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Register a new userAdaptive Radar Detection of a Subspace Signal Embedded in Subspace Structured plus Gaussian Interference Via Invariance
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This paper deals with adaptive radar detection of a subspace signal competing with two sources of interference. The former is Gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise. The latter is structured as a subspace signal and models coherent pulsed jammers impinging on the radar antenna. The problem is solved via the Principle of Invariance which is based on the identification of a suitable group of transformations leaving the considered hypothesis testing problem invariant. A maximal invariant statistic, which completely characterizes the class of invariant decision rules and significantly compresses the original data domain, as well as its statistical characterization are determined. Thus, the existence of the optimum invariant detector is addressed together with the design of practically implementable invariant decision rules. At the analysis stage, the performance of some receivers belonging to the new invariant class is established through the use of analytic expressions.
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Sparsity-based subspace clustering algorithms have attracted significant attention thanks to their excellent performance in practical applications. A prominent example is the sparse subspace clustering (SSC) algorithm by Elhamifar and Vidal, which performs spectral clustering based on an adjacency matrix obtained by sparsely representing each data point in terms of all the other data points via the Lasso. When the number of data points is large or the dimension of the ambient space is high, the computational complexity of SSC quickly becomes prohibitive. Dyer et al. observed that SSC-OMP obtained by replacing the Lasso by the greedy orthogonal matching pursuit (OMP) algorithm results in significantly lower computational complexity, while often yielding comparable performance. The central goal of this paper is an analytical performance characterization of SSC-OMP for noisy data. Moreover, we introduce and analyze the SSC-MP algorithm, which employs matching pursuit (MP) in lieu of OMP. Both SSC-OMP and SSC-MP are proven to succeed even when the subspaces intersect and when the data points are contaminated by severe noise. The clustering conditions we obtain for SSC-OMP and SSC-MP are similar to those for SSC and for the thresholding-based subspace clustering (TSC) algorithm due to Heckel and Bolcskei. Analytical results in combination with numerical results indicate that both SSC-OMP and SSC-MP with a data-dependent stopping criterion automatically detect the dimensions of the subspaces underlying the data. Moreover, experiments on synthetic and on real data show that SSC-MP compares very favorably to SSC, SSC-OMP, TSC, and the nearest subspace neighbor algorithm, both in terms of clustering performance and running time. In addition, we find that, in contrast to SSC-OMP, the performance of SSC-MP is very robust with respect to the choice of parameters in the stopping criteria.
Rudolph (1967) introduced one-step majority logic decoding for linear codes derived from combinatorial designs. The decoder is easily realizable in hardware and requires that the dual code has to contain the blocks of so called geometric designs as codewords. Peterson and Weldon (1972) extended Rudolphs algorithm to a two-step majority logic decoder correcting the same number of errors than Reeds celebrated multi-step majority logic decoder. Here, we study the codes from subspace designs. It turns out that these codes have the same majority logic decoding capability as the codes from geometric designs, but their majority logic decoding complexity is sometimes drastically improved.
The quantum entropy-typical subspace theory is specified. It is shown that any mixed state with von Neumann entropy less than h can be preserved approximately by the entropy-typical subspace with entropy= h. This result implies an universal compression scheme for the case that the von Neumann entropy of the source does not exceed h.
In this paper, we propose a novel subspace learning framework for one-class classification. The proposed framework presents the problem in the form of graph embedding. It includes the previously proposed subspace one-class techniques as its special cases and provides further insight on what these techniques actually optimize. The framework allows to incorporate other meaningful optimization goals via the graph preserving criterion and reveals spectral and spectral regression-based solutions as alternatives to the previously used gradient-based technique. We combine the subspace learning framework iteratively with Support Vector Data Description applied in the subspace to formulate Graph-Embedded Subspace Support Vector Data Description. We experimentally analyzed the performance of newly proposed different variants. We demonstrate improved performance against the baselines and the recently proposed subspace learning methods for one-class classification.
We address adaptive radar detection of targets embedded in ground clutter dominated environments characterized by a symmetrically structured power spectral density. At the design stage, we leverage on the spectrum symmetry for the interference to come up with decision schemes capable of capitalizing the a-priori information on the covariance structure. To this end, we prove that the detection problem at hand can be formulated in terms of real variables and, then, we apply design procedures relying on the GLRT, the Rao test, and the Wald test. Specifically, the estimates of the unknown parameters under the target presence hypothesis are obtained through an iterative optimization algorithm whose convergence and quality guarantee is thoroughly proved. The performance analysis, both on simulated and on real radar data, confirms the superiority of the considered architectures over their conventional counterparts which do not take advantage of the clutter spectral symmetry.
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