in its Fourier domain into bandpass regions (Doppler data) centered around the harmonics of the FM-CW signal, and then processed in the spatial Doppler-based inversion of pulsed SAR. The second imaging problem involves a quasi-monostatic or bistatic phased array system that utilizes FM-CW signaling for spatial-velocity imaging of a nonrigid moving target. the authors show that this phased array imaging system provides information regarding targets that are moving with a specific velocity vector on a specific contour of data in the spectral distribution of FM-CW phased array Doppler data.>

The paper presents a method for imaging from the data obtained from a synthetic aperture radar that does not utilize spotlighting. The SAR database, that is commonly encountered in reconnaissance imaging with stripmap SAR, is passed through a digital spotlighting algorithm for range and cross-range gating. The resultant filtered SAR data is used in the high-resolution spotlight SAR inversion to image the desired target area. A subaperture processing and coherent imaging method to implement the algorithm is presented.>

This paper presents a method for range-speed imaging of moving targets. The approach is based on illuminating the target region with an FM-CW signal. The inversion in this imaging problem involves a partitioning of the echoed signals in the frequency domain followed by a transformation. The system model and inversion in this imaging method does not approximate a moving target's Doppler shift to be a constant over the bandwidth of the transmitted signal and does not put any restrictions on the target's range.

A synthetic aperture radio/inverse synthetic aperture radar (SAR/ISAR) coherent system model and inversion to image a target moving with an unknown constant velocity in a stationary background are presented. The approach is based on a recently developed system modelling and inversion principle for SAR/ISAR imaging that utilizes the spatial Fourier decomposition of SAR data in the synthetic aperture domain to convert the SAR system model's nonlinear phase functions into linear phase functions suitable for a computationally manageable inversion. It is shown that SAR/ISAR imaging of a moving target can be converted into imaging the target in a stationary squint-mode SAR problem where the parameters of the squint-mode geometry depend on the target's velocity. A method for estimating the moving target's velocity that utilizes a spatial Doppler analysis of the SAR data within overlapping subapertures is presented. The spatial Doppler technique does not require the radar signal to be narrowband, so the reconstructed image's resolution is not sacrificed to improve the target's velocity estimator.

The authors present a synthetic aperture radar (SAR) coherent system model and inversion (ISAR) to image a target moving with an unknown constant velocity in a stationary background. It is shown that SAR imaging of a moving target can be converted into imaging the target in a stationary squint-mode SAR problem where the parameters of the squint-mode geometry depend on the target's velocity. A method for estimating the moving target's velocity that utilizes a spatial Doppler analysis of the SAR data within overlapping subapertures is presented. On estimating a moving target's velocity, unlike the temporal Doppler processing methods, the spatial Doppler technique does not require the radar signal to be narrowband. Thus, the reconstructed image's resolution is not sacrificed to improve the target's velocity estimator.>

A system model and its corresponding inversion for synthetic aperture radar (SAR) imaging are presented. The system model incorporates the spherical nature of a radar's radiation pattern at far field. The inverse method based on this model performs a spatial Fourier transform (Doppler processing) on the recorded signals with respect to the available coordinates of a translational radar (SAR) or target (inverse SAR). It is shown that the transformed data provide samples of the spatial Fourier transform of the target's reflectivity function. The inverse method can be modified to incorporate deviations of the radar's motion from its prescribed straight line path. The effects of finite aperture on resolution, reconstruction, and sampling constraints for the imaging problem are discussed.

The author presents a system model and inversion for the beam-steered data obtained by linearly varying the relative phase among the elements of an array, also known as phased array scan data. The system model and inversion incorporate the radiation pattern of the array's elements. The inversion method utilizes the time samples of the echoed signals for each scan angle instead of range focusing. It is shown that the temporal Fourier transform of the phased array scan data provides the distribution of the spatial Fourier transform of the reflectivity function for the medium to be imaged. The extent of this coverage is related to the array's length and the temporal frequency bandwidth of the transmitted pulsed signal. Sampling constraints and reconstruction procedure for the imaging system are discussed. It is shown that the imaging information obtained by the inversion of phased array scan data is equivalent to the image reconstructed from its synthesized array counterpart.

Methods for addressing two types of multiplicative noise in synthetic aperture radar (SAR) imaging are presented. The authors consider a multiplicative noise with a real phase (i.e. the SAR signal's phase is contaminated but its amplitude is uncorrupted) that possesses unknown functional characteristics with respect to the radar signal's temporal frequencies. A perturbation solution for phase reconstruction from amplitude is developed from a wave equation governing the SAR signal and a Riccati equation that relates the amplitude and phase functions of the SAR signal. This solution is converted into a noniterative analytical solution in terms of the moments and powers of the log amplitude function. Next, the authors consider a multiplicative noise with a complex phase (i.e. both the amplitude and phase of the SAR signal are contaminated) that varies linearly with respect to the radar signal's temporal frequencies. The two wave equations governing the SAR signal at two temporal frequencies of the radar signal are combined to derive a method to reconstruct the complex phase error function.

An inversion method is presented for bistatic synthetic aperture radar imaging. The method is based on a Fourier analysis (Doppler processing) of the bistatic synthesized array's data followed by a phase modulation analysis of the Doppler data. The Doppler data are shown to provide samples of the reflectivity function's spatial Fourier transform within a band that depends upon the bistatic angles and ranges. Finally, the bistatic SAR inversion is used to formulate an inversion for multistatic measurements made along a physical linear array due to a single transmission to image a dynamic object.>

A perturbation method is presented for reconstructing phase from uncorrupted amplitude measurements in synthetic aperture radar (SAR) imaging via a wave equation governing SAR data and a Riccati equation that relates the amplitude and phase functions of SAR data. The two wave equations governing SAR data at two temporal frequencies of the radar signal are combined to derive a method to reconstruct complex phase errors, i.e., fading as well as loss of coherence, that vary linearly with respect to the radar signal's temporal frequencies.>

A system model and its corresponding inversion for synthetic aperture radar imaging are presented. The system model incorporates the spherical nature of a radar's radiation pattern at far field. The inverse method based on this model integrates the recorded signals at various coordinates of a translational radar (linear array) via a spatial Fourier transform. The transformed data are shown to provide samples of the spatial Fourier transform of the target's reflectivity function. The inverse method can be modified to incorporate deviations of the radar's motion from its prescribed straight-line path. These principles are also applicable in inverse synthetic aperture imaging of a rotational target (circular array).>

Addresses the problem of reconstructing an image from two pairs of its orthogonal projections. The range and support information of the image function is utilised in conjunction with the available projections to develop an iterative reconstruction method; the iterative algorithm is an error energy reduction scheme. Reconstruction results for two classes of image functions are presented.>

Examines the implications of reconstruction based on measurements of echoed waves from an object. The Helmholtz wave equation model is used for the inversion (diffraction imaging). It is shown that the resultant inverted data provides coverage in a one-quadrant of the spatial frequency domain. This coverage yields accurate information regarding the surface structure of the object under study.>

This paper addresses the problem of reconstructing a bandlimited signal from a finite number of its unevenly-spaced sampled data. We present the main results for a Fourier analysis of the available data [10] done in a framework similar to Shannon's sampling theorem for evenly-spaced data. The results are then utilized to determine the required constraints and algorithms for accurate reconstruction.

This paper addresses the problems of image reconstruction in fan beam straight-path tomography from complete and incomplete data. A method for restoring the parallel beam projections of an object from its fan beam projections is introduced. The scheme utilizes FFT routines for this purpose. It is shown that the approach reduces the required amount of the collected fan beam data by half. Moreover, a noniterative method of image reconstruction, when arbitrary segments of the object projections cannot be detected, is presented. The technique exploits the functional properties of the object projections, in conjunction with a priori information available about the test object, to restore the unknown data.

This paper presents a new view of the problem of image reconstruction in the spatial Fourier domain based on the generalized projections of a two-dimensional image. The algorithms that are presented are derived from the exact continuous relations between the Fourier transforms of a spatially limited image and those of its generalized projections. A Fourier domain reconstruction formula is derived that is a natural consequence of these relations giving values of the two-dimensional transform on a regular grid useful for inverse FFT. This approach is contrasted with the more ad hoc methods of Fourier domain interpolation and with the spatial domain approaches such as the backprojection and backpropagation methods.

Theoretical, algorithmic and experimental results on the use of Rytov's approximation in acoustic tomography are presented. The approximation error is related to the disturbance size and magnitude. A method of phase unwrapping which is based on a combination of profile to profile phase comparison coupled with some well-known phase unwrapping algorithms used in signal processing is introduced. Frequency and spatial domain reconstructions are compared with respect to computational efficiency and accuracy of interpolation.

Methods that include diffraction effects are discussed for the tomographic reconstruction of the complex index of refraction within a soft-scattering object. The methods are Fourier-domain based and are threfore computationally efficient. An important signal-processing issue is shown to be the determination of the unwrapped phase of the sensed fields. The theoretical presentation is followed by examples of experimental results.