Reconstruction of audio signal from Spectrogram

I have a set of songs for which I extracted the magnitude spectrogram using a Hamming Window with 50% overlap. After extracting the spectrogram, I did some dimensionality reduction using Principal Components Analysis (PCA). After reducing it to lower dimensionality, I reconstructed the spectrograms from lower dimensions. So now, there would be some error between the original spectrogram and the reconstructed spectrogram. I would like to convert this spectrogram back to the audio signal and play it, so that I would be able to know when reconstructed from lower dimensions, how does the audio sound.

Is there any function available in say Matlab. to convert a magnitude Spectrogram to an audio signal ??