Ahmed H. Tewfik

Adaptive Strategies for Target Detection and Localization in Noisy Environments

This paper studies the problem of recovering a signal with a sparse representation in a given orthonormal basis using as few noisy observations as possible. Herein, observations are subject to the type of background clutter noise encountered in radar applications. Given this model, this paper proves for the first time that highly sparse signals contaminated with Gaussian background noise can be recovered by adaptive methods using fewer noisy linear measurements than required by any possible recovery method based on nonadaptive Gaussian measurement ensembles.

Multi-Channel Sparse Data Conversion With a Single Analog-to-Digital Converter

We address the problem of performing simultaneous analog-to-digital (A/D) conversion on multi-channel signals using a single A/D converter (ADC). Assuming that each input has an unknown sparse representation in known dictionaries, we find that multi-channel information can be sampled with a single ADC. The proposed ADC architecture consists of a mixed signal block and a digital signal processing (DSP) block. The channel inputs are sampled by switched-capacitor-based sample-and-hold circuits, and then mixed using sequences of plus or minus ones, leading to no bandwidth expansion. The resulting discrete-time signals are converted to digital sequences by a single ADC or quantizer. At the DSP block, each channel is separated from the digitized mixture through various separation algorithms that are widely used in compressive sensing. For this, we study several techniques for separating the mixture of the channel inputs into the sample number of digital sequences corresponding to each channel. We show that with an ideal ADC, perfect reconstruction of the signals is possible if the input signals are sufficiently sparse. We also show simulation results with a 16-bit ADC model, and the reconstruction is possible up to the accuracy of the ADCs.

Primary Traffic Characterization and Secondary Transmissions

Channel idle time distribution based secondary transmission strategies have been studied intensively in the literature. Under various performance metrics, the ultimate performance of secondary devices are eventually dictated by the presumed channel idle time distribution. Such distributions can take any arbitrary form in practice. In this work, we study idle time distributions in wireless local area networks (WLAN) using large amount of the channel idle time data collected in real-world WLAN networks. We demonstrate with experimental data that the channel idle time distribution can be closely modeled by hyper-exponential distribution. Furthermore, one can treat the primary packet arrival process as a semi-Markov modulated Poisson process. Several secondary transmission strategies are discussed under this model. It is shown that using only one hyper-exponential distribution, the secondary user can achieve a desirable performance when the primary packet arrival process is stationary. However, experimental data suggests that in practice, this process is not stationary and the secondary user can experience a large performance loss with stationary transmission strategy. We propose a novel transmission strategy that achieves suboptimal secondary user performance when the idle time distribution is not stationary. The performances of secondary transmission strategies are demonstrated using experimental data.

A single SAR ADC converting multi-channel sparse signals

This paper presents a simple but high performance architecture for multi-channel analog-to-digital conversion. Based on compressive sensing, only one SAR ADC is needed to convert multi-channel sparse inputs, leading to significant analog power saving and hardware saving. Moreover, it helps avoid problems occurring in conventional multi-channel ADCs such as timing skew, offset mismatch, and gain mismatch. A 12-bit SAR ADC converting 4-channel sparse signals simultaneously is designed in 130nm CMOS process. The design reaches a SNDR of 66.3dB and consumes an average power of 58μW at the sampling frequency of 1MHz. The L1 minimization method is chosen to reconstruct the input signals. The single-tone and multi-tone inputs can be reconstructed with a minimum precision of 68dB and 55dB THD, respectively.

Under-sampled functional MRI using low-rank plus sparse matrix decomposition

High spatial resolution in functional magnetic resonance imaging improves its sensitivity to brain activation signals by reducing partial volume effects. However, the long acquisition times required for high spatial resolution limit the temporal resolution in fMRI studies. Consequently, the low temporal sampling bandwidth leads to increase in physiological noise and poor modeling of the functional activation dynamics. Thus, fast techniques capable of recovering fMRI time-series from under-sampled data are desirable to improve the sensitivity and specificity of fMRI for functional brain mapping. This paper presents an under-sampled fMRI recovery using low-rank plus sparse matrix decomposition signal model. This model is suited for blocked or slow event-related fMRI studies, where the low-rank matrix captures the temporally static T*2-weighted image patterns and, the sparse matrix captures the pseudo-periodic brain activation signal. The preliminary results of under-sampled recovery on in-vivo fMRI data show recovery of BOLD activation in human superior colliculus with contrast-to-noise ratio ≥ 4.4 (85% of reference) up to acceleration factors of 3.

Hyperexponential approximation of channel idle time distribution with implication to secondary transmission strategy

Channel idle time distribution (CITD) based secondary transmission strategies have been studied intensively in the literature. The performance of secondary devices are limited by the presumed CITD. But none of them provides a reasonable characterization of the CITD in reality. In this paper, we carefully examine the feature of the CITD using large amount of channel idle time data collected in various WLAN networks. It is demonstrated that the CITD can be well approximated by hyperexponential densities. Based on the estimated density, we propose a novel multiple-shot transmission strategy which takes advantage of the hyperexponential feature of the CITD. This strategy achieves at least twice the increase for the data we examine in average secondary access time compared to conventional transmission strategies.

Ultra-low power multi-channel data conversion with a single SAR ADC for mobile sensing applications

Based on the recently emerging compressive sensing theory, the paper proposes an ultra-low power multichannel data conversion system whose architecture is almost as simple as a single SAR ADC. The proposed architecture is capable of simultaneously converting multi-channel sparse signals while running at the Nyquist rate of only one channel. A chip is fabricated in a 0.13μm CMOS process. Operating at 1MS/s, the SAR ADC itself achieves a 66dB SNDR and a 25fJ/step FoM at 0.8V. Using convex optimization methods, 4-channel 500kHz-bandwidth signals can be reconstructed with a 66dB peak SNDR and a 41% max occupancy, leading to an effective FoM per channel of 6.25 fJ/step.

Greedy solutions for the construction of sparse spatial and spatio-spectral filters in brain computer interface applications

In the original formulation of common spatial pattern (CSP), all recording channels are combined when extracting the variance as input features for a brain computer interface (BCI). This results in overfitting and robustness problems of the constructed system. Here, we introduce a sparse CSP method in which only a subset of all available channels is linearly combined when extracting the features, resulting in improved generalization in classification. We propose a greedy search based generalized eigenvalue decomposition approach for identifying multiple sparse eigenvectors to compute the spatial projections. We evaluate the performance of the proposed sparse CSP method in binary classification problems using electrocorticogram (ECoG) and electroencephalogram (EEG) datasets of brain computer interface competition 2005. We show that the results obtained by sparse CSP outperform those obtained by traditional (non-sparse) CSP. When averaged over five subjects in the EEG dataset, the classification error is 12.3% with average sparseness level of 11.6 compared to 18.4% error obtained by the traditional CSP with 118 channels. The classification error is 10% with sparseness level of 7 compared to that of 13% obtained by the traditional CSP using 64 channels in the ECoG dataset. Furthermore, we explored the effectiveness of the proposed sparse methods for extracting sparse common spatio-spectral patterns (CSSP).

Semi-supervised event detection using higher order statistics for multidimensional time series accelerometer data

In this study, we target to automatically detect stereotypical behavioral patterns (stereotypy) and self-injurious behaviors (SIB) of Autistic children which can lead to critical damages or wounds as they tend to repeatedly harm oneself. Our custom designed accelerometer based wearable sensors are placed at wrists, ankles and upper body to detect stereotypy and SIB. The analysis was done on four children diagnosed with ASD who showed repeated behaviors that involve part of the body such as flapping arms, body rocking and self-injurious behaviors such as punching their face, or hitting their legs. Our goal of detecting novel events relies on the fact that the limitation of training data and variability in the possible combination of signals and events also make it impossible to design a single algorithm to understand all events in natural setting. Therefore, a semi-supervised method to discover and track unknown events in a multidimensional sensor data rises as a very important topic in classification and detection problems. In this paper, we show how the Higher Order Statistics (HOS) features can be used to design dictionaries and to detect novel events in a multichannel time series data. We explain our methods to detect novel events in a multidimensional time series data and combine the proposed semi-supervised learning method to improve the adaptability of the system while maintaining comparable detection accuracy as the supervised method. We, compare our results to the supervised methods that we have previously developed and show that although semi-supervised method do not achieve better performance compared to supervised methods, it can efficiently find new events and anomalies in multidimensional time series data with similar performance of the supervised method. We show that our proposed method achieves recall rate of 93.3% compared to 94.1% for the supervised method studied earlier.

Adaptive compressed sensing for sparse signals in noise

This paper studies the problem of recovering a signal with a sparse representation in a given orthonormal basis using as few noisy observations as possible. Herein, observations are subject to the type of background clutter noise encountered in radar applications. Given this model, this paper proves for the first time that highly sparse signals contaminated with Gaussian background noise can be recovered by adaptive methods using fewer noisy linear measurements than required by any possible recovery method based on non-adaptive Gaussian measurement ensembles.