Irving S. Reed

Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution

A constant false alarm rate (CFAR) detection algorithm (see J.Y. Chen and I.S. Reed, IEEE Trans. Aerosp. Electron. Syst., vol.AES-23, no.1, Jan. 1987) is generalized to a test which is able to detect the presence of known optical signal pattern which has nonnegligible unknown relative intensities in several signal-plus-noise bands or channels. This test and its statistics are analytically evaluated, and the signal-to-noise ratio (SNR) performance improvement is analyzed. Both theoretical and computer simulation results show that the SNR improvement factor of this algorithm using multiple band scenes over the single scene of maximum SNR can be substantial. The SNR gain of this detection algorithm is compared to the previously published one. It illustrates that the generalized SNR of the test using the full data array is always greater than that of using partial data array. The database used to simulate this adaptive CFAR test is obtained from actual image scenes. >

A multistage representation of the Wiener filter based on orthogonal projections

The Wiener filter is analyzed for stationary complex Gaussian signals from an information theoretic point of view. A dual-port analysis of the Wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the Wiener filter using a nested chain of scalar Wiener filters. This new representation of the Wiener filter provides the capability to perform an information-theoretic analysis of previous, basis-dependent, reduced-rank Wiener filters. This analysis demonstrates that the cross-spectral metric is optimal in the sense that it maximizes mutual information between the observed and desired processes. A new reduced-rank Wiener filter is developed based on this new structure which evolves a basis using successive projections of the desired signal onto orthogonal, lower dimensional subspaces. The performance is evaluated using a comparative computer analysis model and it is demonstrated that the low-complexity multistage reduced-rank Wiener filter is capable of outperforming the more complex eigendecomposition-based methods.

On a moment theorem for complex Gaussian processes

A general theorem is provided for the moments of a complex Gaussian video process. This theorem is analogous to the well-known property of the multivariate normal distribution for real variables, which states that an n th order central product moment is zero if n is odd and is equal to a sum of products of covariances when n is even.

A Detection Algorithm for Optical Targets in Clutter

There is active interest in the development of algorithms for detecting weak stationary optical and IR targets in a heavy opticalclutter background. Often only poor detectability of low signal-to-noise ratio (SNR) targets is achieved when the direct correlation method is used. In many cases, this is partly obviated by using detection with correlated reference scenes [1, 2].This paper uses the experimentally justified assumption that most optical clutter can be modeled as a whitened Gaussian randomprocess with a rapidly space-varying mean and a more slowlyvarying covariance [2]. With this assumption, a new constant falsealarm rate (CFAR) detector is developed as an application of the classical generalized maximum likelihood ratio test of Neyman and Pearson. The final CFAR test is a dimensionless ratio. This test exhibits the desirable property that its probability of a false alarm(PFA) is independent of the covariance matrix of the actual noiseencountered. When the underlying noise processes are complex intime, similar considerations can yield a sidelobe canceler CFARdetection criterion for radar and communications. Performance analyses based on the probability of detection (PD)versus signal-to-noise ratio for several given fixed false alarm probabilities are presented. Finally these performance curves are validated by computer simulations of the detection process which use real image data with artificially implanted signals.

The use of finite fields to compute convolutions

A transform is defined in the Galois field of q^2 elements GF(q^2) , a finite field analogous to the field of complex numbers, when q is a prime such that (--1) is not a quadratic residue. It is shown that the action of this transform over GF(q^2) is equivalent to the discrete Fourier transform of a sequence of complex integers of finite dynamic range. If q is a Mersenne prime, one can utilize the fast Fourier transform (FFT) algorithm to yield a fast convolution without the usual roundoff problem of complex numbers.

A new CFAR detection test for radar

In a well-known paper [2], Reed, Mallett, and Brennan (RMB ) discuss an adaptive procedure for the detection of a signal of known form in the presence of noise (or interference) which is assumed to be Gaussian, but whose covariance matrix is totally unknown. Two sets of input data are distinguished and are called for convenience the primary and the secondary input data. The primary data allow for the possibility of signal presence, while the secondary inputs are assumed to contain only noise, independent of and statistically identical to the noise components of the primary data. In the RMB procedure, the secondary inputs are used to form an estimate of the noise covariance, from which a weight vector for the detection of the known signal is determined. This weight vector is applied then to the primary data in the form of a standard colored-noise matched filter. The implication is that the output of this filter is compared with a threshold in order to achieve signal detection. However, no special rule is given for the determination of the threshold needed to control the probability of a false alarm ( PFA ) . In [l] Kelly used the generalized likelihood ratio to derive a hypothesis test for the above problem. This test exhibits the desirable property that its PFA is independent of the covariance matrix (level and structure) of the actual noise encountered; i.e., it is a CFAR (constant false alarm rate) test. However, the derivation of Kelly’s test statistic is complicated. A new related test is developed in this paper. This test is based on the optimal decision rule for a known signal template and a known noise covariance matrix. Then this classical test variable is normalized to have a unit variance. In the usual case of an unknown noise covariance matrix, the maximum likelihood estimate

Optical moving target detection with 3-D matched filtering

Three-dimensional (3-D) matched filtering has been suggested as a powerful processing technique for detecting weak, moving optical targets immersed in a background noise field. The procedure requires the processing of entire sequences of frames of optical scenes containing the moving targets. The 3-D processor must be properly matched to the target signature and its velocity vector, but will simultaneously detect all targets to which it is matched. The results of a study to evaluate the 3-D processor are presented. Simulation results are reported which show the ability of the processor to detect targets well below the background level. These results demonstrate the capability and robustness of the processor, and show that the algorithms, although somewhat complicated, can be implemented readily. Some effects on the number of frames processed, target flight scenarios, and velocity and signature mismatch are also presented. The ability to detect multiple targets is demonstrated. >

Application of Three-Dimensional Filtering to Moving Target Detection

The standard approach to the detection of a stationary target immersed within an optically observed scene is to use integration to separate the target energy from the background clutter. When the target is nonstationary and moves with fixed velocity relative to the clutter, the procedure for integrating the target signal is no longer obvious. In this paper it is shown that the problem of tracking a target having a fixed velocity can be cast into a general framework of three-dimensional filter theory. From this point of view, the target detection problem reduces to the problem of finding optimal three-dimensional filters in the three-dimensional transform domain and processing the observed scene via this filtering. The design of these filters is presented, taking into account the target, clutter, and optical detection models. Performance is computed for a basic clutter model, showing the effective increase in detectability as a function of the target velocity. The three-dimensional transform approach is readily compatible with VLSI array processing technology.

A comparison of VLSI architecture of finite field multipliers using dual, normal, or standard bases

Three different finite-field multipliers are presented: (1) a dual-basis multiplier due to E.R. Berlekamp (1982); the Massey-Omura normal basis multiplier; and (3) the Scott-Tavares-Peppard standard basis multiplier. These algorithms are chosen because each has its own distinct features that apply most suitably in particular areas. They are implemented on silicon chips with NMOS technology so that the multiplier most desirable for VLSI implementation can readily be ascertained. >

Comparative performance analysis of adaptive multispectral detectors

The fully adaptive hypothesis testing algorithm developed by I.S. Reed and X. Yu (1990) for detecting low-contrast objects of unknown spectral features in a nonstationary background is extended to the case in which the relative spectral signatures of objects can be specified in advance. The resulting background-adaptive algorithm is analyzed and shown to achieve robust spectral feature discrimination with a constant false-alarm rate (CFAR) performance. A comparative performance analysis of the two algorithms establishes some important theoretical properties of adaptive spectral detectors and leads to practical guidelines for applying the algorithms to multispectral sensor data. The adaptive detection of man-made artifacts in a natural background is demonstrated by processing multiband infrared imagery collected by the Thermal Infrared Multispectral Scanner (TIMS) instrument. >