The detection of moving objects on the ground by airborne radar is one application of space-time adaptive processing (STAP). The goal is to estimate the position and velocity of objects. This paper considers the problem as a linear inverse problem and uses ℓ1-norm regularization to promote sparsity in the solution. It is proposed that the angle-Doppler plane be explicitly segmented into the clutter ridge component and a non-clutter-ridge component. We propose that the second component be modeled as sparse - as the moving objects are assumed to be well isolated in the angle-Doppler plane.

We consider receiver design for doubly-selective, rapidly time-varying channels with the goal of maximizing the signal to noise ratio at the sampling instant. Three types of receivers are studied: the optimum adaptive matched filter that requires accurate channel tracking, a statistical matched filter design, and a receiver concept that approximates the adaptive matched filter by coherently combining the outputs of a limited number of channel eigenfunction filters.

Optimal detection of a target return contaminated by signal-dependent interference, as well as additive channel noise, requires the design of a transmit pulse f(t) and a receiver impulse response h(t) jointly maximizing the output signal to interference plus noise ratio (SINR). Despite the highly nonlinear nature of this problem, it has been possible to show that f(t) may always be chosen minimum-phase. A full analysis concludes with the construction of an effective numerical procedure for the determination of optimal pairs (f,h) that appears to converge satisfactorily for most values of input SINR. Extensive simulation reveals that the shape of f(t) can be a critical factor. In particular, the performance of a chirp-like pulse is often unacceptable, especially when clutter and channel noise are low-pass dominant and comparable.

In this correspondence, a new viewpoint is proposed for estimating an image from its distorted versions in presence of noise without the a priori knowledge of the distortion functions. In z-domain, the desired image can be regarded as the greatest common polynomial divisor among the distorted versions. With the assumption that the distortion filters are finite impulse response (FIR) and relatively coprime, in the absence of noise, this becomes a problem of taking the greatest common divisor (GCD) of two or more two-dimensional (2-D) polynomials. Exact GCD is not desirable because even extremely small variations due to quantization error or additive noise can destroy the integrity of the polynomial system and lead to a trivial solution. Our approach to this blind deconvolution approximation problem introduces a new robust interpolative 2-D GCD method based on a one-dimensional (1-D) Sylvester-type GCD algorithm. Experimental results with both synthetically blurred images and real motion-blurred pictures show that it is computationally efficient and moderately noise robust.

A major issue in space-time adaptive processing (STAP) for airborne moving target indicator (MTI) radar is the so-called sample support problem. Often, the available sample support for estimating the interference covariance matrix leads to severe rank deficiency, thereby precluding STAP beamforming based on the direct sample matrix inversion (SMI) method. The intrinsic interference subspace removal (ISR) technique, which is a computationally and analytically useful form of diagonally loaded SMI method, is derived here. It covers from Hung-Turner (1983) projection (HTP) algorithm to the matched filter according to the loading factor. Also the optimum loading factor which gives the maximum signal-to-interference-plus-noise ratio (SINR) is derived from the viewpoint of singular value decomposition of the covariance matrix. The simulation results with synthetic data show that the maximum SINR indeed coincides with the proposed optimum loading factor in various data sample situations.

A major issue in space-time adaptive processing (STAP) for airborne moving target indicator (MTI) radar is the so-called sample support problem. Often, the available sample support for estimating the interference covariance matrix leads to severe rank deficiency, thereby precluding STAP beamforming based on the direct sample matrix inversion (SMI) method. The intrinsic interference subspace removal (ISR) technique, which is a computationally useful form of diagonally loaded SMI method, can handle this case, although the performance is poor in low sample situations. In this context, new subarray-subpulse schemes using forward and backward data vectors are introduced to overcome the data deficiency problem. It is shown that a multiplicative improvement in data samples can be obtained at the expense of negligible loss in space-time aperture of the steering vector.

We examine the applicability of the previously proposed greatest common divisor (GCD) method to blind image deconvolution. In this method, the desired image is approximated as the GCD of the two-dimensional polynomials corresponding to the z-transforms of two or more distorted and noisy versions of the same scene, assuming that the distortion filters are FIR and relatively co-prime. We justify the breakdown of two-dimensional GCD into one-dimensional Sylvester-type GCD algorithms, which lowers the computational complexity while maintaining the noise robustness. A way of determining the support size of the true image is also described. We also provide a solution to deblurring using the GCD method when only one blurred image is available. Experimental results are shown using both synthetically blurred images and real motion-blurred pictures.

Space-time adaptive array processing has emerged as a key technology thrust area for the next generation of airborne radar systems due to its inherent potential for vastly improving moving target indicator (MTI) performance. Unfortunately, these performance gains come with a commensurate increase in on-line computational complexity if full degree-of-freedom (DOF) space time adaptive processing (STAP) processors are employed. In this paper we introduce a class of efficient STAP processors which exploit the fact that the full DOF space-time clutter covariance matrix is rank deficient with respect to a coherent processing interval.

The paper addresses the problem of identifying the class of all stable system transfer functions that interpolate the given partial impulse response sequence. In this context, classical Pade approximations that are also stable, are shown to be a special case of this general formulation. The theory developed in this connection is utilized to obtain a new criterion for determining the model order and system parameters for rational systems, and, further, to generate nonminimum phase optimal stable rational approximations of nonrational systems from their impulse response sequences.>

In the context of nonrandom parameter estimation from a finite set of observations, the situation associated with weak Cramer-Rao bounds is addressed. It is shown that it is possible to improve the Cramer-Rao bound by incorporating higher-order derivatives of the joint probability density function (PDF) such that the sequence (of bounds) so generated converges to a definite limit. The limit so obtained is shown to coincide with the variance of the actual uniformly minimum variance unbiased estimator (UMVUE) for this parameter, provided the underlying PDF is of the Korpman-Darmois exponential family. This technique also provides a constructive procedure to evaluate the UMVUE for any unknown parameter (or its functions) contained in the data. From a practical standpoint this is useful, since this procedure only involves the first-/and higher-order derivatives of the joint PDF and their cross covariance.>

Given (n+1) consecutive autocorrelations of a stationary discrete-time stochastic process, one interesting question is how to extend this finite sequence so that the power spectral density associated with the resulting infinite sequence of correlations is nonnegative everywhere. It is well known that when the Hermitian Toeplitz matrix generated from the given correlations is positive-definite the problem has an infinite number of solutions and the particular solution that maximizes entropy results in a stable all-pole model of order n. Since maximization of entropy is equivalent to maximization of the minimum mean square error associated with one-step predictors, the problem of obtaining admissible extensions that maximize the minimum mean square error associated with k-step (k>

A new method for reconstructing images from one bit of phase information of a function that is closely related to the original image is reported here. The result is based on properties of zeros of the real part of the discrete Fourier transform of certain monotonic sequenes that are related to the original image in an interesting fashion.

An important question in array design is that of where to place the elements of a sparse array for optimal performance in terms of its ability to detect and resolve a greater number of sources than conventionally possible. In particular, it has been shown that when sensor elements are arranged in the minimum redundancy fashion, by performing an augmentation technique on the covariances obtained from the array outputs, an M element array can be made to estimate the directions of arrival of as many as M(M-1)/2 uncorrelated sources unambiguously. Constructive procedures are developed to evaluate integer locations for an array of given sensors that span a prescribed distance, such that any missing integer is expressible as the difference of two sensor locations. New upper bounds for the ratio of the square of the minimum number of elements to the spanning distance are also established.>

The problem of finding the optimal minimum-redundancy integer locations for an array of given sensors that span a prescribed distance N, such that any missing integer i (0>

In this paper, we address the problem of element placement in a linear aperiodic array for use in spatial spectrum estimation. By making use of a theorem by Caratheódory, it is shown that, for a given number of elements, there exists a distribution of element positions which, for uncorreleated sources, results in superior spatial spectrum estimators than are otherwise achievable. The improvement is obtained by constructing an augmented covariance matrix, made possible by the choice of element positions, with dimension greater than the number of array elements. The augmented matrix is then used in any of the known spectrum estimation methods in conjunction with a correspondingly augmented search pointing vector. Examples are given to show the superior detection capability, the larger dynamic range for spectral peak to background level, the lower sidelobes and the relatively low bias values, when one of the known spectrum estimation techniques based on eigenstructure is used.

It is shown here that when extrapolation of a sequence of data with unknown statistics is performed under two optimization constraints, viz. maximizing the entropy and maximizing the a posteriori (MAP) probability density function (PDF) of the unknown sample, the resulting estimate is the same as that of an Autoregressive (AR) model. This leads to the conclusion that the estimate from an AR model is optimum in the sense that it is the MAP estimate which maximizes entropy.

In this letter, we address the problem of element placement in a linear aperiodic array for use in spatial spectrum estimation. By making use of a theorem by Caratheodory, it is shown that, for a given number of elements, there exists a distribution of element positions which, for uncorrelated sources, results in superior spatial spectrum estimators than are otherwise achievable. The improvement is obtained by constructing an augmented covariance matrix, made possible by the choice of element positions, with dimension greater than the number of array elements. The augmented matrix is then used in any of the known spectrum estimation methods in conjunction with a correspondingly augmented search pointing vector. Examples are given to show the superior detection capability, the larger dynamic range for spectral peak to background level, the lower sidelobes, and the relatively low bias values, when one of the known spectrum estimation techniques based on eigenstructure is used.