Fig. 1.

Block diagram of the DWI denoising algorithm exemplified with a fetal dataset. Note PF data $\mathbf{z}$ has been acquired which produces a non-symmetric spectrum in the PE (horizontal) dimension. After the inversion of the DFT and spatial unfolding during the reconstruction, we have access to the magnitude and phase of $\mathbf{y}$ and the noise covariance ${\mathbf{\Lambda }}_{\mathbf{y}}$, here illustrated by the spatial noise amplification levels. Later on, a linear phase $\mathbf{\Phi }$ is estimated and removed from the data, so we obtain $\tilde{\mathbf{y}}$. Optimal patch size $\hat{\gamma }$ is estimated to perform signal prediction, $\widehat{\tilde{\mathbf{x}}}$, and phase demodulation is reversed to provide the final estimate $\hat{\mathbf{x}}$.