  Traditional speech enhancement techniques modify the magnitude of a speech in
time-frequency domain, and use the phase of a noisy speech to resynthesize a
time domain speech. This work proposes a complex-valued Gaussian process latent
variable model (CGPLVM) to enhance directly the complex-valued noisy spectrum,
modifying not only the magnitude but also the phase. The main idea that
underlies the developed method is the modeling of short-time Fourier transform
(STFT) coefficients across the time frames of a speech as a proper complex
Gaussian process (GP) with noise added. The proposed method is based on
projecting the spectrum into a low-dimensional subspace. The likelihood
criterion is used to optimize the hyperparameters of the model. Experiments
were carried out on the CHTTL database, which contains the digits zero to nine
in Mandarin. Several standard measures are used to demonstrate that the
proposed method outperforms baseline methods.
