Speech enhancement method based on low-rank approximation in a reproducing kernel Hilbert space

•A speech enhancement algorithm is proposed using low-rank approximation.•It can reduce storage space and running time with very little performance loss.•The error bound is analyzed between the enhanced vectors.

Speech signal is corrupted unavoidably by noisy environment in subway, factory, and restaurant or speech from other speakers in speech communication. Speech enhancement methods have been widely studied to minimize noise influence in different linear transform domain, such as discrete Fourier transform domain, Karhunen-Loeve transform domain or discrete cosine transform domain. Kernel method as a nonlinear transform has received a lot of interest recently and is commonly used in many applications including audio signal processing. However this kind of method typically suffers from the computational complexity. In this paper, we propose a speech enhancement algorithm using low-rank approximation in a reproducing kernel Hilbert space to reduce storage space and running time with very little performance loss in the enhanced speech. We also analyze the root mean squared error bound between the enhanced vectors obtained by the approximation kernel matrix and the full kernel matrix. Simulations show that the proposed method can improve the computation speed of the algorithm with the approximate performance compared with that of the full kernel matrix.