Faculty Bibliography

This paper seeks to combine linear time-invariant (LTI) filtering and sparsity-based denoising in a principled way in order to effectively filter (denoise) a wider class of signals. LTI filtering is most suitable for signals restricted to a known frequency band, while sparsity-based denoising is suitable for signals admitting a sparse representation with respect to a known transform. However, some signals cannot be accurately categorized as either band-limited or sparse. This paper addresses the problem of filtering noisy data for the particular case where the underlying signal comprises a low-frequency component and a sparse or sparse-derivative component. A convex optimization approach is presented and two algorithms derived: one based on majorization-minimization (MM), and the other based on the alternating direction method of multipliers (ADMM). It is shown that a particular choice of discrete-time filter, namely zero-phase noncausal recursive filters for finite-length data formulated in terms of banded matrices, makes the algorithms effective and computationally efficient. The efficiency stems from the use of fast algorithms for solving banded systems of linear equations. The method is illustrated using data from a physiological-measurement technique (i.e., near infrared spectroscopic time series imaging) that in many cases yields data that is well-approximated as the sum of low-frequency, sparse or sparse-derivative, and noise components.

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e. g., sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization.

The fused lasso problem involves the minimization of the sum of a quadratic, a TV term and an l(1) term. The solution can be obtained by applying a TV denoising filter followed by soft-thresholding. However, soft-thresholding introduces a certain bias to the non-zero coefficients. In order to prevent this bias, we propose to replace the l(1) penalty with a non-convex penalty. We show that the solution can similarly be obtained by applying a modified thresholding function to the result of the TV-denoising filter.

This study investigates the feasibility of using binaural dichotic presentation of speech components decomposed using a recently proposed resonance-based decomposition method to release listeners from intra-speech masking and yield better perceived sound quality. Resonance-based decomposition is a nonlinear signal analysis method based not on frequency or scale but on resonance. We decomposed different categories of speech stimuli (vowels, consonants, and sentences) into low-and high-resonance component using various combination of low-and high-Q-factors {Q1,Q2}. 10 normal hearing listeners were asked to rate the perceived quality of each individual decomposed component presented diotically, and in pair presented dichotically. We found that the perceived quality rating of these resonance components when presented in pair was higher than the mean of perceived quality ratings of these resonance components when presented individually. Our result suggests that listeners were able to fuse binaural dichotic presentation of high-and low-resonance components and perceived better sound quality.

This paper addresses signal denoising when large-amplitude coefficients form clusters (groups). The L1-norm and other separable sparsity models do not capture the tendency of coefficients to cluster (group sparsity). This work develops an algorithm, called 'overlapping group shrinkage' (OGS), based on the minimization of a convex cost function involving a group-sparsity promoting penalty function. The groups are fully overlapping so the denoising method is translation-invariant and blocking artifacts are avoided. Based on the principle of majorization-minimization (MM), we derive a simple iterative minimization algorithm that reduces the cost function monotonically. A procedure for setting the regularization parameter, based on attenuating the noise to a specified level, is also described. The proposed approach is illustrated on speech enhancement, wherein the OGS approach is applied in the short-time Fourier transform (STFT) domain. The OGS algorithm produces denoised speech that is relatively free of musical noise. (C) 2013 Elsevier B.V. All rights reserved.

This paper addresses the problem of dynamic clutter mitigation by focusing on the mitigation of the wind turbine clutter from the radar data. The basis pursuit and morphological component analysis approach are used to decompose the radar returns into the sum of oscillatory and transient components. The success of the morphological component analysis rely on sparsity, thus different transform domains needs to be identified correctly to represent each component sparsely. The method is illustrated on a radar data collected from a small custom built radar system to show the success of the proposed algorithm for wind turbine clutter mitigation.

Electrocardiography (ECG) signals are often contaminated by various kinds of noise or artifacts, for example, morphological changes due to motion artifact, non-stationary noise due to muscular contraction (EMG), etc. Some of these contaminations severely affect the usefulness of ECG signals, especially when computer aided algorithms are utilized. In this paper, a novel ECG enhancement algorithm is proposed based on sparse derivatives. By solving a convex optimization problem, artifacts are reduced by modeling the clean ECG signal as a sum of two signals whose second and third-order derivatives (differences) are sparse respectively. The algorithm is applied to a QRS detection system and validated using the MIT-BIH Arrhythmia database (109,452 anotations), resulting a sensitivity of Se = 99.87% and a positive prediction of +P = 99.88%. (C) 2013 Elsevier Ltd. All rights reserved.