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GroupSparse Signal Denoising: NonConvex Regularization, Convex Optimization
, 2014
"... Abstract—Convex optimization with sparsitypromoting 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 nonconvex optimization. In this paper, we take a t ..."
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Abstract—Convex optimization with sparsitypromoting 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 nonconvex optimization. In this paper, we take a third approach. We utilize a nonconvex 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 groupsparse signals. The algorithm is applied to the problem of speech enhancement with favorable results in terms of both SNR and perceptual quality. Index Terms—group sparse model; convex optimization; nonconvex optimization; sparse optimization; translationinvariant denoising; denoising; speech enhancement I.
1 Image Restoration using Total Variation with Overlapping Group Sparsity
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ECG Denoising Based on Translation Invariant Wavelet Transform and Overlapping Group Shrinkage
"... Abstract: Electrocardiogram (ECG) signal plays an important role in the diagnosis of cardiovascular disease. However, ECG signal is very faint and always affected by a variety of noise in the process of collecting. How to eliminate the noise effectively is an important issue and has been widely stu ..."
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Abstract: Electrocardiogram (ECG) signal plays an important role in the diagnosis of cardiovascular disease. However, ECG signal is very faint and always affected by a variety of noise in the process of collecting. How to eliminate the noise effectively is an important issue and has been widely studied for many years. In this paper, we propose a new ECG denoising method based on translation invariant (TI) wavelet transform and overlapping group shrinkage (OGS). The OGS is a new thresholding function, which is especially suitable for processing the largeamplitude coefficients form groups. The proposed method is tested on white Gaussian noise added the analog signals and ECG signals. Signal to Noise Ratio (SNR) and Root Mean Square Error (RMSE) are used to compare the performance of the proposed method with other denoising methods. The experimental results indicate that the proposed denoising method is the best in aspects of the improvement of SNR and remaining the geometrical characteristics of the ECG signals.
EMPLOYING PHASE INFORMATION FOR AUDIO DENOISING
"... Spectral audio denoising methods usually make use of the magnitudes of a timefrequency representation of the signal. However, if the timefrequency frame consists of quadrature pairs of atoms (as in the shorttime Fourier transform), then the phases of the coefficients also follow a predictable p ..."
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Spectral audio denoising methods usually make use of the magnitudes of a timefrequency representation of the signal. However, if the timefrequency frame consists of quadrature pairs of atoms (as in the shorttime Fourier transform), then the phases of the coefficients also follow a predictable pattern, for which simple models are viable. In this paper, we propose a scheme that takes into account the phase information of the signals for the audio denoising problem. The scheme requires to minimize a cost function composed of a diagonally weighted quadrature data term and a fusedlasso type penalty. We formulate the problem as a saddle point search problem and propose an algorithm that numerically finds the solution. Based on the optimality conditions of the problem, we present a guideline on how to select the parameters of the problem. We discuss the performance and the influence of the parameters through experiments. Index Terms — Audio denoising, nonnegative garrote, total variation, fused lasso, audio phase.
TOTAL VARIATION DENOISINGWITH OVERLAPPING GROUP SPARSITY
"... This paper describes an extension to total variation denoising wherein it is assumed the firstorder difference function of the unknown signal is not only sparse, but also that large values of the firstorder difference function do not generally occur in isolation. This approach is designed to alle ..."
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This paper describes an extension to total variation denoising wherein it is assumed the firstorder difference function of the unknown signal is not only sparse, but also that large values of the firstorder 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 majorizationminimization. The algorithm is both fast converging and computationally efficient due to the use of fast solvers for banded systems. Index Terms — total variation, sparse signal processing, L1 norm, group sparsity, denoising, filter, convex optimization. 1.