John Lipor

Fourier-Based Transmit Beampattern Design Using MIMO Radar

In multiple-input multiple-output (MIMO) radar settings, it is often desirable to transmit power only to a given location or set of locations defined by a beampattern. Transmit waveform design is a topic that has received much attention recently, involving synthesis of both the signal covariance matrix, R, as well as the actual waveforms. Current methods involve a two-step process of designing R via iterative solutions and then using R to generate waveforms that fulfill practical constraints such as having a constant-envelope or drawing from a finite alphabet. In this paper, a closed-form method to design R for a uniform linear array is proposed that utilizes the discrete Fourier transform (DFT) coefficients and Toeplitz matrices. The resulting covariance matrix fulfills the practical constraints such as positive semidefiniteness and the uniform elemental power constraint and provides performance similar to that of iterative methods, which require a much greater computation time. Next, a transmit architecture is presented that exploits the orthogonality of frequencies at discrete DFT values to transmit a sum of orthogonal signals from each antenna. The resulting waveforms provide a lower mean-square error than current methods at a much lower computational cost, and a simulated detection scenario demonstrates the performance advantages achieved.

Seizure Detection Using the Phase-Slope Index and Multichannel ECoG

Detection and analysis of epileptic seizures is of clinical and research interest. We propose a novel seizure detection and analysis scheme based on the phase-slope index (PSI) of directed influence applied to multichannel electrocorticogram data. The PSI metric identifies increases in the spatio-temporal interactions between channels that clearly distinguish seizure from interictal activity. We form a global metric of interaction between channels and compare this metric to a threshold to detect the presence of seizures. The threshold is chosen based on a moving average of recent activity to accommodate differences between patients and slow changes within each patient over time. We evaluate detection performance over a challenging population of five patients with different types of epilepsy using a total of 47 seizures in nearly 258 h of recorded data. Using a common threshold procedure, we show that our approach detects all of the seizures in four of the five patients with a false detection rate less than two per hour. A variation on the global metric is proposed to identify which channels are strong drivers of activity in each patient. These metrics are computationally efficient and suitable for real-time application.

Optimized Wavelength Selection for Molecular Absorption Thermometry

A differential evolution (DE) algorithm is applied to a recently developed spectroscopic objective function to select wavelengths that optimize the temperature precision of water absorption thermometry. DE reliably finds optima even when many-wavelength sets are chosen from large populations of wavelengths (here 120 000 wavelengths from a spectrum with 0.002 cm−1 resolution calculated by 16 856 transitions). Here, we study sets of fixed wavelengths in the 7280–7520 cm−1 range. When optimizing the thermometer for performance within a narrow temperature range, the results confirm that the best temperature precision is obtained if all the available measurement time is split judiciously between the two most temperature-sensitive wavelengths. In the wide temperature range case (thermometer must perform throughout 280–2800 K), we find (1) the best four-wavelength set outperforms the best two-wavelength set by an average factor of 2, and (2) a complete spectrum (all 120 000 wavelengths from 16 856 transitions) is 4.3 times worse than the best two-wavelength set. Key implications for sensor designers include: (1) from the perspective of spectroscopic temperature sensitivity, it is usually sufficient to monitor two or three wavelengths, depending on the sensors anticipated operating temperature range; and (2) although there is a temperature precision penalty to monitoring a complete spectrum, that penalty may be small enough, particularly at elevated pressure, to justify the complete-spectrum approach in many applications.

Margin-based active subspace clustering

Subspace clustering has typically been approached as an unsupervised machine learning problem. However in several applications where the union of subspaces model is useful, it is also reasonable to assume you have access to a small number of labels. In this paper we investigate the benefit labeled data brings to the subspace clustering problem. We focus on incorporating labels into the k-subspaces algorithm, a simple and computationally efficient alternating estimation algorithm. We find that even a very small number of randomly selected labels can greatly improve accuracy over the unsupervised approach. We demonstrate that with enough labels, we get a significant improvement by using actively selected labels chosen for points that are nearly equidistant to more than one estimated subspace. We show this improvement on simulated data and face images.

Quantile search: A distance-penalized active learning algorithm for spatial sampling

Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in ℝd with an optimal number of samples. We generalize this problem to when the cost of sampling is not only the number of samples but also the distance traveled between samples. This is motivated by our work studying regions of low oxygen concentration in the Great Lakes. We show that for one-dimensional threshold classifiers, a tradeoff between number of samples and distance traveled can be achieved using a generalization of binary search, which we refer to as quantile search. We derive the expected total sampling time for noiseless measurements and the expected number of samples for an extension to the noisy case. We illustrate our results in simulations relevant to our sampling application.

Distance-Penalized Active Learning Using Quantile Search

Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in

Closed form fourier-based transmit beamforming for MIMO radar

\mathbb {R}^d

Improving K-Subspaces via Coherence Pursuit

with an optimal number of samples. We generalize this problem to the case of spatial signals, where the sampling cost is a function of both the number of samples taken and the distance traveled during estimation. This is motivated by our work studying regions of low oxygen concentration in the Great Lakes. We show that for one-dimensional threshold classifiers, a tradeoff between the number of samples taken and distance traveled can be achieved using a generalization of binary search, which we refer to as quantile search. We characterize both the estimation error after a fixed number of samples and the distance traveled in the noiseless case, as well as the estimation error in the case of noisy measurements. We illustrate our results in both simulations and experiments and show that our method outperforms existing algorithms in a large range of sampling scenarios.

Subspace Clustering using Ensembles of

In multiple-input multiple-output (MIMO) radar setting, it is often desirable to design correlated waveforms such that power is transmitted only to a given set of locations, a process known as beampattern design. To design desired beam-pattern, current research uses iterative algorithms, first to synthesize the waveform covariance matrix, R, then to design the actual waveforms to realize R. In contrast to this, we present a closed form method to design R that exploits discrete Fourier transform and Toeplitz matrix. The resulting covariance matrix fulfills the practical constraints and performance is similar to that of iterative methods. Next, we present a radar architecture for the desired beampattern that does not require the synthesis of covariance matrix nor the design of correlated waveforms.