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

• 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.

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.