Optimal design of Hermitian transform and vectors of both mask and window coefficients for denoising applications with both unknown noise characteristics and distortions

• Published in: Signal processing Vol. 98; pp. 1 - 22
• Main Authors: Ling, Bingo Wing-Kuen, Ho, Charlotte Yuk-Fan, Subramaniam, Suba R., Georgakis, Apostolos, Cao, Jiangzhong, Dai, Qingyun
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2014; Elsevier
• Subjects: Applied sciences; Biological and medical sciences; Computerized, statistical medical data processing and models in biomedicine; Detection, estimation, filtering, equalization, prediction; Distortion; Exact sciences and technology; Hermitian transform; Information, signal and communications theory; Mask operation; Masks; Mathematical analysis; Medical management aid. Diagnosis aid; Medical sciences; Noise; Noise reduction; Optimization; Orthogonal Procrustes; Quadratic complex valued matrix equality constraint; Quadratically constrained programming; Signal and communications theory; Signal processing; Signal, noise; Speech processing; Telecommunications and information theory; Transforms; Vectors (mathematics); Windowing; Windowing; Hermitian transform; Quadratically constrained programming; Mask operation; Orthogonal Procrustes; Quadratic complex valued matrix equality constraint; Performance evaluation; Acoustic signal; Noise reduction; Hermite interpolation; Hermitian matrix; Algorithm; Optimal design; Complex variable method; Time domain method; Vocal signal; Electrocardiography; Signal processing
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2013.11.018

This paper proposes an optimal design of a Hermitian transform and vectors of both mask and window coefficients for denoising signals with both unknown noise characteristics and distortions. The signals are represented in the vector form. Then, they are transformed to a new domain via multiplying these vectors to a Hermitian matrix. A vector of mask coefficients is point by point multiplied to the transformed vectors. The processed vectors are transformed back to the time domain. A vector of window coefficients is point by point multiplied to the processed vectors. An optimal design of the Hermitian matrix and the vectors of both mask and window coefficients is formulated as a quadratically constrained programming problem subject to a Hermitian constraint. By initializing the window coefficients, the Hermitian matrix and the vector of mask coefficients are derived via an orthogonal Procrustes approach. Based on the obtained Hermitian matrix and the vector of mask coefficients, the vector of window coefficients is derived. By iterating these two procedures, the final Hermitian matrix and the vectors of both mask and window coefficients are obtained. The convergence of the algorithm is guaranteed. The proposed method is applied to denoise both clinical electrocardiograms and electromyograms as well as speech signals with both unknown noise characteristics and distortions. Experimental results show that the proposed method outperforms existing denoising methods. •This paper proposes an optimal design of a Hermitian transform and vectors of both mask and window coefficients.•This is a generalization of existing mask operations via discrete fractional Fourier transform.•The results are applied to denoising applications with both unknown noise characteristics and distortions.•The design is formulated as a quadratically constrained programming problem subject to a Hermitian constraint.•An orthogonal Procrustes approach is employed for solving the problem.