Table 2 Proposed algorithm

H_P, W_R, and H_R are randomly initialized with non-negative values, and W_P is initialized using (17), (18), and (19). Following initialization, the following process is iteratively performed until convergence:

1. \(\nabla _{\mathbf {H_{P}}}^{+}C_{E}\), \(\nabla _{\mathbf {H_{P}}}^{-}C_{E}\), \(\nabla _{\mathbf {H_{P}}}^{+}C_{T}\), \(\nabla _{\mathbf {H_{P}}}^{-}C_{T}\), \(\nabla _{\mathbf {H_{P}}}^{+}C_{L}\), and \(\nabla _{\mathbf {H_{P}}}^{-}C_{L}\) are calculated using (27), (28), (31), (32), (36), and (37), respectively;

2. \(\nabla _{\mathbf {H_{P}}}^{+}C\) and \(\nabla _{\mathbf {H_{P}}}^{-}C\) are calculated using (23) and (24), respectively, and H_P is updated using (25);

3. H_R is updated using (38);

4. H is updated with H_P and H_R using (14);

5. W_R is updated using (39);

6. W is updated with W_R using (13).

Following convergence, the resulting spectrogram \(\mathbf {\hat {V}}_{\text {out}}\) is calculated using (40).