The Astronomical Journal, 130:1951–1960, 2005 October # 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A.
MATCHED FILTER PROCESSING FOR ASTEROID DETECTION Peter S. Gural Science Applications International Corporation, 4501 Daly Drive, Suite 400, Chantilly, VA 20151;
[email protected]
and 1
Jeffrey A. Larsen and Arianna E. Gleason 2 Lunar and Planetary Laboratory, University of Arizona, 1629 East University Boulevard, Tucson, AZ 85721;
[email protected],
[email protected] Received 2004 March 9; accepted 2005 June 13
ABSTRACT Matched filter (MF) processing has been shown to provide significant performance gains when processing stellar imagery used for asteroid detection, recovery, and tracking. This includes extending detection ranges to fainter magnitudes at the noise limit of the imagery and operating in dense cluttered star fields as encountered at low Galactic latitudes. The MF software has been shown to detect 40% more asteroids in high-quality Spacewatch imagery relative to the currently implemented approaches, which are based on moving target indicator (MTI) algorithms. In addition, MF detections were made in dense star fields and in situations in which the asteroid was collocated with a star in an image frame, cases in which the MTI algorithms failed. Thus, using legacy sensors and optics, improved detection sensitivity is achievable by simply upgrading the image-processing stream. This in turn permits surveys of the nearEarth asteroid (NEA) population farther from opposition, for smaller sizes, and in directions previously inaccessible to current NEA search programs. A software package has been developed and made available on the NASA data services Web site that can be used for asteroid detection and recovery operations utilizing the enhanced performance capabilities of MF processing. Key words: methods: data analysis — minor planets, asteroids — techniques: image processing
1. INTRODUCTION
NEA detection rates via software, using legacy telescope systems and detectors. Asteroid detection can be characterized as searching for moving targets in a star-cluttered background. Due to the short timescales between exposures, asteroids can be assumed to maintain a fairly constant intensity and follow a uniform-velocity, linear track across the field of view. The background star clutter has a spatial frequency content similar to that of the asteroids, along with an underlying noise component that can depend on pixel value and star scintillation. Local and global levels of the background can change with time due to variable seeing conditions during multiple exposures. All these effects must be dealt with to maximize the probability of detection for the surveying system. This paper attempts to address these aspects and is broken into several parts covering the MF detection formulation, imageprocessing steps, and finally a discussion on performance results on several data sets covering a variety of NEA detection issues. The software developed for this work is entitled SALTAD (SAIC Algorithm Test Bed for Asteroid Detection) and comprises a set of C function modules that were used to explore various imageprocessing algorithms during the course of this development. It has been tested extensively on the archived imagery of the University of Arizona’s Spacewatch project. A current version of the software is available from the NASA data services Web site or from the authors.
The detection of near-Earth asteroids (NEAs) has taken on special significance for both NASA and the general public in recent years. Clearly, the need to measure and catalog all potential Earth impactors to avoid a global catastrophe is of paramount concern to humankind and is reflected in NASA’s goal to discover 90% of NEAs measuring 1 km or larger by 2008. When this paper was written it had been estimated that just over half of that goal had been achieved, but now the search will get more difficult, as the larger and brighter objects have already been discovered (Jedicke et al. 2003). To push the discovery rate along at a greater rate, a larger volume of space needs to be surveyed to a deeper limiting magnitude. Although improving the limiting magnitude of the telescopic systems used is not an absolute requirement for the larger planet-killer surveys (area or sky coverage has been emphasized), having a fainter detection limit allows one to discover and track asteroids farther from solar opposition and/or farther in distance from the Earth. Improving the limiting magnitude of detection also leads one into the next phase of the surveys, that is, the discovery of smaller NEAs down to a size of 100 m across, which can produce significant destruction on a regional scale. In addition, being able to survey regions of space currently avoided by the NEA survey teams (i.e., densely cluttered star fields around the Milky Way) would also help in opening up the volumetric coverage needed to enhance asteroid detection probabilities. These issues are what provided the motivation to develop, test, and field a matched filter (MF) image-processing procedure to increase
2. MATCHED FILTER FORMULATION The systematic detection of NEAs has grown in scope and sophistication since the first Spacewatch project survey techniques of Rabinowitz (1991) using a 0.91 m telescope, drift scanning, and simple change detection algorithms. Currently, surveys are being performed by the Spacewatch team in Tucson, the Lincoln Near Earth Asteroid Research (LINEAR) project in New
1 Current address: Department of Physics, United States Naval Academy, Annapolis, MD 21401. 2 Current address: Lawrence Berkeley National Laboratory and Department of Earth and Planetary Sciences, University of California, Berkeley, CA 94720.
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Mexico, the Lowell Observatory Near Earth Object Survey (LONEOS) system in Flagstaff, and the Near Earth Asteroid Tracking (NEAT) project on Maui and Palomar. While CCD sensitivities have improved and larger aperture instruments have been brought to bear on the NEA problem, the basic tenet of using moving target indicator (MTI) techniques and/or thresholding on every image frame and forming an object/cluster map remains with us today. The reason is simple: MTI algorithms are easy to implement, can be made fairly robust to image artifacts, and are computationally very fast compared to other more sophisticated algorithms. Thus, detection lists of newly found objects are available to the asteroid hunter literally moments after the last image frame has been collected. Since it is desirable to do same-night reimaging of newly detected, high angle rate NEAs in order to refine their orbital elements sufficiently to ensure next-night recovery, waiting for the following night is sometimes not a viable option. Thus, short-term recovery operations, computational resource limitations, and a legacy of obtaining quick-look results drives the philosophy to continue using fast but less sensitive computational methods. Data for asteroid detection typically involve multiple (three to five) two-dimensional spatial images taken over a sequence of known time steps. Current NEA search techniques essentially process each collected image frame separately by thresholding each image to form lists of objects and their positions. These lists either are compared on a frame-by-frame basis to weed out common objects (Spacewatch), are compared with a star catalog to eliminate known objects (LONEOS), or have the background suppressed prior to object cluster formation (LINEAR). In all cases the remaining set of ‘‘unique’’ objects within each frame are then tested with a ‘‘velocity matching’’ technique that looks for any objects shifting in a linear fashion across the temporal sequence of frames. It should be noted that this is not matched filtering as defined in the signal processing community but a technique referred to as ‘‘detect-before-track.’’ This method of frame-by-frame thresholding followed by a velocity match is currently employed by all the NEA facilities and is characterized by its extremely fast processing and low memory requirements, and has thus been well suited to the computational hardware available in the past. However, Moore’s Law has provided ever increasing CPU speeds and the availability of low cost clusters of small computers, permitting one to consider more sophisticated and computationally intensive image-processing solutions to NEA detection and tracking. The MF techniques described herein fall into a class of algorithms referred to as ‘‘track-before-detect’’ or ‘‘multiple hypothesis testing.’’ Essentially, they attempt to integrate up signal energy based on a hypothesis of the target’s spatial-temporal signature. In the case of asteroid detection, this involves summing the imagery across several frames, after hypothesizing a preselected motion speed and direction and shifting and stacking the frames appropriately. If the motion is fast enough, the asteroid can also smear across a single frame, and so a spatial sum can be attempted along the trail in the direction of motion to provide addition signal gain. The multiframe sum in space and time is then thresholded to find the objects that match the hypothesized motion. This is repeated for every realizable motion hypothesis that an asteroid could take in the imagery. As the position, speed, and direction of undiscovered asteroids are unknown, the size of the hypothesis set grows dramatically in an asteroid search program, as does the associated computational load. This last point is why MF processing has not been a viable option until just recently. In addition, the image-processing steps involve storing a large number of intermediate imagery prod-
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ucts (mean and mean-subtracted imagery, covariance estimates, whitened data frames, stacked imagery, and noise estimates) that require significant amounts of computer memory. With modern PCs and careful implementation of the MF algorithms, both the computational run time and memory usage limits are now no longer significant issues preventing the use of such algorithms. The MF algorithm incorporated into the SALTAD software was based on the formulation originally presented by Mohanty (1981), who first applied this technique to satellite detection in background star fields. It is generally considered to be an optimal detection method in idealized environments with known noise characterization and a priori knowledge of the spatial-temporal signal behavior. Published variants and enhancements of this general approach have been reported in the literature by Kelly (1986), Barniv (1985), Barniv & Kella (1987), Lampropoulos & Boulter (1987), Reed et al. (1988), Pohlig (1989, 1992), Chen (1989), Porat & Friedlander (1990), Auerbach et al. (1996), Ralston et al. (1996), Watson & Watson (1997), and SandersReed (1998). The basic methodology involves a two-step algorithm in which the first stage performs mean removal and background clutter suppression, followed by a second stage incorporating an adaptive MF and detector to enhance the signal component. Information about the individual preprocessing, intermediate, and postprocessing steps is reviewed in greater detail in x 3 as it pertains to the SALTAD software implementation for NEA detection. At this point, the discussion follows the more general Mohanty (1981) formalism for MF detection, and the reader can refer to his paper for the finer details. Given a sequence of image frames V(k) for time index k ¼ 1, : : : , N (the use of bold italic symbols herein represents twodimensional spatial pixels in images that have been lexigraphically reordered), one forms an image mean hV i to be used for the removal of stationary and nonfluctuating image components across the field of view for all time steps. The mean-subtracted data V(k) hV i, however, can typically have a locally changing noise variance (e.g., due to star scintillation, hot pixels, or spatialtemporal changing sensitivity and seeing), and thus, a ‘‘whitening’’ step is usually applied to achieve a more uniform noise level across the scene. To whiten the data, the second-order noise statistics of the imagery is obtained through the estimation of the noise covariance matrix R. Applying the root-inverse of the noise covariance to the mean-subtracted data provides the whitened (clutter suppressed) imagery through the application of equation (1) at each time step k: whitened image frame ¼ R1=2 ½ V ðk Þ hV i:
ð1Þ
To form the MF, a spacetime template T(k) of the signal signature must be hypothesized. This can include the effects of motion within a frame’s collection period, motion between frames, and the signal intensity fluctuations. For an unresolved, constantvelocity, uniform-intensity target this can be formulated as a single pixel set to a signal value in a given frame with a linear spatial displacement occurring temporally across frames. This is the simplest model that is applicable to asteroid searches and one that works well for NEA detection. The signal template must also be whitened by the same noise covariance used previously, thus producing R1/2T(k). Dropping the temporal index k, the generalized MF output can then be simply written with the full covariance inverse as M ¼ T H R1 ðV hV iÞ;
ð2Þ
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For detection, the MF is scaled by a normalization term, namely, T HR1T, and the ratio TRT as expressed in equation (3) is a signal-dependent test relative to some threshold that yields an acceptable false-alarm rate: TRT ¼
M > : T H R1 T
ð3Þ
The signal intensity is another unknown that would need to be hypothesized along with the asteroid’s position, speed, and direction. To avoid the additional computational burden from hypothesizing a wide range of signal levels, the MF detector is very often formulated with a squared numerator, applying a constantintensity assumption (in space and time) to make the resulting ratio TRTSQ independent of signal brightness (see eq. [4]): H 1 2 T R ðV hV iÞ ; ð4Þ TRTSQ ¼ T H R1 T or alternatively using a maximum likelihood estimate MLE ¼
ð M Þ2 > ; Var(M )
ð5Þ
as was selected for the first-pass SALTAD detection processing. Thus the MF output is used in a constant false-alarm rate (CFAR) style detector, where the denominator is replaced by a local variance estimate of the MF statistic in a region around the pixel under test (see eq. [5]). For example, either a localized donut region or even a global estimate could be used. For an unresolved point target covering a single pixel per frame, the variance estimate from each individual frame could also be simply shifted and stacked (via the template operator T ) in a variety of ways. Some implementations that were tried were found to be successful and highly computationally efficient. As the intensity-independent form of the MF (eq. [4] or [5]) can suffer false alarms from bright, multiple targets in the same field of view (as typically occurs in asteroid imagery), this test is used only as a first-pass screener before applying the more robust signal-dependent test of equation (3). Given a handful of first-pass detections arising from equation (5) and knowing the associated motion hypothesis used, the signal intensity can be estimated from the data, and the signal-dependent form of equation (3) can be generated for a dramatically reduced number of test points. Final screening algorithms can also be applied in a postprocessing mode to help mitigate the false-alarm rate. 3. IMAGE-PROCESSING STREAM FUNCTIONALITY AND ISSUES The SALTAD software is an implementation of the clutter suppression and matched filtering processes very generally described in x 2. The software was designed as a test bed that allowed the development and testing of various algorithmic formulations in an end-to-end processing scenario. Many of the details that result in a successful application of MF processing to NEA detection are discussed in the next few subsections. What follows is a module-by-module description of the most successful algorithms used during the software development, as well as suggestions for improvement and issues that arose. It should be pointed out that the LINEAR image processing stream as described in Viggh et al. (1998) and Stokes et al. (2000) is very similar to the preprocessing and clutter suppression in the sections that follow. We attempt, however, to describe the methodology in far greater detail, as it is a necessary and integral part
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of the follow-up processing steps involving matched filtering and detection. We do this because MF processing has not been applied in asteroid search programs to date. To minimize the size of this paper, various imagery examples generated through each stage of the processing have not been included but can be found instead in Gural (2003), published as a NASA technical report. 3.1. Preprocessing The first step in processing any imagery is to input and store in computer memory the multiframe sequence of data. For SALTAD, a FITS file format interface was developed to be compatible with reading the Spacewatch data archives. In addition, a simple yet uniform C language data structure for the imagery was developed that could be used consistently at any product stage in the processing stream. This allowed for a simple and uniform interface between each processing module. Given a sequence of raw imagery stored in system memory, one must preprocess the data to remove pixel artifacts, register the frames spatially, and equalize the background intensities. No capability was incorporated into SALTAD for image cleanup, but the removal of bright pixel singletons and other image flaws and artifacts can go a long way to mitigating false-alarm detection in the final processing stages. Once cleaned, the imagery sequence needs to be registered to align the frames spatially. For stellar imagery this can be readily accomplished, as known star positions provide well-localized tie points for registration algorithms. Due to the small field of view typically encountered in asteroid searches, a quadratic warp-fitting function was found adequate for the interpolation necessary to create a set of registered frames. Remapping with a second-order warp in conjunction with subpixel stellar centroiding accuracy yielded the best performance in the later processing stages involving matched filtering. Registration is a critical area for MF processing, as misregistration causes signal-to-noise ratio (S/N) loss; thus, even higher order registration techniques and using Lagrange or sinc function interpolation are highly recommended, although they were not tried during this project. A critical area of preprocessing that is not documented in the MF literature involves the need to equalize the imagery. To address changes in frame-to-frame signal level from variable seeing or integration time, the frames must be normalized to obtain the same generalized signal and background counts. This was most successfully implemented using a local background estimator (starless mean), with each frame scaled to achieve the same level as a reference frame (first image). The starless mean was found by forming the mean and standard deviation of a region of pixels, removing those pixels in the next iteration that were greater than 2 from the mean, and repeating the procedure until convergence. Typically, only three iterations were necessary to obtain a good starless background estimate for each frame, which was then scaled relative to the reference background of the first frame. 3.2. Clutter Suppression As indicated in equation (1), to whiten the imagery a mean image must be removed from the sequence of image frames. Due to the high spatial frequency content of the star fields, spatially averaging the nearest neighboring pixels (averaging in both space and time) does not perform well at eliminating stationary objects such as stars and galaxies in the field. Instead, a temporalonly average should be formed, which can be problematic when there are very few frames available. Also, the presence of the asteroid in the very frames one is using to estimate the mean causes a loss in S/N when the mean is removed from each frame
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(known as signal capture loss). The successful solution is to use only that subset of frames that does not include the target signal. This is done by eliminating from the temporal average for each spatial pixel the frame with that pixel’s highest value (assuming that the highest pixel in time contains the signal) and averaging the remaining frames. This procedure is suboptimal, as it tends to underestimate the mean, resulting in incomplete star and background removal, but it is found to work far better than other simple averaging techniques. With the mean removed from each temporal frame, the secondorder noise statistics must be estimated to form a noise covariance matrix. Several approaches were tried, including attempts to model any nearest-neighbor spatial and/or temporal correlations in the noise. Most performed no better than a fully uncorrelated assumption, which yields a diagonal covariance matrix. The variance of a given pixel using its 3 ; 3 nearest neighbors and N time frames (again with the brightest pixel removed) forms an estimate of the covariance’s diagonal element representing the variance of that pixel. Inversion of the covariance becomes a simple procedure, as does application of the inverse to the mean-subtracted data. The resulting whitened data set suppresses regions of high variance in the field such as around scintillating stars, noisy pixels, or poorly mean-subtracted regions. The next step involves the hypothesis of a motion model for the asteroid and the formation of the MF output. This is typically followed by the convolution of the system point-spread function (PSF) across the field prior to detection testing. To save computation time, one can perform the PSF convolution directly on the whitened data so that it need not be repeated for each hypothesis. This can be done only if the asteroid can be assumed to be unresolved in the imagery (represented by a single pixel at each time step). For asteroid searches this is usually the case and was the assumption made in the current release of SALTAD. This decision was made because it reduces run-time costs in two ways. First, with the PSF convolution operation pulled outside the hypothesis loop, which can involve several thousand motion templates, lower computational loading is achieved for no loss in performance. Second, even if the asteroid is trailed spatially, one can still detect it with a point motion model because of the gain obtained by integrating temporally across frames (although suboptimally, since we are lacking the spatial integration gain). Typically, the spatial integration would help enhance an extremely faint trailed object, but the human operator would have a difficult time verifying its existence by visual inspection. In addition, one could take advantage of the significant reduction in the number of required speed hypotheses that occurs for fast trailed objects, as pointed out by Chen (1989). Essentially, as an object moves with a higher apparent angular rate, its trail in a given frame becomes longer, and the next speed hypothesis can take a jump of several pixels per frame rather than the fraction of a pixel per frame normally used. Reducing the hypothesis set through exponentially expanding speed increments and lowering the computational load within the hypothesis loop are two of the more significant contributions to obtaining reasonable run times on modern PCs. 3.3. Matched Filter Processing To carry out MF processing, a set of hypothesis templates must be formed that span the realizable possibilities of asteroid position, speed, and direction. For ground-based asteroid searches, in which the time between frames is usually less than an hour, the motion can be well approximated by a linearly propagating track. Curvature can come into play if the time span is on the order of a day (due to Earth’s motion relative to the asteroid)
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Fig. 1.—Baseline detection performance of the MF algorithm of SALTAD as a function of the hypothesis step size. The open and gray bars correspond to new detections, whereas the black bars are MF detections that matched previously found MTI Spacewatch detections.
or in a space-based search system, which induces parallax effects due to the satellite’s motion around the Earth. SALTAD is currently implemented with only a linear motion hypothesis but could be upgraded to include more complicated motion effects. Given the linear motion template and assuming an unresolved point target, the MF formulation simply reduces to a shift and stack operation in the spacetime domain. That is, each frame is simply shifted in the two spatial dimensions relative to the first frame by an amount corresponding to the hypothesized motion shift for that frame. Each shifted frame is then added to a running sum frame that produces the MF output of equation (2). Note that the frames used are the whitened-PSF-convolved data set. To actually shift the frames, another interpolation is required to remap the imagery at each time step. For this stage the algorithms used were nearest neighbor and bilinear interpolation. Half-pixel step sizes for the lowest speed hypothesis were found to produce the greatest detection performance, as seen in Figure 1, but increasing this to full pixel steps resulted in a loss of only 10% in the numbers of asteroids found in the imagery. Full-pixel shifts are desirable from a computational standpoint since the shifting and stacking operation involves no interpolation (simple address shift to align frames) and is thus a very significant run-time advantage. Note that subpixel shifting with bilinear interpolation is an option in the SALTAD package if run-time performance is not a limiting factor. An alternative to spatial shifting and stacking is to do spatial Fourier processing on the sequence of images (take twodimensional fast Fourier transforms of each image). The linear motion of an object in Fourier space appears as a plane of energy at a different angle relative to the background clutter. Applying the motion hypothesis template in the Fourier domain is a simple matter of taking the point-by-point product of the Fouriertransformed hypothesis template with the Fourier-transformed images and inverse transforming, getting the integrated signal energy for all asteroid starting positions. For a limited hypothesis set and large dimensional spatial imagery, this can be a computational advantage. At this time, however, SALTAD does not support this mode of processing. Given the MF output, a first-pass test for detection is made using the maximum likelihood detector form of equation (5). In this case a CFAR detector is used, where a donut region around the pixel under test is used to form a variance estimate locally. The MF output of the pixel squared is then tested for whether it exceeds a user-defined factor applied to the variance. If this threshold is passed, the robust detection parameter of equation (3) is
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Fig. 2.—Detections and false alarms for the two detection statistics TRT and MLE on a sample Spacewatch data set. Crosses show false alarms, filled circles show new MF detections, and open circles show MF detections that were also MTI detections.
computed by estimating the signal strength once the track has been localized. It has been found that combining the two test statistics into a single cost function to make the final detection decision yields the best performance of detection probability versus false-alarm rate (see the example in Fig. 2). Currently, applying a threshold using the expression shown in equation (6), which combines the outputs of equations (3) and (5), has produced a good detection cost function: 0:37MLE þ 0:93TRT > threshold:
ð6Þ
The threshold is set by the asteroid hunter/operator to control the degree of false alarms tolerated in a postprocessing human screening. 3.4. Postprocessing and Run-Time Efficiencies As the detected asteroids approach closer in signal energy to the noise background, a higher percentage of false alarms leak through, as with any detector. To help mitigate some of these, a postdetection screening of the tracks is made in software prior to final reporting. This is done by culling out those detected trails that do not possess a reasonably constant light curve, as is assumed for most asteroid tracks measured over short time frames. Tests are made back at the individual frame-to-frame imagery level to examine signal levels once the target position and track are known and localized in spacetime. Thus, some a priori information about the spatial-temporal characteristics of real asteroid light curves can be of significant importance. A declustering step is also applied to eliminate nearest-neighbor detections of the same asteroid, as well as a detection list culling step after each hypothesis is completed to eliminate common asteroid detections from similar but not identical hypothesis models. In the case of Spacewatch operations, a human-in-the-loop does an additional final scan to determine the validity of any software-discovered asteroids through a visual inspection. It has been noted that the MF processing capabilities have pushed the detection limit so close to the noise floor that it is becoming more difficult for operators to confidently validate software-based asteroid detections based on visual cues alone. Ultimately, this could be the limiting factor in how many fainter asteroids are actually found for a given system sensitivity.
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To create a software package that could perform adequately on a modern 2 GHz PC, a number of computational inefficiencies were addressed relative to the initial proof-of-concept implementation. Most of the array-processing modules have been rewritten to be more highly optimized in code. For example, specific routines were generated for three, four, or five image frames with efficient pointer-style addressing in addition to those functions for a generic number of N frames. Instead of computing standard deviations via square root operations or thresholds in decibels via logarithmic operations, the formulations were rewritten to avoid these function evaluations, which can be computational hogs. All the high-bandwidth data processing currently involves only floating point additions and multiplications, with division operations shunned whenever possible. Finally, sorting processes were reformulated to more efficiently cull out nearly identical hypothesis detections and remove multiple finds of the same asteroid. Each step of the processing chain was reviewed and revised where significant run-time issues appeared. The resulting improvement in run time from the initial implementation was on the order of a factor of 8, with no loss in detection performance. In addition, restricting the hypothesis speed steps to integer shifts (rather than half-pixel steps) improved run time by an additional factor of 4, with only a modest 10% loss in detection efficiency. The approximate run time on a single PC for processing three frames of 2K ; 2K imagery was 10 minutes using a 2 GHz class Pentium IV, which for an archived Spacewatch image of 48 million pixels in size would require 2 hr to process. This was considered to be approaching a usable range of processing time. Since the algorithm is embarrassingly parallelizable by working subimages on separate processors, implementation on a networked cluster of PCs (e.g., Beowulf cluster) would allow for near real-time output of detection lists. Run-time numbers using the newly installed Spacewatch Beowulf cluster were 5 minutes with four 1.2 GHz Pentium III processors per 2K ; 2K subimage. (Pentium III processors are used because they run cooler at high-elevation observatories, where the thin atmosphere affects their cooling capacity.) One issue with matched filtering in normal NEA search operations is that the first detections are not available until the last image has been collected. So, unlike MTI, in which each image is processed immediately after collection and the final unique object list is processed for velocity matching as a last step, the MF begins its processing only after the final image collection in a data sequence. Thus, there will be a time lag before first detection reports are available, but a second image set can be collected while the first is being processed. This will require a change in the daily operations procedures for some NEA survey sites that may employ the MF mode of processing with a limited amount of computing resources. 4. DETECTION PERFORMANCE RESULTS As part of the SALTAD software development project at the Science Applications International Corporation (SAIC), there was a performance assessment done by the University of Arizona’s Spacewatch team on a wide variety of archived imagery under varying SALTAD run parameters. The data used in this analysis included 144 frames (12 scans divided into 12 subimages) of survey imagery from the Spacewatch 0.91 m telescope taken under a wide variety of weather conditions, 48 frames from their 1.8 m telescope possessing different noise characteristics, and 50 ‘‘recoveries’’ collected to reacquire a previously discovered asteroid. Evaluations were made of the overall performance of the software in the probability of detecting asteroids, falsealarm rate, limiting magnitude capability, and ability to handle
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Fig. 3.—Cumulative number of detections for fainter (higher magnitude) asteroids using the IMPACT and SALTAD processing software.
high star clutter. The following subsections discuss the first results from that analysis. 4.1. Detection Enhancement in Limiting Magnitude In both the first-year report to NASA by Gural (2003) and the latest performance analysis results generated by the Spacewatch project, the SALTAD MF algorithms have demonstrated an ability to detect a larger number of asteroids at the fainter limits of the telescopic collection system. In a composite result of several processing scans, comparing the MF with MTI algorithms on identical data sets, the cumulative detection of asteroids as a function of magnitude was generated. The software used in the comparison was the latest incarnation of the Spacewatch MTI algorithms embodied in the software package IMPACT. For the MF results, one of the authors (A. G.) ran the SALTAD software, and final detection lists were screened for false alarms by visual verification. In Figure 3 can be seen the results of several such comparisons. Note the dramatic rise in the number of asteroids discovered in the imagery by the MF algorithms starting near 21 mag. In total, 44% more asteroids were located in this set of scans by the SALTAD software at a 50% false-alarm rate. By placing the detections in histogram bins of 0.5 mag, as in Figure 4, it can be seen that the MF extends the limiting magnitude of detection. An exact measure of the degree of improvement is still forthcoming but has been estimated to be nearly 1 full mag. In fact, the effective increase in detection is nearly 100% between
Fig. 4.—Histogram of detections by each software package vs. magnitude bin. SALTAD uses the MF algorithm, and IMPACT uses an MTI algorithm.
Fig. 5.—Evolution of true detections and false alarms for a single data set. Pushing the limits to fainter asteroids shows an increasing false-alarm rate for each new detection (flattening of the curve).
21 and 22 mag. One issue that arose is in the postdetection verification step by the human observer. Since the MF processing has moved the detection limit closer to the noise limit of the imagery, it has created some problems for the human analysts in verifying the visual existence of real asteroid tracks! To achieve these results, however, the analyst needed to screen through a large number of false-alarm candidates. As seen in Figure 5, for the lower curve, for which no preprocessing image cleanup was performed, the bright asteroids (left side of curve) were essentially free from false alarms. As the list of detections from the MF approached the noise limit of the system, however, the increase in false alarms was substantial, reaching levels of greater than 1 false alarm per real detection. The verification screening done by Spacewatch was stopped at a 20:1 false alarm/true detection ratio to determine the limiting magnitude presented in Figures 3 and 4. In reality, an analyst would stop at a far lower false-alarm rate. For example, if a false-alarm rate of 15% of total detections were imposed on the lower curve in Figure 5, then only a modest 22% gain in MF detections would be obtained over those found with the Spacewatch MTI software. Further refinement in the preprocessing and postdetection evaluation by automated means would help to screen out a greater percentage of these false alarms. In many cases image artifacts present in the original raw imagery are the root cause. Bright single-pixel flares in one frame, edge-collection effects produced by the scanning process, or CCD pixel bleed lines from bright stars elsewhere in the field of view can and should be removed prior to application of the image processing stream outlined in this paper. A simple example of this is demonstrated by the upper curve in Figure 5. The application of a hot pixel removal algorithm increased the level of true detections before the false-alarm rate turned the curve over to the right. The net result for MF processing with a preprocessing cleanup step was to extend the detection improvement from 22% to 43% over that of the MTI technique (derived from a comparison of the lower and upper curves in Fig. 5 for a fixed 15% false-alarm rate). In the postdetection processing, the development of an improved joint detection statistic, such as the TRT and MLE combination shown in Figure 2, would also help to separate false alarms from detections in a more robust fashion. Figures 6, 7,
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Fig. 8.—Detection signal strength vs. the combined (eq. [6]) detection statistic, where black circles show detections and gray circles show false alarms. Fig. 6.—Detection signal strength vs. the MLE detection statistic, where black circles show detections and gray circles show false alarms.
Fig. 7.—Detection signal strength vs. the TRT detection statistic, where black circles show detections and gray circles show false alarms.
and 8 respectively show how the asteroid signal strength for detections is distributed among the false alarms for the MLE-only, TRT-only, and combined figure of merit for equation (6), where 27,000 candidates from one scan are combined into a single display. The goal is to maximize separation of the false alarms (gray symbols) from the true detections (black symbols), since a threshold must be drawn across this distribution. Without good separation, accepting more detections by moving a threshold line results in higher numbers of false alarms. For example, in the MLE-only and TRT-only cases, setting a threshold (vertical line) such that all true detections fall to the right of the threshold inadvertently also accepts a large number of false alarms. However, greater separation of detections from false alarms is possible when one uses some combined cost function as seen in Figure 8, in which the thresholding vertical line avoids a large portion of the false-alarm region of the plot. Choosing an improved detection statistic is an area that needs to be explored further, using perhaps other outputs from the processing. Figure 9 is similar to Figure 2 in showing a clearer separation between true asteroids and false alarms by working in a combined MLE and TRT space rather than in either parameter plotted separately against signal strength. It should be noted that the NEAT project has also collected and archived a large sample of asteroid imagery and had supplied
Fig. 9.—Separation of true detections (black circles) from false alarms (gray circles) in TRT/MLE space.
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Fig. 10.—Early Spacewatch detection in a cluttered star field using the SALTAD MF processing. The asteroid is located in the white box.
SAIC with an image set just prior to the completion of this project. The data set processed was collected on 2001 August 1 and consisted of three frames of 4K ; 4K imagery plus the detection list of asteroids found by the NEAT processing system software. After processing was completed, the SALTAD software identified 26 of the 26 previously known asteroids with the addition of five new detections, yielding a 20% improvement in detection performance. The new detections were typically of asteroids in the fainter range of magnitudes previously discovered by NEAT, and the processing yielded very few false alarms. Once again, it was found that image artifacts, in this case an image quadrant filled with numerous hot pixels in the first collection frame, were the cause for reduced detection sensitivity in the quarter of the image space where they existed. However, in good-quality regions of the collected imagery, the software demonstrates improved performance on a Spacewatch-independent collection system and also emphasizes the preprocessing removal of image artifacts as a requirement for reliable MF processing. 4.2. Performance in Cluttered Star Fields One claim for the MF image-processing procedure is that it allows one to detect moving objects even in heavily cluttered backgrounds. The gain is primarily due to the star removal procedure in the clutter suppression step prior to matched filtering. For example, the LINEAR stream follows a similar approach for clutter suppression that has permitted them to make observations near the Milky Way. For an asteroid search in a stellar field, the term ‘‘heavily cluttered’’ corresponds to dense star regions. An MTI technique that searches for stars that appear in common across multiple image frames will exclude an extensive portion of the dense star field and eliminate a large percentage of asteroid tracks due to their close proximity to the myriads of stars. The MF clutter-suppression procedure outlined here attempts to remove the stationary background objects before searching for moving objects of interest, followed by an enhancement of signal energy through temporal integration. The combined effects allow for a significant performance improvement in cluttered fields. First results of asteroid discoveries for which the asteroid was either near or superposed on stars in the field are shown in Figures 10 and 11. In each case the MTI technique would have failed to detect the asteroid motion, and in many cases even very bright asteroids would have been missed. A few dense star-field regions were also processed by the Spacewatch analysts using both the IMPACT and SALTAD software, although this was difficult, as archived Spacewatch imagery typically avoids low Galactic latitudes. In one analyzed scan, the MF detector identified nine asteroids, whereas the MTI
technique located only six. In general, the results were that at least 50% more asteroids were found in the denser star fields. Limiting magnitude and performance characterization in available dense star field image sets are awaiting further analysis. 4.3. Usefulness in Recovery Operations One particular observational procedure for which matched filtering was recognized as being of significant relevance concerned the area of asteroid recovery and tracking. For NEA search methodologies to be useful, one cannot only provide detections of asteroids but must also be able to do high-accuracy astrometry and collect multiple positional measurements over a period of several days. This is required in order to refine the orbital elements of an NEA detection to the point that it can be reacquired during a future favorable observational epoch. Unfortunately, since many faint asteroids are detected at opposition when their signal strength is highest, the days following the discovery can see a fading of the intensity to an undetectable level. Also, the earliest orbital elements from the discovery measurements are not well determined and can only be used in an approximate way to localize the asteroid on the next day’s reacquisition imagery collection. In actual operations, operators have the greatest difficulty in knowing the position in the field that the asteroid will appear in the future. The direction and speed of motion are usually better defined and can be used as a priori information to severely narrow the number of motion hypotheses that need to be performed with the MF. Thus, an entire field of view can be scanned in a matter of seconds by searching over a limited range of directions and apparent angular velocities for the asteroid, undergoing a recovery type search. This eliminates any run-time issues, and the processing can be run at the highest level of detection performance. As an example, the asteroid Apollo 1998 VD35 (one of 538 asteroids classified as potentially hazardous) is shown in Figure 12 not long after its discovery in 1998. During this time its position was relatively uncertain despite its relatively bright magnitude. A full SALTAD analysis of its uncertainty region took 2 minutes and 31 s for all 2563 hypotheses (all possible directions and speeds) on a 2.2 GHz Pentium IV. By using the known rate (between 8.2 and 11.2 pixels of motion between each image) and direction of motion (52 south of east on the sky with an error of 30 assumed), the processing time was cut to 3.7 s. The full usefulness of SALTAD will be realized in searching for much fainter detections with positional uncertainty over a larger region of the sky. Typically, experience has shown that SALTAD will find the moving object if it is observable to the human eye in the image sequence. In addition, with a limited hypothesis set, the
Fig. 11.—Examples of asteroid detections missed by the MTI technique (due to common star/galaxy exclusion regions) yet detected by the MF. Images are displayed using a three-color multiframe display technique (i.e., frame 1 is red, frame 2 is green, and frame 3 is blue; thus, stationary objects appear gray).
Fig. 12.—Example of an asteroid recovery reacquisition of Apollo 1998 VD35 (within the white box).
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false-alarm rates will be dramatically reduced along with runtime costs. 4.4. Conclusions Application of matched filter processing has been shown to improve detection rates in a given set of imagery by roughly 40%, with the greatest gains occurring for the fainter asteroids approaching the limiting magnitude of the imaging system. For Spacewatch imagery, a doubling of the number of asteroids found in a scene occurred between 21 and 22 mag, which will be helpful in the search for NEAs smaller than 1 km or larger NEAs farther away from opposition with the Sun. At issue is the increasing level of false alarms as the image-processing system approaches the limiting magnitude of the data. Improved preprocessing and image cleanup of the data sets is recommended, as well as further study toward forming more robust postprocessing automated screening prior to human verification.
Finally, the application of matched filtering to NEA recovery and tracking operations is a very promising application of this technology for the NEA community and can be fielded with minimal processing capability due to the drastically reduced runtime requirements (very limited hypothesis set) in this mode of operation.
The authors would like to acknowledge Steve Pravdo of the NEAT program for his cooperation in providing further data sets to help execute this program. Furthermore, the Spacewatch project team has also been instrumental in providing data and analysis support and in recognizing the future potential that advanced image processing holds for this field. This work was sponsored by NASA’s Office of Space Science Applied Information Systems Research Program under contract NAS5-01121.
REFERENCES Auerbach, S. P., Hauser, L. E., Boynton, F. P., Janda, R. S., & Sofianos, D. J. Porat, B., & Friedlander, B. 1990, IEEE Trans. Pattern Anal. Machine Intell., 1996, Proc. SPIE, 2759, 25 12, 398 Barniv, Y. 1985, IEEE Trans. Aerosp. Electron. Syst., 21, 144 Rabinowitz, D. L. 1991, AJ, 101, 1518 Barniv, Y., & Kella, O. 1987, IEEE Trans. Aerosp. Electron. Syst., 23, 776 Ralston, K., et al. 1996, Airborne InfraRed Measurement System (AIRMS) Chen, Y. 1989, IEEE Trans. Aerosp. Electron. Syst., 25, 343 Final Report (Arlington: DARPA) Gural, P. S. 2003, Asteroid Search with Advanced Detection Algorithms Reed, I. S., Gagliardi, R. M., & Stotts, L. B. 1988, IEEE Trans. Aerosp. ( NASA Tech. Rep. 20040021361; Hanover: NASA) Electron. Syst., 24, 327 Jedicke, R., Morbidelli, A., Spahr, T., Petit, J., & Bottke, W. F. 2003, Icarus, Sanders-Reed, J. N. 1998, IEEE Trans. Aerosp. Electron. Syst., 34, 844 161, 17 Stokes, G. H., Evans, J. B., Viggh, H. E. M., Shelly, F. C., & Pearce, E. C. Kelly, E. J. 1986, IEEE Trans. Aerosp. Electron. Syst., 22, 115 2000, Icarus, 148, 21 Lampropoulos, G. A., & Boulter, J. E. 1987, Soc. Photo-Opt. Instrum. Eng., Viggh, H. E. M., Stokes, G. H., Shelly, F. C., Blythe, M. S., & Stuart, J. S. 1998, in 3163, 138 Proc. Sixth Int. Conf. and Exposition on Engineering, Construction, and Mohanty, N. C. 1981, IEEE Trans. Pattern Anal. Machine Intell., 3, 606 Operations in Space, ed. R. G. Galloway & S. Lokaj ( New York: Society), 373 Pohlig, S. C. 1989, IEEE Trans. Aerosp. Electron. Syst., 25, 56 Watson, G. H., & Watson, S. K. 1997, Proc. SPIE, 3163, 45 ———. 1992, Maximum Likelihood Detection of Electro-optic Moving Targets ( Tech. Rep. 940; Lexington: MIT), 37
