Faculty Bibliography

To quantify the thickness of the inner retinal layers in the foveal pit where the nerve fiber layer (NFL) is absent, and quantify changes in the ganglion cells and inner plexiform layer. Pixel-by-pixel volumetric measurements were obtained via Spectral-Domain optical coherence tomography (SD-OCT) from 50 eyes of Parkinson disease (PD) (n = 30) and 50 eyes of healthy control subjects (n = 27). Receiver operating characteristics (ROC) were used to classify individual subjects with respect to sensitivity and specificity calculations at each perifoveolar distance. Three-dimensional topographic maps of the healthy and PD foveal pit were created. The foveal pit is thinner and broader in PD. The difference becomes evident in an annular zone between 0.5 and 2 mm from the foveola and the optimal (ROC-defined) zone is from 0.75 to 1.5 mm. This zone is nearly devoid of NFL and partially overlaps the foveal avascular zone. About 78 % of PD eyes can be discriminated from HC eyes based on this zone. ROC applied to OCT pixel-by-pixel analysis helps to discriminate PD from HC retinae. Remodeling of the foveal architecture is significant because it may provide a visible and quantifiable signature of PD. The specific location of remodeling in the fovea raises a novel concept for exploring the mechanism of oxidative stress on retinal neurons in PD. OCT is a promising quantitative tool in PD research. However, larger scale studies are needed before the method can be applied to clinical follow-ups.

This paper addresses the problem of smoothing data with additive step discontinuities. The problem formulation is based on least square polynomial approximation and total variation denoising. In earlier work, an ADMM algorithm was proposed to minimize a suitably defined sparsity-promoting cost function. In this paper, an algorithm is derived using the majorization-minimization optimization procedure. The new algorithm converges faster and, unlike the ADMM algorithm, has no parameters that need to be set. The proposed algorithm is formulated so as to utilize fast solvers for banded systems for high computational efficiency. This paper also gives optimality conditions so that the optimality of a result produced by the numerical algorithm can be readily validated.

This paper describes an extension to total variation denoising wherein it is assumed the first-order difference function of the unknown signal is not only sparse, but also that large values of the first-order difference function do not generally occur in isolation. This approach is designed to alleviate the staircase artifact often arising in total variation based solutions. A convex cost function is given and an iterative algorithm is derived using majorization-minimization. The algorithm is both fast converging and computationally efficient due to the use of fast solvers for banded systems.

Implantable high-accuracy, and low-power seizure detection is a challenge. In this paper, we propose a cascade architecture to combine different seizure detection algorithms to optimize power and accuracy of the overall seizure detection system. The proposed architecture consists of a cascade of two seizure detection stages. In the first-stage detector, a lightweight (low-power) algorithm is used to detect seizure candidates with the understanding that there will be a high number of false positives. In the second-stage detector-and only for the seizure candidates detected in the first detector-a high-accuracy algorithm is used to eliminate the false positives. We show that the proposed cascade architecture can reduce power consumption of seizure detection by 80% with high accuracy, offering a suitable option for real-time implantable seizure detectors.

Magnetic resonance imaging (MRI) is one of the fields that the compressed sensing theory is well utilized to reduce the scan time significantly leading to faster imaging or higher resolution images. It has been shown that a small fraction of the overall measurements are sufficient to reconstruct images with the combination of compressed sensing and parallel imaging. Various reconstruction algorithms have been proposed for compressed sensing, among which augmented Lagrangian based methods have been shown to often perform better than others for many different applications. In this paper, we propose new augmented Lagrangian based solutions to the compressed sensing reconstruction problem with analysis and synthesis prior formulations. We also propose a computational method which makes use of properties of the sampling pattern and the singular value decomposition of the system transfer function to significantly improve the speed of the reconstruction for the proposed algorithms in Cartesian sampled MRI. The proposed algorithms are shown to outperform earlier methods especially for the case of dynamic MRI for which the transfer function tends to be a very large matrix and significantly ill conditioned. It is also demonstrated that the proposed algorithm can be accelerated much further than other methods in case of a parallel implementation with graphics processing units.

Missing radar data may be reconstructed by using the structure present in surrounding data to make intelligent estimates of values at missing locations. We formulate the interrupted radar data scenario as an l(1)-regularized least squares problem, and take advantage of the radar data's demonstrated sparsity in the discrete Fourier domain. Applying the split-variable augmented Lagrangian technique results in an iterative algorithm consisting of two alternating minimizations. The fast algorithm avoids explicit linear inverse solutions, and demonstrates good phase history reconstruction and improved imaging irrespective of the structure of the data loss. Experimental results are presented for synthetic aperture radar (SAR) image formation; however, the approach may also be used with other types of radar data.

This paper presents a new method for data recovery exploiting low rank structure and convexity constraints. It is capable of handling arbitrary observation patterns and it can incorporate additional convex constraints such as non-negativity and finite band width.

This paper addresses the problem of estimating simultaneously a local polynomial signal and an approximately piece-wise constant signal from a noisy additive mixture. The approach developed in this paper synthesizes the total variation filter and least-square polynomial signal smoothing into a unified problem formulation. The method is based on formulating an l(1)-norm regularized inverse problem. A computationally efficient algorithm, based on variable splitting and the alternating direction method of multipliers (ADMM), is presented. Algorithms are derived for both unconstrained and constrained formulations. The method is illustrated on experimental data involving the detection of nano-particles with applications to real-time virus detection using a whispering-gallery mode detector.

In this correspondence, we introduce a dual-tree rational-dilation complex wavelet transform for oscillatory signal processing. Like the short-time Fourier transform and the dyadic dual-tree complex wavelet transform, the introduced transform employs quadrature pairs of time-frequency atoms which allow to work with the analytic signal. The introduced wavelet transform is a constant-transform, a property lacked by the short-time Fourier transform, which in turn makes the introduced transform more suitable for models that depend on scale. Also, the frequency resolution can be as high as desired, a property lacked by the dyadic dual-tree complex wavelet transform, which makes the introduced transform more suitable for processing oscillatory signals like speech, audio and various biomedical signals.