Table 1 Detailed process of the proposed speech enhancement algorithm

In the training stage

Input: Speech signal, noise signal, and noisy speech of training set

Output: Trained joint dictionary

Step 1: Divide the training signals into frames by a rectangular window.

Step 2: Use the K-SVD algorithm to obtain the sub-dictionaries corresponding to the speech signal and noise signal of the training set, and then concatenate them to get the initial joint dictionary.

Step 3: Use the BP algorithm to calculate the sparse coefficient matrix of noisy speech on the joint dictionary.

Step 4: Use the L-BFGS algorithm to solve the proposed optimization function and update the joint dictionary.

In the enhancement stage

Input: Noisy speech signal of the testing set

Output: Reconstructed speech signal

Step 1: Preprocess the input signal by framing.

Step 2: Use the BP algorithm to calculate the sparse coefficients of noisy speech on the joint dictionary.

Step 3: Use the speech sub-dictionary in the joint dictionary and the corresponding sparse coefficients to recover the frame-level speech signals.

Step 4: Connect all the frame-level signals to reconstruct speech signals.