Faculty Bibliography

Adaptive transforms are required for better signal analysis and processing. Key issue in finding the optimal expansion basis for a given signal is the representation of signal information with very few elements of the basis. In this context a key role is played by the multiscale transforms that allow signal representation at different resolutions. This paper presents a method for building a multiscale transform with adaptive scale dilation factors. The aim is to promote sparsity and adaptiveness both in time and scale. To this aim interscale relationships of wavelet coefficients are used for the selection of those scales that measure significant changes in signal information. Then, a wavelet transform with variable dilation factor is defined accounting for the selected scales and the properties of coprime numbers. Preliminary experimental results in image denoising by Wiener filtering show that the adaptive multiscale transform is able to provide better reconstruction quality with a minimum number of scales and comparable computational effort with the classical dyadic transform.

The aim of this paper is to introduce an adaptive preprocessing procedure based on human perception in order to increase the performance of some standard image processing techniques. Specifically, image frequency content has been weighted by the corresponding value of the contrast sensitivity function, in agreement with the sensitiveness of human eye to the different image frequencies and contrasts. The 2D Rational dilation wavelet transform has been employed for representing image frequencies. In fact, it provides an adaptive and flexible multiresolution framework, enabling an easy and straightforward adaptation to the image frequency content. Preliminary experimental results show that the proposed preprocessing allows us to increase the performance of some standard image enhancement algorithms in terms of visual quality and often also in terms of PSNR.

This paper addresses the suppression of transient artifacts in signals, e.g., biomedical time series. To that end, we distinguish two types of artifact signals. We define "Type 1" artifacts as spikes and sharp, brief waves that adhere to a baseline value of zero. We define "Type 2" artifacts as comprising approximate step discontinuities. We model a Type 1 artifact as being sparse and having a sparse time-derivative, and a Type 2 artifact as having a sparse time-derivative. We model the observed time series as the sum of a low-pass signal (e.g., a background trend), an artifact signal of each type, and a white Gaussian stochastic process. To jointly estimate the components of the signal model, we formulate a sparse optimization problem and develop a rapidly converging, computationally efficient iterative algorithm denoted TARA ("transient artifact reduction algorithm"). The effectiveness of the approach is illustrated using near infrared spectroscopic time-series data.

This paper jointly addresses the problems of chromatogram baseline correction and noise reduction. The proposed approach is based on modeling the series of chromatogram peaks as sparse with sparse derivatives, and on modeling the baseline as a low-pass signal. A convex optimization problem is formulated so as to encapsulate these non-parametric models. To account for the positivity of chromatogram peaks, an asymmetric penalty function is utilized. A robust, computationally efficient, iterative algorithm is developed that is guaranteed to converge to the unique optimal solution. The approach, termed Baseline Estimation and Denoising With Sparsity (BEADS), is evaluated and compared with two state-of-the-art methods using both simulated and real chromatogram data. (C) 2014 Elsevier B.V. All rights reserved.

Spectral-domain Optical coherence tomography (OCT) has shown remarkable utility in the study of retinal disease and has helped to characterize the fovea in Parkinson disease (PD) patients. We developed a detailed mathematical model based on raw OCT data to allow differentiation of foveae of PD patients from healthy controls. Of the various models we tested, a difference of a Gaussian and a polynomial was found to have "the best fit". Decision was based on mathematical evaluation of the fit of the model to the data of 45 control eyes versus 50 PD eyes. We compared the model parameters in the two groups using receiver-operating characteristics (ROC). A single parameter discriminated 70 % of PD eyes from controls, while using seven of the eight parameters of the model allowed 76 % to be discriminated. The future clinical utility of mathematical modeling in study of diffuse neurodegenerative conditions that also affect the fovea is discussed.

Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a non-convex regularization term chosen such that the total cost function (consisting of data consistency and regularization terms) is convex. Therefore, sparsity is more strongly promoted than in the standard convex formulation, but without sacrificing the attractive aspects of convex optimization (unique minimum, robust algorithms, etc.). We use this idea to improve the recently developed ` overlapping group shrinkage' (OGS) algorithm for the denoising of group-sparse signals. The algorithm is applied to the problem of speech enhancement with favorable results in terms of both SNR and perceptual quality.

Vagal inputs control pacemaking and conduction systems in the heart. Anatomical evidence suggests a direct ventricular action, but functional evidence that separates direct and indirect (via the conduction system) vagal actions is less well established. We studied vagus nerve stimulation (VNS) during sinus rhythm and ventricular fibrillation (VF) in pigs and sheep to determine: 1) the range of unilateral and bilateral actions (inotropic and chronotropic) and 2) whether VNS alters left ventricular motion and/or electrical activity during VF, a model of abnormal electrical conduction of the left ventricle that excludes sinus and atrioventricular nodal function. Adult pigs (N=8) and sheep (N=10) were anesthetized with urethane and mechanically ventilated. VNS was performed in animals at 1, 2, 5, 10, 20, 50, and 100Hz for 20s. VF was induced with direct current to the ventricles or occlusion of the left anterior descending coronary artery. In 4 pigs and 3 sheep, left ventricular wall motion was assessed from endocardial excursion in epicardial echocardiography. In sheep and pigs, the best frequency among those tested for VNS during sinus rhythm to produce sustained electrical and mechanical ventricular standstill was 50Hz for unilateral or bilateral stimulation. When applied during VF, bilateral VNS increased the variability of the dominant VF frequency, indicating a direct impact on the excitability of ventricular myocytes, and decreased endocardial excursion by more than 50% during VF. We conclude that the vagus nerve directly modulates left ventricular function independently from its effects on the conduction system.