Faculty Bibliography

We address the problem of estimating a sparse low-rank matrix from its noisy observation. We propose an objective function consisting of a data-fidelity term and two parameterized non-convex penalty functions. Further, we show how to set the parameters of the non-convex penalty functions, in order to ensure that the objective function is strictly convex. The proposed objective function better estimates sparse low-rank matrices than a convex method which utilizes the sum of the nuclear norm and the El norm. We derive an algorithm (as an instance of ADMM) to solve the proposed problem, and guarantee its convergence provided the scalar augmented Lagrangian parameter is set appropriately. We demonstrate the proposed method for denoising an audio signal and an adjacency matrix representing protein interactions in the 'Escherichia coli' bacteria. (C) 2017 Elsevier B.V. All rights reserved.

The class of majorization-minimization algorithms is based on the principle of successively minimizing upper bounds of the objective function. Each upper bound, or surrogate function, is locally tight at the current estimate, and each minimization step decreases the value of the objective function. We present a majorization-minimization approach based on a novel convex-nonconvex upper bounding strategy for the solution of a certain class of nonconvex nonsmooth optimization problems. We propose an efficient algorithm for minimizing the (convex) surrogate function based on the alternating direction method of multipliers. A preliminary convergence analysis for the proposed approach is provided. Numerical experiments show the effectiveness of the proposed method for the solution of nonconvex nonsmooth minimization problems.

The Savitzky-Golay (SG) filter is widely used to smooth and differentiate time series, especially biomedical data. However, time series that exhibit abrupt departures from their typical trends, such as sharp waves or steps, which are of physiological interest, tend to be oversmoothed by the SG filter. Hence, the SG filter tends to systematically underestimate physiological parameters in certain situations. This article proposes a generalization of the SG filter to more accurately track abrupt deviations in time series, leading to more accurate parameter estimates (e.g., peak velocity of saccadic eye movements). The proposed filtering methodology models a time series as the sum of two component time series: a low-frequency time series for which the conventional SG filter is well suited, and a second time series that exhibits instantaneous deviations (e.g., sharp waves, steps, or more generally, discontinuities in a higher order derivative). The generalized SG filter is then applied to the quantitative analysis of saccadic eye movements. It is demonstrated that (a) the conventional SG filter underestimates the peak velocity of saccades, especially those of small amplitude, and (b) the generalized SG filter estimates peak saccadic velocity more accurately than the conventional filter.

Sparse approximate solutions to linear equations are classically obtained via L1 norm regularized least squares, but this method often underestimates the true solution. As an alternative to the L1 norm, this paper proposes a class of nonconvex penalty functions that maintain the convexity of the least squares cost function to be minimized, and avoids the systematic underestimation characteristic of L1 norm regularization. The proposed penalty function is a multivariate generalization of the minimax-concave penalty. It is defined in terms of a new multivariate generalization of the Huber function, which in turn is defined via infimal convolution. The proposed sparse-regularized least squares cost function can be minimized by proximal algorithms comprising simple computations.

BACKGROUND: Automated single-channel spindle detectors, for human sleep EEG, are blind to the presence of spindles in other recorded channels unlike visual annotation by a human expert. NEW METHOD: We propose a multichannel spindle detection method that aims to detect global and local spindle activity in human sleep EEG. Using a non-linear signal model, which assumes the input EEG to be the sum of a transient and an oscillatory component, we propose a multichannel transient separation algorithm. Consecutive overlapping blocks of the multichannel oscillatory component are assumed to be low-rank whereas the transient component is assumed to be piecewise constant with a zero baseline. The estimated oscillatory component is used in conjunction with a bandpass filter and the Teager operator for detecting sleep spindles. RESULTS AND COMPARISON WITH OTHER METHODS: The proposed method is applied to two publicly available databases and compared with 7 existing single-channel automated detectors. F1 scores for the proposed spindle detection method averaged 0.66 (0.02) and 0.62 (0.06) for the two databases, respectively. For an overnight 6 channel EEG signal, the proposed algorithm takes about 4min to detect sleep spindles simultaneously across all channels with a single setting of corresponding algorithmic parameters. CONCLUSIONS: The proposed method attempts to mimic and utilize, for better spindle detection, a particular human expert behavior where the decision to mark a spindle event may be subconsciously influenced by the presence of a spindle in EEG channels other than the central channel visible on a digital screen.

Objective: To describe a case of gaze-position dependent opsoclonus and discuss potential localization. Background: Opsoclonus is characterized by bursts of involuntary, back-to-back saccades without an intersaccadic interval at frequency of 10-25 Hz in horizontal, vertical, and torsional planes. Opsoclonus with gaze-directional selectivity has been rarely described. Design/Methods: We report a 50 year-old man who sustained a concussion three years prior followed by postconcussive headaches and disequilibrium. Exam revealed very small amplitude oscillations in left gaze that could not be further characterized on clinical exam. Different larger amplitude horizontal oscillations were present with convergence. There were no other posterior fossa signs. Brain MRI was unremarkable. Results: Video-oculography demonstrated opsoclonus predominantly in left gaze [median amplitude 5 deg (range <1- 11 deg), frequency 30 Hz] and during leftward smooth pursuit, which improved [median amplitude 2 deg (range < 1-10 deg), frequency 10 Hz] as post-concussive symptoms improved. Conclusions: This case demonstrates opsoclonus with eye position selectivity in post-concussive syndrome. Various theories of opsoclonus exist, including lesions of saccade burst, omnipause, or cerebellar fastigial pause neurons which project to brainstem burst neurons. Ultimately, all of these lead to increased excitability in the inherently unstable saccade generators. Burst and omnipause neuron firing rates are not influenced by eye position. The leftward gaze-dependence in our case supports dysfunction of cerebellar dorsal vermis Purkinje cells leading to disinhibition of the fastigial ocular motor nucleus, as vermal pause neurons have gaze-directional selectivity. Vermal pause neurons exhibit a pause of discharge immediately before and during contralateral saccades. Thus, selective dysfunction, possibly related to concussion-related membrane instability, could create an imbalance in burst neuron excitability, resulting in triggering of unidirectional opsoclonus. Further, our patient's saccade system may be inherently prone to oscillations given the presence of larger amplitude horizontal oscillations consistent with 'voluntary flutter', which persisted when leftward opsoclonus improved

Objective: To assess relationships between classic saccade sequences and rapid number naming on the King Devick (K-D) test in concussion. Background: The K-D test is sensitive for concussion detection on athletic sidelines, with longer test times in concussion largely due to inter-saccadic interval (ISI) prolongation. The ISI is a measure of time between saccades that represents a combination of fixation duration and saccade latency. K-D saccade latency cannot be directly measured, as numbers are simultaneously displayed. We assessed saccade latency independent of K-D test. Design/Methods: Twenty-seven chronically concussed participants (mean age 32+/-13 years, range 17-61) and 19 healthy controls (mean age 29+/-8 years, range 19-48) performed K-D and saccade sequences: reflexive, gap, overlap, and antisaccades. Eye movements were recorded with EyeLink 1000+ video-oculography. Results: K-D test times were longer in concussion (54.6s vs 41.5s, p=0.001), as were ISIs (301.9ms vs 241.4ms, p=0.01). Longer reflexive and overlap latencies (reflexive: 198.1ms vs 176.7ms, p=0.04; overlap: 222.3ms vs 182.8ms, p=0.003) and worse accuracy were seen in concussion. Gap latencies showed no difference (160.6ms vs 148.8ms, p=0.13). Antisaccade latencies were longer in concussion (204.9ms vs 182.3ms, p=0.04) for saccades initially made in the incorrect direction, though there was no difference in error rates. Peak velocity and duration versus amplitude relationships showed no differences between groups. Conclusions: ISI prolongation during K-D performance could be due to increased saccade latencies and/or attention and cognitive impairment. In this study, saccade latency prolongation is seen in several saccade types in concussion, suggesting that it may, indeed, contribute to K-D ISI prolongation in concussion. Further, overlap saccade latency prolongation suggests that pre-saccade visual fixation disengagement is altered in concussion. These results suggest that saccade motor planning is impaired in concussion, possibly from damage to frontal lobe saccade control centers prone to traumatic injury

Objective: To compare video-oculography performed by EyeTribe versus EyeLink during a rapid number naming task. Background: With increasing accessibility of portable, economical, video-based, infrared eye trackers, such as EyeTribe, there is growing interest in eye movement recordings, including in the setting of sports-related concussion. However, prior to implementation, there is a primary need to establish the validity of these low-resolution (30-60 Hz) eye trackers via comparison with high-resolution (500-1000 Hz) devices such as EyeLink. Design/Methods: A convenience sample of 30 controls performed a digitized version of the King-Devick (K-D) test with EyeTribe and EyeLink eye movement recordings. Results: Signal loss and tracings inconsistent with eye movement physiology were common with EyeTribe. Saccade main sequence parameters (fit to decaying exponentials) were significantly different for the two devices (reported as best-fit parameter and 95% confidence interval). Peak velocity versus amplitude relationships revealed a main sequence asymptote of 1674degree/s (CI: 1527, 1852degree/s) for EyeTribe vs. 506degree/s (CI: 499, 513degree/s) for EyeLink and a time constant of 102.9degree (CI: 93.5,115.7degree) for EyeTribe vs. 6.1degree (CI: 5.3, 6.3degree) for EyeLink. Duration versus amplitude relationships also demonstrated significant differences, with an asymptote of 62.7ms (CI: 61.0, 64.3ms) for EyeTribe vs. 83.2ms (CI: 82.2, 84.4ms) for EyeLink and time constant of 4.9degree (CI: 4.6, 5.3degree) for EyeTribe vs. 13.8degree (CI: 13.6, 14.1degree) for EyeLink. Total number of saccades to complete the K-D was significantly lower with EyeTribe, with an average of 110.2 vs. 120.5 saccades recorded by EyeTribe and EyeLink respectively (paired t-test, p=0.001). There was no significant difference in the inter-saccadic interval, despite a discrepancy of 42ms between devices. Conclusions: The EyeTribe device was unable to capture valid saccade data during rapid number naming. Caution is advised regarding the implementation of eye trackers with low temporal resolution for objective saccade assessment or sideline concussion screening