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Functional Magnetic Resonance Imaging is a noninvasive tool used to study brain function. Detecting activation is challenged by many factors, and even more so in low-signal scenarios that arise in the performance of high-level cognitive tasks. We provide a fully automated and fast adaptive smoothing and thresholding (FAST) algorithm that uses smoothing and extreme value theory on correlated statistical parametric maps for thresholding. Performance on simulation experiments spanning a range of low-signal settings is very encouraging. The methodology also performs well in a study to identify the cerebral regions that perceive only-auditory-reliable and only-visual-reliable speech stimuli as well as those that perceive one but not the other.

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.

Communications receivers are commonly optimized with respect to a stationary interference source. When the interference originates in a composite source, the optimal receiver may be represented as a collection of generically similar subreceivers each one of which is optimized with respect to one of the interference subsources. Selection of the correct subreceiver is conditioned on identifying the subsource that is interfering at a given time. This selection process is controlled by a statistical demultiplexer, In the absence of real communications, when the statistical demultiplexer operates on uncorrelated noise, its function is to estimate the present state of a spectrally white, non-Gaussian, nonstationary random process. To evaluate the performance of the statistical demultiplexer, it is necessary to assert that the state of the observed process is itself a stationary (unobservable) process. Consideration is given to the case in which the unobservable is Markov. When the receiver is an isolated system that draws power from a limited reservior of energy, and messages arrive only sporadically, the statistical demultiplexer in its simplest form detects the mere presence of the message and control a switch in the power line to the main receiver subsystem. The alertness strategy embodied in this scheme can greatly extend the life-time of the system under conditions that are considered in some detail.

The problem of weak signal reception in non-Gaussian noise has been shown to have an optimal solution the structure of which involves a no-memory nonlinearity followed by a matched filter. The shape of the nonlinearity is completely determined by the noise amplitude probability density function. The assumptions underlying this theory are examined and applications to radio communication in atmospheric noise are considered. Since the likelihood ratio test on which the theory is based is not a robust procedure, the receiver system must adjust the shape of the nonlinearity to account for the statistics of the prevailing noise environment. (Author)

The problem of target detection and signal parameter estimation in a background of unknown interference is studied, using a multidimensional generalization of the signal models usually employed for radar, sonar, and similar applications. The required techniques of multivariate statistical analysis are developed and extensively used throughout the study, and the necessary mathematical background is provided in Appendices. Target detection performance is shown to be governed by a form of the Wilks' Lambda statistic, and a new method for its numerical evaluation is given which applies to the probability of false alarm of the detector. Signal parameter estimation is shown to be directly related to known techniques of adaptive nulling, and several new results relevant to adaptive nulling performance are obtained.

Wireless OFDM channels can be approximated by a time varying filter with sparse time domain taps. Recent achievements in sparse signal processing such as compressed sensing have facilitated the use of sparsity in estimation, which improves the performance significantly. The problem of these sparse-based methods is the need for a stable transformation matrix which is not fulfilled in the current transmission setups. To assist the analog filtering at the receiver, the transmitter leaves some of the subcarriers at both edges of the bandwidth unused which results in an ill-conditioned DFT submatrix. To overcome this difficulty we propose Adaptive Thresholding for Sparse Signal Detection (ATSSD). Simulation results confirm that the proposed method works well in time-invariant and specially time-varying channels where other methods may not work as well.

This paper considers the general signal detection and parameter estimation problem in the presence of colored Gaussian noise disturbance. By modeling the disturbance with an autoregressive process, we present three signal detectors with different unknown parameters under the general framework of binary hypothesis testing. The closed form of parameter estimates and the asymptotic distributions of these three tests are also given. Given two examples of frequency modulated signal detection problem and time series moving object detection problem, the simulation results demonstrate the effectiveness of three presented detectors.

This paper considers the general signal detection and parameter estimation problem in the presence of colored Gaussian noise disturbance. By modeling the disturbance with an autoregressive process, we present three signal detectors with different unknown parameters under the general framework of binary hypothesis testing. The closed form of parameter estimates and the asymptotic distributions of these three tests are also given. Given two examples of frequency modulated signal detection problem and time series moving object detection problem, the simulation results demonstrate the effectiveness of three presented detectors.

Estimation of the time of change of a parameter governing an observed sequence of independent multivariate random data samples is considered when the magnitude of the change is unknown and there exist unknown nuisance parameters that may be nonstationary. The particular application considered is the detection of the onset of a narrowband signal with unknown amplitude and phase at an array of sensors for radar or sonar processing in the presence of unknown, nonstationary, spatially distinct interferences hindering detection. The solution proposed in this dissertation entails segmenting the multivariate data into nonoverlapping blocks, from which univariate statistics are formed that are invariant to the unknown interference parameters. The log likelihood ratio for a specific signal-to-interference ratio (SIR) and the locally optimal nonlinearities are applied to two level statistics formed by generalized likelihood ratio (GLR) methods for data compression prior to submission to Page's test for rapid detection of the change. Once Page's test has determined that a change has occurred at the block level, the estimate of the change time is improved by post block processing in the form of a maximum likelihood estimator for the change time. Application of the locally optimal nonlinearity to the block level statistic formed from a GLR for the unknown signal and interference parameters achieved the best asymptotic performance. (MM)

This project is concerned with the adaptive digital processing to remove (or reduce) noisy signals generated by sensors at large distance away from the sensors. The noisy signals need to be removed because only those signals near the sensors are of interest for detection. The signals to be detected may correspond to footsteps of a walking man. Two classes of digital processing techniques are considered; namely the adaptive Kalman filtering and the adaptive digital filtering.

In this research, optimum ocean-model-based detection algorithms were developed for signals received through an inhomogeneous acoustic ocean medium. These optimal algorithms are driven by the knowledge of the underlying wavefront propagation in an inhomogeneous ocean medium. Comparison of narrowband and broadband performance as a function of range for both range- independent and range-dependent ocean environments were made. In addition, sensitivity of detection performance to mismatch in the sound speed profile as a function of range and transmitted were obtained. A new a posteriori probability source localization algorithm was developed which exhibits much less sensitivity to the underlying assumptions of the ocean acoustic medium (sound speed profiles) than do the classical matched field algorithms. The design and performance of optimal and fault-tolerant distributed detection networks, from a signal detection theory point of view, were also developed. (AN)

This paper considers the problem of space-time adaptive processing (STAP) in non-homogeneous environments where the disturbance covariance matrices of the training and test signals are assumed random and different with each other. A Bayesian detection statistic is proposed by incorporating the randomness of the disturbance covariance matrices, utilizing a priori knowledge, and exploring the inherent Block-Toeplitz structure of the spatial-temporal covariance matrix. Speci cally the Block-Toeplitz structure of the covariance matrix allows us to model the training signals as a multichannel auto-regressive (AR) process and hence, develop the Bayesian parametric adaptive matched lter (B-PAMF) to mitigate the training requirement and alleviate the computational complexity. Simulation using both simulated multichannel AR data and the challenging KASSPER data validates the effectiveness of the B-PAMF in non-homogeneous environments.

New parametric space-time adaptive processing (STAP) based detectors are introduced and examined. Unlike conventional techniques that estimate the characteristics of the disturbance from only the secondary data, the proposed detectors obtain such knowledge jointly from the primary and secondary data. When the number of pulses within a coherent processing interval is sufficiently large, the proposed detectors can function even without any secondary data, making them strong candidates for detection in non-homogeneous environments. The proposed detectors are investigated by both theoretical analysis and numerical study using simulated and real radar data. Extensive comparison with conventional STAP methods shows that the proposed detectors can better deal with training-limited scenarios while being computationally simpler. The proposed techniques are also extended for target detection in hyperspectral imaging (HSI).

This investigation is motivated by the problem of weak signal detection in a strong clutter background. The concept of the Locally optimum Detector has been used to address this problem. The problem of weak signal detection has been extensively addressed in the literature when the received radar samples can be modeled as independent and identically distributed. However, this issue has not received much attention when the received radar samples are correlated and have a non-Gaussian probability density function. Also, performance analysis is not generally carried out for finite sample sizes. This thesis addresses the performance of Locally Optimum Detectors in radar weak signal detection for finite sample sizes where the radar disturbance is modeled as a correlated non-Gaussian random process. The theory of Spherically Invariant Random Process is used for statistical characterization of non-Gaussian radar clutter. In particular, the K-distribution and the Student-T distributions have been considered as models for radar clutter. A canonical form is established for the Locally Optimum Detector that is a product of the Gaussian linear receiver and a zero memory nonlinearity. The functional form of the zero memory nonlinearity depends on the approximation used for the underlying radar clutter probability density function. Since the weak signal detector is nonlinear, thresholds for specified false alarm probability cannot be established in closed form. Given a specified false alarm probability a new method for threshold estimation based on extreme value theory is derived that reduces by orders of magnitude the computation and sample size required to set the threshold.

The design of a locally optimal detector for a known signal in non-Gaussian noise is discussed. The optimal detector non-linearity is approximated adaptively in the noise pdf tail region, and a polynomial is used to approximate the non-linearity near the mean. Examples for several different noise environments are presented, showing in these cases that the adaptive detector is able to achieve a high level of performance.

The focus of this research is to determine the impact of our knowledge of ocean variability, as characterized by the sound speed profile, on ocean surveillance detection performance for situations of interest to the U. S. Navy. Signal detection theory provides a framework for determining optimal phase coherent detection and source localization algorithms and determining their performance. This framework allows us to incorporate directly the physics of acoustic propagation through a space-time variable medium into the structure of optimal algorithms. Thus the signal processing algorithms designed from this viewpoint have a built-in robustness to the environmental variability. Using these optimal algorithms we can determine the maximum attainable detection performance.

In signal processing applications it is common to assume Gaussian statistics in the design of optimal signal processors. However, non-Gaussian processes do arise in many situations. For example, measurements reveal that radar clutter may be approximated by either Weibull, K-distributed, Lognormal, or Gaussian distributions depending upon the scenario. When the possibility of a non-Gaussian problem is encountered, the question as to which probability distributions should be utilized in a specific situation for modeling the data needs to be answered. In practice, the underlying probability distributions are not known a priori. Consequently, an assessment must be made by monitoring the environment. Another consideration is that radar detection problems can usually be divided into strong, intermediate, and weak signal cases. Hence, the system that monitors a radar environment must be able to subdivide the surveillance volume into weak background noise and clutter patches in addition to approximating the underlying probability distributions for each patch. This is in contrast to current practice where a single robust detector, usually based on the Gaussian assumption, is employed. The objective of this work is to develop techniques that monitor the environment and select the appropriate detector for processing the data. The main contributions are: (1) an image processing technique is devised which enables partitioning of the surveillance volume into background noise and clutter patches, (2) the Ozturk algorithm is used to identify suitable approximations to the probability density function for each clutter patch, and (3) rules to be used with an expert system shell under development at the University of Massachusetts and Boston University are formulated for monitoring the environment and selecting the appropriate detector for processing the data.

In radar signal detection, the problem is to automatically detect a target in a nonstationary noise and clutter background while maintaining a constant probability of false-alarm. Classical detection using a matched filter receiver and a fixed threshold is not applicable due to the nonstationary nature of the background noise. Therefore, adaptive threshold techniques are needed to maintain a constant false-alarm rate(CFAR). One approach to adaptive detection in nonstationary noise and clutter background is to compare the processed target signal to an adaptive threshold. In the cell-averaging CFAR processing, an estimate of the background noise from the leading and the lagging reference windows is used to set the adaptive threshold. A threshold multiplier(or scaling factor)is used to scale the threshold to achieve the desired probability of false-alarm. In the first part of this report, we have proposed two modified cell-averaging detectors for multiple target situations. The first one is a weighted cell-averaging CFAR detector, WCA-CFAR, where weighted leading and lagging reference windows are used to obtain the adaptive threshold. The second is a cell-censored, cell averaging CFAR processor where a predetermined fixed threshold is used to eliminate those cells that may contain interference.