Faculty Bibliography

The calculation of a sparse approximate solution to a linear system of equations is often performed using either L1-norm regularization and convex optimization or nonconvex regularization and nonconvex optimization. Combining these principles, this paper describes a type of nonconvex regularization that maintains the convexity of the objective function, thereby allowing the calculation of a sparse approximate solution via convex optimization. The preservation of convexity is viable in the proposed approach because it uses a regularizer that is nonseparable. The proposed method is motivated and demonstrated by the calculation of sparse signal approximation using tight frames. Examples of denoising demonstrate improvement relative to L1 norm regularization.

Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular nondifferentiable convex cost function. This letter describes a generalization of this cost function that can yield more accurate estimation of piecewise constant signals. The new cost function involves a nonconvex penalty (regularizer) designed to maintain the convexity of the cost function. The new penalty is based on the Moreau envelope. The proposed total variation denoising method can be implemented using forward-backward splitting.

The King-Devick (K-D) test of rapid number naming is a visual performance measure that captures saccadic eye movements. Patients with multiple sclerosis (MS) have slowed K-D test times associated with neurologic disability and reduced quality of life. We assessed eye movements during the K-D test to identify characteristics associated with slowed times. Participants performed a computerized K-D test with video-oculography. The 25-Item National Eye Institute Visual Functioning Questionnaire (NEI-VFQ-25) and its 10-Item Neuro-Ophthalmic Supplement measured vision-specific quality of life (VSQOL). Among 25 participants with MS (age 37 +/- 10 years, range 20-59) and 42 controls (age 33 +/- 9 years, range 19-54), MS was associated with significantly longer (worse) K-D times (58.2 +/- 19.8 vs. 43.8 +/- 8.6 s, P = 0.001, linear regression models, accounting for age). In MS, test times were slower among patients with higher (worse) Expanded Disability Status Scale scores (P = 0.01). Average inter-saccadic intervals (ISI) were significantly longer in MS participants compared to controls (362 +/- 103 vs. 286 +/- 50 ms, P = 0.001), and were highly associated with prolonged K-D times in MS (P = 0.006). MS participants generated greater numbers of saccades (P = 0.007). VSQOL scores were reduced in MS patients with longer (worse) K-D times (P = 0.04-0.001) and longer ISI (P = 0.002-0.001). Patients with MS have slowed K-D times that may be attributable to prolonged ISI and greater numbers of saccades. The K-D test and its requisite eye movements capture VSQOL and make rapid number naming a strong candidate efferent visual performance measure in MS.

Rolling-element bearing vibrations are random cyclostationary. This paper addresses the problem of noise reduction with simultaneous components extraction in vibration signals for faults diagnosis of bearing. The observed vibration signal is modeled as a summation of two components contaminated by noise, and each component composes of repetitive transients. To extract the two components simultaneously, an approach by solving an optimization problem is proposed in this paper. The problem adopts convex sparsity based regularization scheme for decomposition, and non-convex regularization is used to further promote the sparsity but preserving the global convexity. A synthetic example is presented to illustrate the performance of the proposed approach for repetitive feature extraction. The performance and effectiveness of the proposed method are further demonstrated by applying to compound faults and single fault diagnosis of a locomotive bearing. The results show the proposed approach can effectively extract the features of outer and inner race defects. (C) 2016 Elsevier Ltd. All rights reserved.

This paper proposes a parametric model for saccadic waveforms. The model has a small number of parameters, yet it effectively simulates a variety of physiologic saccade properties. In particular, the model reproduces the established relationship between peak saccadic angular velocity and saccadic amplitude (i.e., the saccadic main sequence). The proposed saccadic waveform model can be used in the evaluation and validation of methods for quantitative saccade analysis. For example, we use the proposed saccade model to evaluate four well-known saccade detection algorithms. The comparison indicates the most reliable algorithm is one by Nystrom et al. We further use the proposed saccade model to evaluate the standard technique used for the estimation of peak saccadic angular velocity. The evaluation shows the occurrence of systematic errors. We thus suggest that saccadic angular velocity values determined by the standard technique (low-pass differentiation) should be interpreted and used with caution.