Covert communication is achieved if a transmitter (Alice) sends a message to a legitimate receiver (Bob) without being detected by an attentive warden (Willie). Recent work has taken an outage approach that considers an infinite blocklength and analyzes the probability that channel conditions are such that communication is reliable and/or covert. Power adaptation via truncated channel inversion (TCI) has been examined in previous work in an attempt to minimize outage under the covertness constraint. However, the optimality of TCI was not established, and the associated parameters in the TCI scheme were only found numerically. We provide the exact optimal power adaptation schemes under different covertness constraints and with different channel models: 1) when the channel between Willie and an uninformed jammer is AWGN; and 2) when the channel is a Rayleigh fading channel. We also examine the performance improvement of these schemes over standard approaches. This establishes that TCI is optimal in some, but not all, scenarios of interest.

Graphs have been widely used in image processing and understanding tasks. We introduce a novel graph generation model which greatly reduces the size of the traditional pixel-based graph. Based on the generated graph, we propose two feature extraction methods which utilize spectral graph information, and apply the features to image. Experiments show that our proposed oscillatory image heat content and weighted heat content spectrum features are more robust to small distortions and changes of viewpoint than the image heat content feature we proposed previously. The features are also capable of capturing important image structural information of the image and perform well alone or in combination with other low-level image features.

In applications including radar and ultrasonic inspection, an observed signal can often be modeled as the output over a finite interval of a linear, time-invariant (LTI) operator having a short-duration impulse response. For processing such as filtering and compression it would be useful to have approximations to eigenfunctions of the operator. It has been shown that discrete-time complex exponentials are asymptotic pseudomodes (i.e., approximate eigenvectors) of sequences of Toeplitz matrices. In this letter we show that complex exponentials over the observation interval are pseudomodes of LTI operators, corresponding to pseudoeigenvalues that are samples from the operator's frequency response, and how the level of approximation depends on the ratio of the impulse response duration to observation interval length. This implies that the Fourier Series basis for the observation interval can be used as an orthonormal set of approximate eigenfunctions.

In this paper, we propose a complex network based low-level feature for image retrieval systems based on the graph representation of the image and the mathematical theory of diffusion over manifolds. We show that the proposed image feature is invariant to non-structural changes on images and performs well in hand written digits classification task. We also show that performance of image retrieval with existing low-level features could be improved by combining with the proposed feature.

Orthogonal frequency division multiplexing (OFDM) systems have been used extensively in wireless communications in recent years; thus, there is significant interest in analyzing the properties of the transmitted signal in such systems. In particular, a large amount of work has focused on analyzing the variation of the complex envelope of the transmitted signal and on designing methods to minimize this variation. In this paper, it is established that the complex envelope of a bandlimited uncoded OFDM signal converges weakly to a Gaussian random process as the number of subcarriers goes to infinity. This shows that the properties of the OFDM signal will asymptotically approach those of a Gaussian random process over any finite time interval. The convergence proof is then extended to two important cases, namely, coded OFDM systems and systems with an unequal power allocation across subcarriers.

Orthogonal frequency division multiplexing (OFDM) is a promising framework for future wireless communication systems. One of the main impediments that has limited the applicability of OFDM systems in low-power wireless communication systems is the highly variable amplitude of the baseband transmitted signal; thus, a number of previous analyses have characterized this variation. These analyses have generally employed the following two components: (1) the assumption that the complex envelope of the OFDM signal converges to a Gaussian random process in some sense as the number of subcarriers becomes large, and (2) Rice's (1945) classical results on level-crossing rates for the envelope of Gaussian random processes. In this work, we improve on both of these components to arrive at a simple, accurate, and rigorously-established expression for the peak distribution of the OFDM envelope. In particular, using a rigorous (and non-trivial) proof establishing the convergence in (1) above as justification, the modern extreme value theory for chi-squared processes is applied to the problem. Numerical results for both uncoded and coded systems establish that the simple expression obtained for the distribution of the peaks of the envelope process is extremely accurate, even for a modest number of subcarriers.

Practical sequential estimation algorithms inherently involve "iterated conditioning"; that is, the estimate at any algorithm step is conditioned on information passed from the previous step. Except in special cases, standard probability theory cannot deal with operations like iterated conditioning, so it is difficult even to formulate algorithms that make optimal use of the available information. The previously developed product space conditional event algebra (PS-CEA) allows for the definition of "conditional events" as regular events in a probability space, and thus for the extension of Bayesian analysis to cases of iterated conditioning. We describe the PS-CEA approach and give an example of its use in deriving iterated image estimators when the information passed from one stage to the next is the current image estimate.

Diffusion networks (i.e., networks with stochastic differential neuron equations) are attractive as means of implementing segmentation algorithms because of their potential for fast, parallel processing. However, the complexity of the required neuron circuitry makes many analog implementations impractical. In this paper, we consider a digital version of a diffusion network proposed by Wong (1991). The analog neuron equations are first discretized into versions driven by binary noise sequences. The discretized equations are then implemented with digital differential analyzers (DDAs) to produce a digital diffusion network. While much work remains to be done to finalize the digital network design, preliminary simulation test results of the digital network applied to image segmentation are encouraging.

The stability with respect to model uncertainty of linear estimators of the coefficients of a linear combination of deterministic signals in noise is investigated. A class of estimators having nominal performances constrained to be close to that of the nominal linear, unbiased, minimum-variance (LUMV) estimator is specified. Two estimator stability indexes are defined, one based on a worst-case estimate mean-square error and the other on a type of signal-to-noise ratio. The estimator minimizing each index, subject to the optimality constraints, is found by reference to related LUMV estimation results. In most cases, the minimizing (or most stable) estimator is the same under the two indexes.>

Discrete-index Markov-type random processes in one and two dimensions are considered, with emphasis on two-dimensional processes (or fields). Important classes of Markov-type models, their properties, and their relationship are described. Although some new results are given, the authors mainly present a systematic study and grouping of processes according to two fundamental Markov-type properties: strict-sense Markov, defined in terms of conditional probabilities, and wide-sense Markov, defined in terms of linear minimum-mean-square error estimates. Classes of models having special cases of the fundamental properties, including many models which are widely used to represent images are obtained by specifying the index set, the conditioning set used to define the Markov property, and the process distribution. The relationships between unilateral and bilateral models in each class are carefully investigated. Particular attention is given to simultaneous autoregressive models which are shown to be both strict-sense and wide-sense Markov. Classification of processes according to their Markov-type properties helps to clarify the consequences of and relationships between different model assumptions.>

A hierarchical random field model and segmentation algorithm is presented for multilook speckled images. Speckle is modeled using Gaussian random fields that have separable autocorrelations. The model incorporates the correlation found in real speckle. The speckle fields are Markov with second-order neighborhoods, a property used in the segmentation. The segmentation algorithm, which is based on a posteriori formulation, estimating the value of the region field given the speckled observation.>

The statistical properties of speckle are examined. A general joint probability description is derived; special cases of the formulation are then given in detail, including a local statistical description of speckle which goes beyond the marginal statistics. The statistical model developed for speckle is then used in developing a segmentation algorithm for speckled images. The model parameters necessary for the segmentation algorithm are estimated.

The stability of linear detectors for signals nominally known except for amplitude in correlated nominally Gaussian noise is considered. Stability is defined in terms of bounds on the distribution of the test statistic as the true probability measure on the observation space varies in a Prokhorov neighborhood of the nominal; the derived stability index is independent of the neighborhood size. An optimization problem is formulated and solved to give the most stable linear detector meeting a Constraint on the nominal level of detectability.